diff --git a/wemm/lib/python3.10/site-packages/botocore/data/m2/2021-04-28/endpoint-rule-set-1.json.gz b/wemm/lib/python3.10/site-packages/botocore/data/m2/2021-04-28/endpoint-rule-set-1.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..d0aa1a73a74cc61b82d2e97882170cc9f4216188 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/botocore/data/m2/2021-04-28/endpoint-rule-set-1.json.gz @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:88c6e0a16a1567c4c2925bb8a62d4d85d50d8d666ab5d0a0341e0de61892b4a5 +size 1134 diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/__init__.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..7839db96a712bd5db28c29112ac20864c15d9539 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/__init__.py @@ -0,0 +1,87 @@ +r"""This module provides functions and operations for bipartite +graphs. Bipartite graphs `B = (U, V, E)` have two node sets `U,V` and edges in +`E` that only connect nodes from opposite sets. It is common in the literature +to use an spatial analogy referring to the two node sets as top and bottom nodes. + +The bipartite algorithms are not imported into the networkx namespace +at the top level so the easiest way to use them is with: + +>>> from networkx.algorithms import bipartite + +NetworkX does not have a custom bipartite graph class but the Graph() +or DiGraph() classes can be used to represent bipartite graphs. However, +you have to keep track of which set each node belongs to, and make +sure that there is no edge between nodes of the same set. The convention used +in NetworkX is to use a node attribute named `bipartite` with values 0 or 1 to +identify the sets each node belongs to. This convention is not enforced in +the source code of bipartite functions, it's only a recommendation. + +For example: + +>>> B = nx.Graph() +>>> # Add nodes with the node attribute "bipartite" +>>> B.add_nodes_from([1, 2, 3, 4], bipartite=0) +>>> B.add_nodes_from(["a", "b", "c"], bipartite=1) +>>> # Add edges only between nodes of opposite node sets +>>> B.add_edges_from([(1, "a"), (1, "b"), (2, "b"), (2, "c"), (3, "c"), (4, "a")]) + +Many algorithms of the bipartite module of NetworkX require, as an argument, a +container with all the nodes that belong to one set, in addition to the bipartite +graph `B`. The functions in the bipartite package do not check that the node set +is actually correct nor that the input graph is actually bipartite. +If `B` is connected, you can find the two node sets using a two-coloring +algorithm: + +>>> nx.is_connected(B) +True +>>> bottom_nodes, top_nodes = bipartite.sets(B) + +However, if the input graph is not connected, there are more than one possible +colorations. This is the reason why we require the user to pass a container +with all nodes of one bipartite node set as an argument to most bipartite +functions. In the face of ambiguity, we refuse the temptation to guess and +raise an :exc:`AmbiguousSolution ` +Exception if the input graph for +:func:`bipartite.sets ` +is disconnected. + +Using the `bipartite` node attribute, you can easily get the two node sets: + +>>> top_nodes = {n for n, d in B.nodes(data=True) if d["bipartite"] == 0} +>>> bottom_nodes = set(B) - top_nodes + +So you can easily use the bipartite algorithms that require, as an argument, a +container with all nodes that belong to one node set: + +>>> print(round(bipartite.density(B, bottom_nodes), 2)) +0.5 +>>> G = bipartite.projected_graph(B, top_nodes) + +All bipartite graph generators in NetworkX build bipartite graphs with the +`bipartite` node attribute. Thus, you can use the same approach: + +>>> RB = bipartite.random_graph(5, 7, 0.2) +>>> RB_top = {n for n, d in RB.nodes(data=True) if d["bipartite"] == 0} +>>> RB_bottom = set(RB) - RB_top +>>> list(RB_top) +[0, 1, 2, 3, 4] +>>> list(RB_bottom) +[5, 6, 7, 8, 9, 10, 11] + +For other bipartite graph generators see +:mod:`Generators `. + +""" + +from networkx.algorithms.bipartite.basic import * +from networkx.algorithms.bipartite.centrality import * +from networkx.algorithms.bipartite.cluster import * +from networkx.algorithms.bipartite.covering import * +from networkx.algorithms.bipartite.edgelist import * +from networkx.algorithms.bipartite.matching import * +from networkx.algorithms.bipartite.matrix import * +from networkx.algorithms.bipartite.projection import * +from networkx.algorithms.bipartite.redundancy import * +from networkx.algorithms.bipartite.spectral import * +from networkx.algorithms.bipartite.generators import * +from networkx.algorithms.bipartite.extendability import * diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/__pycache__/__init__.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/__pycache__/__init__.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..caea81e5ecb3906329fcce5c7d721c176566a1c7 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/__pycache__/__init__.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/__pycache__/generators.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/__pycache__/generators.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..694b2136ca5b8e908caee95fa46031ecc8a5f63c Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/__pycache__/generators.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/centrality.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/centrality.py new file mode 100644 index 0000000000000000000000000000000000000000..42d7270ee7d0bb18b56a55dc4c17dc19f5dc77a7 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/centrality.py @@ -0,0 +1,290 @@ +import networkx as nx + +__all__ = ["degree_centrality", "betweenness_centrality", "closeness_centrality"] + + +@nx._dispatchable(name="bipartite_degree_centrality") +def degree_centrality(G, nodes): + r"""Compute the degree centrality for nodes in a bipartite network. + + The degree centrality for a node `v` is the fraction of nodes + connected to it. + + Parameters + ---------- + G : graph + A bipartite network + + nodes : list or container + Container with all nodes in one bipartite node set. + + Returns + ------- + centrality : dictionary + Dictionary keyed by node with bipartite degree centrality as the value. + + Examples + -------- + >>> G = nx.wheel_graph(5) + >>> top_nodes = {0, 1, 2} + >>> nx.bipartite.degree_centrality(G, nodes=top_nodes) + {0: 2.0, 1: 1.5, 2: 1.5, 3: 1.0, 4: 1.0} + + See Also + -------- + betweenness_centrality + closeness_centrality + :func:`~networkx.algorithms.bipartite.basic.sets` + :func:`~networkx.algorithms.bipartite.basic.is_bipartite` + + Notes + ----- + The nodes input parameter must contain all nodes in one bipartite node set, + but the dictionary returned contains all nodes from both bipartite node + sets. See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + For unipartite networks, the degree centrality values are + normalized by dividing by the maximum possible degree (which is + `n-1` where `n` is the number of nodes in G). + + In the bipartite case, the maximum possible degree of a node in a + bipartite node set is the number of nodes in the opposite node set + [1]_. The degree centrality for a node `v` in the bipartite + sets `U` with `n` nodes and `V` with `m` nodes is + + .. math:: + + d_{v} = \frac{deg(v)}{m}, \mbox{for} v \in U , + + d_{v} = \frac{deg(v)}{n}, \mbox{for} v \in V , + + + where `deg(v)` is the degree of node `v`. + + References + ---------- + .. [1] Borgatti, S.P. and Halgin, D. In press. "Analyzing Affiliation + Networks". In Carrington, P. and Scott, J. (eds) The Sage Handbook + of Social Network Analysis. Sage Publications. + https://dx.doi.org/10.4135/9781446294413.n28 + """ + top = set(nodes) + bottom = set(G) - top + s = 1.0 / len(bottom) + centrality = {n: d * s for n, d in G.degree(top)} + s = 1.0 / len(top) + centrality.update({n: d * s for n, d in G.degree(bottom)}) + return centrality + + +@nx._dispatchable(name="bipartite_betweenness_centrality") +def betweenness_centrality(G, nodes): + r"""Compute betweenness centrality for nodes in a bipartite network. + + Betweenness centrality of a node `v` is the sum of the + fraction of all-pairs shortest paths that pass through `v`. + + Values of betweenness are normalized by the maximum possible + value which for bipartite graphs is limited by the relative size + of the two node sets [1]_. + + Let `n` be the number of nodes in the node set `U` and + `m` be the number of nodes in the node set `V`, then + nodes in `U` are normalized by dividing by + + .. math:: + + \frac{1}{2} [m^2 (s + 1)^2 + m (s + 1)(2t - s - 1) - t (2s - t + 3)] , + + where + + .. math:: + + s = (n - 1) \div m , t = (n - 1) \mod m , + + and nodes in `V` are normalized by dividing by + + .. math:: + + \frac{1}{2} [n^2 (p + 1)^2 + n (p + 1)(2r - p - 1) - r (2p - r + 3)] , + + where, + + .. math:: + + p = (m - 1) \div n , r = (m - 1) \mod n . + + Parameters + ---------- + G : graph + A bipartite graph + + nodes : list or container + Container with all nodes in one bipartite node set. + + Returns + ------- + betweenness : dictionary + Dictionary keyed by node with bipartite betweenness centrality + as the value. + + Examples + -------- + >>> G = nx.cycle_graph(4) + >>> top_nodes = {1, 2} + >>> nx.bipartite.betweenness_centrality(G, nodes=top_nodes) + {0: 0.25, 1: 0.25, 2: 0.25, 3: 0.25} + + See Also + -------- + degree_centrality + closeness_centrality + :func:`~networkx.algorithms.bipartite.basic.sets` + :func:`~networkx.algorithms.bipartite.basic.is_bipartite` + + Notes + ----- + The nodes input parameter must contain all nodes in one bipartite node set, + but the dictionary returned contains all nodes from both node sets. + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + + References + ---------- + .. [1] Borgatti, S.P. and Halgin, D. In press. "Analyzing Affiliation + Networks". In Carrington, P. and Scott, J. (eds) The Sage Handbook + of Social Network Analysis. Sage Publications. + https://dx.doi.org/10.4135/9781446294413.n28 + """ + top = set(nodes) + bottom = set(G) - top + n = len(top) + m = len(bottom) + s, t = divmod(n - 1, m) + bet_max_top = ( + ((m**2) * ((s + 1) ** 2)) + + (m * (s + 1) * (2 * t - s - 1)) + - (t * ((2 * s) - t + 3)) + ) / 2.0 + p, r = divmod(m - 1, n) + bet_max_bot = ( + ((n**2) * ((p + 1) ** 2)) + + (n * (p + 1) * (2 * r - p - 1)) + - (r * ((2 * p) - r + 3)) + ) / 2.0 + betweenness = nx.betweenness_centrality(G, normalized=False, weight=None) + for node in top: + betweenness[node] /= bet_max_top + for node in bottom: + betweenness[node] /= bet_max_bot + return betweenness + + +@nx._dispatchable(name="bipartite_closeness_centrality") +def closeness_centrality(G, nodes, normalized=True): + r"""Compute the closeness centrality for nodes in a bipartite network. + + The closeness of a node is the distance to all other nodes in the + graph or in the case that the graph is not connected to all other nodes + in the connected component containing that node. + + Parameters + ---------- + G : graph + A bipartite network + + nodes : list or container + Container with all nodes in one bipartite node set. + + normalized : bool, optional + If True (default) normalize by connected component size. + + Returns + ------- + closeness : dictionary + Dictionary keyed by node with bipartite closeness centrality + as the value. + + Examples + -------- + >>> G = nx.wheel_graph(5) + >>> top_nodes = {0, 1, 2} + >>> nx.bipartite.closeness_centrality(G, nodes=top_nodes) + {0: 1.5, 1: 1.2, 2: 1.2, 3: 1.0, 4: 1.0} + + See Also + -------- + betweenness_centrality + degree_centrality + :func:`~networkx.algorithms.bipartite.basic.sets` + :func:`~networkx.algorithms.bipartite.basic.is_bipartite` + + Notes + ----- + The nodes input parameter must contain all nodes in one bipartite node set, + but the dictionary returned contains all nodes from both node sets. + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + + Closeness centrality is normalized by the minimum distance possible. + In the bipartite case the minimum distance for a node in one bipartite + node set is 1 from all nodes in the other node set and 2 from all + other nodes in its own set [1]_. Thus the closeness centrality + for node `v` in the two bipartite sets `U` with + `n` nodes and `V` with `m` nodes is + + .. math:: + + c_{v} = \frac{m + 2(n - 1)}{d}, \mbox{for} v \in U, + + c_{v} = \frac{n + 2(m - 1)}{d}, \mbox{for} v \in V, + + where `d` is the sum of the distances from `v` to all + other nodes. + + Higher values of closeness indicate higher centrality. + + As in the unipartite case, setting normalized=True causes the + values to normalized further to n-1 / size(G)-1 where n is the + number of nodes in the connected part of graph containing the + node. If the graph is not completely connected, this algorithm + computes the closeness centrality for each connected part + separately. + + References + ---------- + .. [1] Borgatti, S.P. and Halgin, D. In press. "Analyzing Affiliation + Networks". In Carrington, P. and Scott, J. (eds) The Sage Handbook + of Social Network Analysis. Sage Publications. + https://dx.doi.org/10.4135/9781446294413.n28 + """ + closeness = {} + path_length = nx.single_source_shortest_path_length + top = set(nodes) + bottom = set(G) - top + n = len(top) + m = len(bottom) + for node in top: + sp = dict(path_length(G, node)) + totsp = sum(sp.values()) + if totsp > 0.0 and len(G) > 1: + closeness[node] = (m + 2 * (n - 1)) / totsp + if normalized: + s = (len(sp) - 1) / (len(G) - 1) + closeness[node] *= s + else: + closeness[node] = 0.0 + for node in bottom: + sp = dict(path_length(G, node)) + totsp = sum(sp.values()) + if totsp > 0.0 and len(G) > 1: + closeness[node] = (n + 2 * (m - 1)) / totsp + if normalized: + s = (len(sp) - 1) / (len(G) - 1) + closeness[node] *= s + else: + closeness[node] = 0.0 + return closeness diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/edgelist.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/edgelist.py new file mode 100644 index 0000000000000000000000000000000000000000..db6ef9d8e2773de9ec698db151661fac28adc326 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/edgelist.py @@ -0,0 +1,360 @@ +""" +******************** +Bipartite Edge Lists +******************** +Read and write NetworkX graphs as bipartite edge lists. + +Format +------ +You can read or write three formats of edge lists with these functions. + +Node pairs with no data:: + + 1 2 + +Python dictionary as data:: + + 1 2 {'weight':7, 'color':'green'} + +Arbitrary data:: + + 1 2 7 green + +For each edge (u, v) the node u is assigned to part 0 and the node v to part 1. +""" + +__all__ = ["generate_edgelist", "write_edgelist", "parse_edgelist", "read_edgelist"] + +import networkx as nx +from networkx.utils import not_implemented_for, open_file + + +@open_file(1, mode="wb") +def write_edgelist(G, path, comments="#", delimiter=" ", data=True, encoding="utf-8"): + """Write a bipartite graph as a list of edges. + + Parameters + ---------- + G : Graph + A NetworkX bipartite graph + path : file or string + File or filename to write. If a file is provided, it must be + opened in 'wb' mode. Filenames ending in .gz or .bz2 will be compressed. + comments : string, optional + The character used to indicate the start of a comment + delimiter : string, optional + The string used to separate values. The default is whitespace. + data : bool or list, optional + If False write no edge data. + If True write a string representation of the edge data dictionary.. + If a list (or other iterable) is provided, write the keys specified + in the list. + encoding: string, optional + Specify which encoding to use when writing file. + + Examples + -------- + >>> G = nx.path_graph(4) + >>> G.add_nodes_from([0, 2], bipartite=0) + >>> G.add_nodes_from([1, 3], bipartite=1) + >>> nx.write_edgelist(G, "test.edgelist") + >>> fh = open("test.edgelist", "wb") + >>> nx.write_edgelist(G, fh) + >>> nx.write_edgelist(G, "test.edgelist.gz") + >>> nx.write_edgelist(G, "test.edgelist.gz", data=False) + + >>> G = nx.Graph() + >>> G.add_edge(1, 2, weight=7, color="red") + >>> nx.write_edgelist(G, "test.edgelist", data=False) + >>> nx.write_edgelist(G, "test.edgelist", data=["color"]) + >>> nx.write_edgelist(G, "test.edgelist", data=["color", "weight"]) + + See Also + -------- + write_edgelist + generate_edgelist + """ + for line in generate_edgelist(G, delimiter, data): + line += "\n" + path.write(line.encode(encoding)) + + +@not_implemented_for("directed") +def generate_edgelist(G, delimiter=" ", data=True): + """Generate a single line of the bipartite graph G in edge list format. + + Parameters + ---------- + G : NetworkX graph + The graph is assumed to have node attribute `part` set to 0,1 representing + the two graph parts + + delimiter : string, optional + Separator for node labels + + data : bool or list of keys + If False generate no edge data. If True use a dictionary + representation of edge data. If a list of keys use a list of data + values corresponding to the keys. + + Returns + ------- + lines : string + Lines of data in adjlist format. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> G = nx.path_graph(4) + >>> G.add_nodes_from([0, 2], bipartite=0) + >>> G.add_nodes_from([1, 3], bipartite=1) + >>> G[1][2]["weight"] = 3 + >>> G[2][3]["capacity"] = 12 + >>> for line in bipartite.generate_edgelist(G, data=False): + ... print(line) + 0 1 + 2 1 + 2 3 + + >>> for line in bipartite.generate_edgelist(G): + ... print(line) + 0 1 {} + 2 1 {'weight': 3} + 2 3 {'capacity': 12} + + >>> for line in bipartite.generate_edgelist(G, data=["weight"]): + ... print(line) + 0 1 + 2 1 3 + 2 3 + """ + try: + part0 = [n for n, d in G.nodes.items() if d["bipartite"] == 0] + except BaseException as err: + raise AttributeError("Missing node attribute `bipartite`") from err + if data is True or data is False: + for n in part0: + for edge in G.edges(n, data=data): + yield delimiter.join(map(str, edge)) + else: + for n in part0: + for u, v, d in G.edges(n, data=True): + edge = [u, v] + try: + edge.extend(d[k] for k in data) + except KeyError: + pass # missing data for this edge, should warn? + yield delimiter.join(map(str, edge)) + + +@nx._dispatchable(name="bipartite_parse_edgelist", graphs=None, returns_graph=True) +def parse_edgelist( + lines, comments="#", delimiter=None, create_using=None, nodetype=None, data=True +): + """Parse lines of an edge list representation of a bipartite graph. + + Parameters + ---------- + lines : list or iterator of strings + Input data in edgelist format + comments : string, optional + Marker for comment lines + delimiter : string, optional + Separator for node labels + create_using: NetworkX graph container, optional + Use given NetworkX graph for holding nodes or edges. + nodetype : Python type, optional + Convert nodes to this type. + data : bool or list of (label,type) tuples + If False generate no edge data or if True use a dictionary + representation of edge data or a list tuples specifying dictionary + key names and types for edge data. + + Returns + ------- + G: NetworkX Graph + The bipartite graph corresponding to lines + + Examples + -------- + Edgelist with no data: + + >>> from networkx.algorithms import bipartite + >>> lines = ["1 2", "2 3", "3 4"] + >>> G = bipartite.parse_edgelist(lines, nodetype=int) + >>> sorted(G.nodes()) + [1, 2, 3, 4] + >>> sorted(G.nodes(data=True)) + [(1, {'bipartite': 0}), (2, {'bipartite': 0}), (3, {'bipartite': 0}), (4, {'bipartite': 1})] + >>> sorted(G.edges()) + [(1, 2), (2, 3), (3, 4)] + + Edgelist with data in Python dictionary representation: + + >>> lines = ["1 2 {'weight':3}", "2 3 {'weight':27}", "3 4 {'weight':3.0}"] + >>> G = bipartite.parse_edgelist(lines, nodetype=int) + >>> sorted(G.nodes()) + [1, 2, 3, 4] + >>> sorted(G.edges(data=True)) + [(1, 2, {'weight': 3}), (2, 3, {'weight': 27}), (3, 4, {'weight': 3.0})] + + Edgelist with data in a list: + + >>> lines = ["1 2 3", "2 3 27", "3 4 3.0"] + >>> G = bipartite.parse_edgelist(lines, nodetype=int, data=(("weight", float),)) + >>> sorted(G.nodes()) + [1, 2, 3, 4] + >>> sorted(G.edges(data=True)) + [(1, 2, {'weight': 3.0}), (2, 3, {'weight': 27.0}), (3, 4, {'weight': 3.0})] + + See Also + -------- + """ + from ast import literal_eval + + G = nx.empty_graph(0, create_using) + for line in lines: + p = line.find(comments) + if p >= 0: + line = line[:p] + if not len(line): + continue + # split line, should have 2 or more + s = line.rstrip("\n").split(delimiter) + if len(s) < 2: + continue + u = s.pop(0) + v = s.pop(0) + d = s + if nodetype is not None: + try: + u = nodetype(u) + v = nodetype(v) + except BaseException as err: + raise TypeError( + f"Failed to convert nodes {u},{v} to type {nodetype}." + ) from err + + if len(d) == 0 or data is False: + # no data or data type specified + edgedata = {} + elif data is True: + # no edge types specified + try: # try to evaluate as dictionary + edgedata = dict(literal_eval(" ".join(d))) + except BaseException as err: + raise TypeError( + f"Failed to convert edge data ({d}) to dictionary." + ) from err + else: + # convert edge data to dictionary with specified keys and type + if len(d) != len(data): + raise IndexError( + f"Edge data {d} and data_keys {data} are not the same length" + ) + edgedata = {} + for (edge_key, edge_type), edge_value in zip(data, d): + try: + edge_value = edge_type(edge_value) + except BaseException as err: + raise TypeError( + f"Failed to convert {edge_key} data " + f"{edge_value} to type {edge_type}." + ) from err + edgedata.update({edge_key: edge_value}) + G.add_node(u, bipartite=0) + G.add_node(v, bipartite=1) + G.add_edge(u, v, **edgedata) + return G + + +@open_file(0, mode="rb") +@nx._dispatchable(name="bipartite_read_edgelist", graphs=None, returns_graph=True) +def read_edgelist( + path, + comments="#", + delimiter=None, + create_using=None, + nodetype=None, + data=True, + edgetype=None, + encoding="utf-8", +): + """Read a bipartite graph from a list of edges. + + Parameters + ---------- + path : file or string + File or filename to read. If a file is provided, it must be + opened in 'rb' mode. + Filenames ending in .gz or .bz2 will be uncompressed. + comments : string, optional + The character used to indicate the start of a comment. + delimiter : string, optional + The string used to separate values. The default is whitespace. + create_using : Graph container, optional, + Use specified container to build graph. The default is networkx.Graph, + an undirected graph. + nodetype : int, float, str, Python type, optional + Convert node data from strings to specified type + data : bool or list of (label,type) tuples + Tuples specifying dictionary key names and types for edge data + edgetype : int, float, str, Python type, optional OBSOLETE + Convert edge data from strings to specified type and use as 'weight' + encoding: string, optional + Specify which encoding to use when reading file. + + Returns + ------- + G : graph + A networkx Graph or other type specified with create_using + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> G = nx.path_graph(4) + >>> G.add_nodes_from([0, 2], bipartite=0) + >>> G.add_nodes_from([1, 3], bipartite=1) + >>> bipartite.write_edgelist(G, "test.edgelist") + >>> G = bipartite.read_edgelist("test.edgelist") + + >>> fh = open("test.edgelist", "rb") + >>> G = bipartite.read_edgelist(fh) + >>> fh.close() + + >>> G = bipartite.read_edgelist("test.edgelist", nodetype=int) + + Edgelist with data in a list: + + >>> textline = "1 2 3" + >>> fh = open("test.edgelist", "w") + >>> d = fh.write(textline) + >>> fh.close() + >>> G = bipartite.read_edgelist( + ... "test.edgelist", nodetype=int, data=(("weight", float),) + ... ) + >>> list(G) + [1, 2] + >>> list(G.edges(data=True)) + [(1, 2, {'weight': 3.0})] + + See parse_edgelist() for more examples of formatting. + + See Also + -------- + parse_edgelist + + Notes + ----- + Since nodes must be hashable, the function nodetype must return hashable + types (e.g. int, float, str, frozenset - or tuples of those, etc.) + """ + lines = (line.decode(encoding) for line in path) + return parse_edgelist( + lines, + comments=comments, + delimiter=delimiter, + create_using=create_using, + nodetype=nodetype, + data=data, + ) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/projection.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/projection.py new file mode 100644 index 0000000000000000000000000000000000000000..7c2a26cf73ddf39e51fbd20d442abe736acedddd --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/projection.py @@ -0,0 +1,526 @@ +"""One-mode (unipartite) projections of bipartite graphs.""" + +import networkx as nx +from networkx.exception import NetworkXAlgorithmError +from networkx.utils import not_implemented_for + +__all__ = [ + "projected_graph", + "weighted_projected_graph", + "collaboration_weighted_projected_graph", + "overlap_weighted_projected_graph", + "generic_weighted_projected_graph", +] + + +@nx._dispatchable( + graphs="B", preserve_node_attrs=True, preserve_graph_attrs=True, returns_graph=True +) +def projected_graph(B, nodes, multigraph=False): + r"""Returns the projection of B onto one of its node sets. + + Returns the graph G that is the projection of the bipartite graph B + onto the specified nodes. They retain their attributes and are connected + in G if they have a common neighbor in B. + + Parameters + ---------- + B : NetworkX graph + The input graph should be bipartite. + + nodes : list or iterable + Nodes to project onto (the "bottom" nodes). + + multigraph: bool (default=False) + If True return a multigraph where the multiple edges represent multiple + shared neighbors. They edge key in the multigraph is assigned to the + label of the neighbor. + + Returns + ------- + Graph : NetworkX graph or multigraph + A graph that is the projection onto the given nodes. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> B = nx.path_graph(4) + >>> G = bipartite.projected_graph(B, [1, 3]) + >>> list(G) + [1, 3] + >>> list(G.edges()) + [(1, 3)] + + If nodes `a`, and `b` are connected through both nodes 1 and 2 then + building a multigraph results in two edges in the projection onto + [`a`, `b`]: + + >>> B = nx.Graph() + >>> B.add_edges_from([("a", 1), ("b", 1), ("a", 2), ("b", 2)]) + >>> G = bipartite.projected_graph(B, ["a", "b"], multigraph=True) + >>> print([sorted((u, v)) for u, v in G.edges()]) + [['a', 'b'], ['a', 'b']] + + Notes + ----- + No attempt is made to verify that the input graph B is bipartite. + Returns a simple graph that is the projection of the bipartite graph B + onto the set of nodes given in list nodes. If multigraph=True then + a multigraph is returned with an edge for every shared neighbor. + + Directed graphs are allowed as input. The output will also then + be a directed graph with edges if there is a directed path between + the nodes. + + The graph and node properties are (shallow) copied to the projected graph. + + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + See Also + -------- + is_bipartite, + is_bipartite_node_set, + sets, + weighted_projected_graph, + collaboration_weighted_projected_graph, + overlap_weighted_projected_graph, + generic_weighted_projected_graph + """ + if B.is_multigraph(): + raise nx.NetworkXError("not defined for multigraphs") + if B.is_directed(): + directed = True + if multigraph: + G = nx.MultiDiGraph() + else: + G = nx.DiGraph() + else: + directed = False + if multigraph: + G = nx.MultiGraph() + else: + G = nx.Graph() + G.graph.update(B.graph) + G.add_nodes_from((n, B.nodes[n]) for n in nodes) + for u in nodes: + nbrs2 = {v for nbr in B[u] for v in B[nbr] if v != u} + if multigraph: + for n in nbrs2: + if directed: + links = set(B[u]) & set(B.pred[n]) + else: + links = set(B[u]) & set(B[n]) + for l in links: + if not G.has_edge(u, n, l): + G.add_edge(u, n, key=l) + else: + G.add_edges_from((u, n) for n in nbrs2) + return G + + +@not_implemented_for("multigraph") +@nx._dispatchable(graphs="B", returns_graph=True) +def weighted_projected_graph(B, nodes, ratio=False): + r"""Returns a weighted projection of B onto one of its node sets. + + The weighted projected graph is the projection of the bipartite + network B onto the specified nodes with weights representing the + number of shared neighbors or the ratio between actual shared + neighbors and possible shared neighbors if ``ratio is True`` [1]_. + The nodes retain their attributes and are connected in the resulting + graph if they have an edge to a common node in the original graph. + + Parameters + ---------- + B : NetworkX graph + The input graph should be bipartite. + + nodes : list or iterable + Distinct nodes to project onto (the "bottom" nodes). + + ratio: Bool (default=False) + If True, edge weight is the ratio between actual shared neighbors + and maximum possible shared neighbors (i.e., the size of the other + node set). If False, edges weight is the number of shared neighbors. + + Returns + ------- + Graph : NetworkX graph + A graph that is the projection onto the given nodes. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> B = nx.path_graph(4) + >>> G = bipartite.weighted_projected_graph(B, [1, 3]) + >>> list(G) + [1, 3] + >>> list(G.edges(data=True)) + [(1, 3, {'weight': 1})] + >>> G = bipartite.weighted_projected_graph(B, [1, 3], ratio=True) + >>> list(G.edges(data=True)) + [(1, 3, {'weight': 0.5})] + + Notes + ----- + No attempt is made to verify that the input graph B is bipartite, or that + the input nodes are distinct. However, if the length of the input nodes is + greater than or equal to the nodes in the graph B, an exception is raised. + If the nodes are not distinct but don't raise this error, the output weights + will be incorrect. + The graph and node properties are (shallow) copied to the projected graph. + + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + See Also + -------- + is_bipartite, + is_bipartite_node_set, + sets, + collaboration_weighted_projected_graph, + overlap_weighted_projected_graph, + generic_weighted_projected_graph + projected_graph + + References + ---------- + .. [1] Borgatti, S.P. and Halgin, D. In press. "Analyzing Affiliation + Networks". In Carrington, P. and Scott, J. (eds) The Sage Handbook + of Social Network Analysis. Sage Publications. + """ + if B.is_directed(): + pred = B.pred + G = nx.DiGraph() + else: + pred = B.adj + G = nx.Graph() + G.graph.update(B.graph) + G.add_nodes_from((n, B.nodes[n]) for n in nodes) + n_top = len(B) - len(nodes) + + if n_top < 1: + raise NetworkXAlgorithmError( + f"the size of the nodes to project onto ({len(nodes)}) is >= the graph size ({len(B)}).\n" + "They are either not a valid bipartite partition or contain duplicates" + ) + + for u in nodes: + unbrs = set(B[u]) + nbrs2 = {n for nbr in unbrs for n in B[nbr]} - {u} + for v in nbrs2: + vnbrs = set(pred[v]) + common = unbrs & vnbrs + if not ratio: + weight = len(common) + else: + weight = len(common) / n_top + G.add_edge(u, v, weight=weight) + return G + + +@not_implemented_for("multigraph") +@nx._dispatchable(graphs="B", returns_graph=True) +def collaboration_weighted_projected_graph(B, nodes): + r"""Newman's weighted projection of B onto one of its node sets. + + The collaboration weighted projection is the projection of the + bipartite network B onto the specified nodes with weights assigned + using Newman's collaboration model [1]_: + + .. math:: + + w_{u, v} = \sum_k \frac{\delta_{u}^{k} \delta_{v}^{k}}{d_k - 1} + + where `u` and `v` are nodes from the bottom bipartite node set, + and `k` is a node of the top node set. + The value `d_k` is the degree of node `k` in the bipartite + network and `\delta_{u}^{k}` is 1 if node `u` is + linked to node `k` in the original bipartite graph or 0 otherwise. + + The nodes retain their attributes and are connected in the resulting + graph if have an edge to a common node in the original bipartite + graph. + + Parameters + ---------- + B : NetworkX graph + The input graph should be bipartite. + + nodes : list or iterable + Nodes to project onto (the "bottom" nodes). + + Returns + ------- + Graph : NetworkX graph + A graph that is the projection onto the given nodes. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> B = nx.path_graph(5) + >>> B.add_edge(1, 5) + >>> G = bipartite.collaboration_weighted_projected_graph(B, [0, 2, 4, 5]) + >>> list(G) + [0, 2, 4, 5] + >>> for edge in sorted(G.edges(data=True)): + ... print(edge) + (0, 2, {'weight': 0.5}) + (0, 5, {'weight': 0.5}) + (2, 4, {'weight': 1.0}) + (2, 5, {'weight': 0.5}) + + Notes + ----- + No attempt is made to verify that the input graph B is bipartite. + The graph and node properties are (shallow) copied to the projected graph. + + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + See Also + -------- + is_bipartite, + is_bipartite_node_set, + sets, + weighted_projected_graph, + overlap_weighted_projected_graph, + generic_weighted_projected_graph, + projected_graph + + References + ---------- + .. [1] Scientific collaboration networks: II. + Shortest paths, weighted networks, and centrality, + M. E. J. Newman, Phys. Rev. E 64, 016132 (2001). + """ + if B.is_directed(): + pred = B.pred + G = nx.DiGraph() + else: + pred = B.adj + G = nx.Graph() + G.graph.update(B.graph) + G.add_nodes_from((n, B.nodes[n]) for n in nodes) + for u in nodes: + unbrs = set(B[u]) + nbrs2 = {n for nbr in unbrs for n in B[nbr] if n != u} + for v in nbrs2: + vnbrs = set(pred[v]) + common_degree = (len(B[n]) for n in unbrs & vnbrs) + weight = sum(1.0 / (deg - 1) for deg in common_degree if deg > 1) + G.add_edge(u, v, weight=weight) + return G + + +@not_implemented_for("multigraph") +@nx._dispatchable(graphs="B", returns_graph=True) +def overlap_weighted_projected_graph(B, nodes, jaccard=True): + r"""Overlap weighted projection of B onto one of its node sets. + + The overlap weighted projection is the projection of the bipartite + network B onto the specified nodes with weights representing + the Jaccard index between the neighborhoods of the two nodes in the + original bipartite network [1]_: + + .. math:: + + w_{v, u} = \frac{|N(u) \cap N(v)|}{|N(u) \cup N(v)|} + + or if the parameter 'jaccard' is False, the fraction of common + neighbors by minimum of both nodes degree in the original + bipartite graph [1]_: + + .. math:: + + w_{v, u} = \frac{|N(u) \cap N(v)|}{min(|N(u)|, |N(v)|)} + + The nodes retain their attributes and are connected in the resulting + graph if have an edge to a common node in the original bipartite graph. + + Parameters + ---------- + B : NetworkX graph + The input graph should be bipartite. + + nodes : list or iterable + Nodes to project onto (the "bottom" nodes). + + jaccard: Bool (default=True) + + Returns + ------- + Graph : NetworkX graph + A graph that is the projection onto the given nodes. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> B = nx.path_graph(5) + >>> nodes = [0, 2, 4] + >>> G = bipartite.overlap_weighted_projected_graph(B, nodes) + >>> list(G) + [0, 2, 4] + >>> list(G.edges(data=True)) + [(0, 2, {'weight': 0.5}), (2, 4, {'weight': 0.5})] + >>> G = bipartite.overlap_weighted_projected_graph(B, nodes, jaccard=False) + >>> list(G.edges(data=True)) + [(0, 2, {'weight': 1.0}), (2, 4, {'weight': 1.0})] + + Notes + ----- + No attempt is made to verify that the input graph B is bipartite. + The graph and node properties are (shallow) copied to the projected graph. + + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + See Also + -------- + is_bipartite, + is_bipartite_node_set, + sets, + weighted_projected_graph, + collaboration_weighted_projected_graph, + generic_weighted_projected_graph, + projected_graph + + References + ---------- + .. [1] Borgatti, S.P. and Halgin, D. In press. Analyzing Affiliation + Networks. In Carrington, P. and Scott, J. (eds) The Sage Handbook + of Social Network Analysis. Sage Publications. + + """ + if B.is_directed(): + pred = B.pred + G = nx.DiGraph() + else: + pred = B.adj + G = nx.Graph() + G.graph.update(B.graph) + G.add_nodes_from((n, B.nodes[n]) for n in nodes) + for u in nodes: + unbrs = set(B[u]) + nbrs2 = {n for nbr in unbrs for n in B[nbr]} - {u} + for v in nbrs2: + vnbrs = set(pred[v]) + if jaccard: + wt = len(unbrs & vnbrs) / len(unbrs | vnbrs) + else: + wt = len(unbrs & vnbrs) / min(len(unbrs), len(vnbrs)) + G.add_edge(u, v, weight=wt) + return G + + +@not_implemented_for("multigraph") +@nx._dispatchable(graphs="B", preserve_all_attrs=True, returns_graph=True) +def generic_weighted_projected_graph(B, nodes, weight_function=None): + r"""Weighted projection of B with a user-specified weight function. + + The bipartite network B is projected on to the specified nodes + with weights computed by a user-specified function. This function + must accept as a parameter the neighborhood sets of two nodes and + return an integer or a float. + + The nodes retain their attributes and are connected in the resulting graph + if they have an edge to a common node in the original graph. + + Parameters + ---------- + B : NetworkX graph + The input graph should be bipartite. + + nodes : list or iterable + Nodes to project onto (the "bottom" nodes). + + weight_function : function + This function must accept as parameters the same input graph + that this function, and two nodes; and return an integer or a float. + The default function computes the number of shared neighbors. + + Returns + ------- + Graph : NetworkX graph + A graph that is the projection onto the given nodes. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> # Define some custom weight functions + >>> def jaccard(G, u, v): + ... unbrs = set(G[u]) + ... vnbrs = set(G[v]) + ... return float(len(unbrs & vnbrs)) / len(unbrs | vnbrs) + >>> def my_weight(G, u, v, weight="weight"): + ... w = 0 + ... for nbr in set(G[u]) & set(G[v]): + ... w += G[u][nbr].get(weight, 1) + G[v][nbr].get(weight, 1) + ... return w + >>> # A complete bipartite graph with 4 nodes and 4 edges + >>> B = nx.complete_bipartite_graph(2, 2) + >>> # Add some arbitrary weight to the edges + >>> for i, (u, v) in enumerate(B.edges()): + ... B.edges[u, v]["weight"] = i + 1 + >>> for edge in B.edges(data=True): + ... print(edge) + (0, 2, {'weight': 1}) + (0, 3, {'weight': 2}) + (1, 2, {'weight': 3}) + (1, 3, {'weight': 4}) + >>> # By default, the weight is the number of shared neighbors + >>> G = bipartite.generic_weighted_projected_graph(B, [0, 1]) + >>> print(list(G.edges(data=True))) + [(0, 1, {'weight': 2})] + >>> # To specify a custom weight function use the weight_function parameter + >>> G = bipartite.generic_weighted_projected_graph( + ... B, [0, 1], weight_function=jaccard + ... ) + >>> print(list(G.edges(data=True))) + [(0, 1, {'weight': 1.0})] + >>> G = bipartite.generic_weighted_projected_graph( + ... B, [0, 1], weight_function=my_weight + ... ) + >>> print(list(G.edges(data=True))) + [(0, 1, {'weight': 10})] + + Notes + ----- + No attempt is made to verify that the input graph B is bipartite. + The graph and node properties are (shallow) copied to the projected graph. + + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + See Also + -------- + is_bipartite, + is_bipartite_node_set, + sets, + weighted_projected_graph, + collaboration_weighted_projected_graph, + overlap_weighted_projected_graph, + projected_graph + + """ + if B.is_directed(): + pred = B.pred + G = nx.DiGraph() + else: + pred = B.adj + G = nx.Graph() + if weight_function is None: + + def weight_function(G, u, v): + # Notice that we use set(pred[v]) for handling the directed case. + return len(set(G[u]) & set(pred[v])) + + G.graph.update(B.graph) + G.add_nodes_from((n, B.nodes[n]) for n in nodes) + for u in nodes: + nbrs2 = {n for nbr in set(B[u]) for n in B[nbr]} - {u} + for v in nbrs2: + weight = weight_function(B, u, v) + G.add_edge(u, v, weight=weight) + return G diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/redundancy.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/redundancy.py new file mode 100644 index 0000000000000000000000000000000000000000..b622b975f0255ee4ac4bc56031c127ac58592abf --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/redundancy.py @@ -0,0 +1,112 @@ +"""Node redundancy for bipartite graphs.""" + +from itertools import combinations + +import networkx as nx +from networkx import NetworkXError + +__all__ = ["node_redundancy"] + + +@nx._dispatchable +def node_redundancy(G, nodes=None): + r"""Computes the node redundancy coefficients for the nodes in the bipartite + graph `G`. + + The redundancy coefficient of a node `v` is the fraction of pairs of + neighbors of `v` that are both linked to other nodes. In a one-mode + projection these nodes would be linked together even if `v` were + not there. + + More formally, for any vertex `v`, the *redundancy coefficient of `v`* is + defined by + + .. math:: + + rc(v) = \frac{|\{\{u, w\} \subseteq N(v), + \: \exists v' \neq v,\: (v',u) \in E\: + \mathrm{and}\: (v',w) \in E\}|}{ \frac{|N(v)|(|N(v)|-1)}{2}}, + + where `N(v)` is the set of neighbors of `v` in `G`. + + Parameters + ---------- + G : graph + A bipartite graph + + nodes : list or iterable (optional) + Compute redundancy for these nodes. The default is all nodes in G. + + Returns + ------- + redundancy : dictionary + A dictionary keyed by node with the node redundancy value. + + Examples + -------- + Compute the redundancy coefficient of each node in a graph:: + + >>> from networkx.algorithms import bipartite + >>> G = nx.cycle_graph(4) + >>> rc = bipartite.node_redundancy(G) + >>> rc[0] + 1.0 + + Compute the average redundancy for the graph:: + + >>> from networkx.algorithms import bipartite + >>> G = nx.cycle_graph(4) + >>> rc = bipartite.node_redundancy(G) + >>> sum(rc.values()) / len(G) + 1.0 + + Compute the average redundancy for a set of nodes:: + + >>> from networkx.algorithms import bipartite + >>> G = nx.cycle_graph(4) + >>> rc = bipartite.node_redundancy(G) + >>> nodes = [0, 2] + >>> sum(rc[n] for n in nodes) / len(nodes) + 1.0 + + Raises + ------ + NetworkXError + If any of the nodes in the graph (or in `nodes`, if specified) has + (out-)degree less than two (which would result in division by zero, + according to the definition of the redundancy coefficient). + + References + ---------- + .. [1] Latapy, Matthieu, Clémence Magnien, and Nathalie Del Vecchio (2008). + Basic notions for the analysis of large two-mode networks. + Social Networks 30(1), 31--48. + + """ + if nodes is None: + nodes = G + if any(len(G[v]) < 2 for v in nodes): + raise NetworkXError( + "Cannot compute redundancy coefficient for a node" + " that has fewer than two neighbors." + ) + # TODO This can be trivially parallelized. + return {v: _node_redundancy(G, v) for v in nodes} + + +def _node_redundancy(G, v): + """Returns the redundancy of the node `v` in the bipartite graph `G`. + + If `G` is a graph with `n` nodes, the redundancy of a node is the ratio + of the "overlap" of `v` to the maximum possible overlap of `v` + according to its degree. The overlap of `v` is the number of pairs of + neighbors that have mutual neighbors themselves, other than `v`. + + `v` must have at least two neighbors in `G`. + + """ + n = len(G[v]) + overlap = sum( + 1 for (u, w) in combinations(G[v], 2) if (set(G[u]) & set(G[w])) - {v} + ) + return (2 * overlap) / (n * (n - 1)) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/spectral.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/spectral.py new file mode 100644 index 0000000000000000000000000000000000000000..cb9388f6cb61cb3c5da865e22449f4e8f2d1e720 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/spectral.py @@ -0,0 +1,69 @@ +""" +Spectral bipartivity measure. +""" + +import networkx as nx + +__all__ = ["spectral_bipartivity"] + + +@nx._dispatchable(edge_attrs="weight") +def spectral_bipartivity(G, nodes=None, weight="weight"): + """Returns the spectral bipartivity. + + Parameters + ---------- + G : NetworkX graph + + nodes : list or container optional(default is all nodes) + Nodes to return value of spectral bipartivity contribution. + + weight : string or None optional (default = 'weight') + Edge data key to use for edge weights. If None, weights set to 1. + + Returns + ------- + sb : float or dict + A single number if the keyword nodes is not specified, or + a dictionary keyed by node with the spectral bipartivity contribution + of that node as the value. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> G = nx.path_graph(4) + >>> bipartite.spectral_bipartivity(G) + 1.0 + + Notes + ----- + This implementation uses Numpy (dense) matrices which are not efficient + for storing large sparse graphs. + + See Also + -------- + color + + References + ---------- + .. [1] E. Estrada and J. A. Rodríguez-Velázquez, "Spectral measures of + bipartivity in complex networks", PhysRev E 72, 046105 (2005) + """ + import scipy as sp + + nodelist = list(G) # ordering of nodes in matrix + A = nx.to_numpy_array(G, nodelist, weight=weight) + expA = sp.linalg.expm(A) + expmA = sp.linalg.expm(-A) + coshA = 0.5 * (expA + expmA) + if nodes is None: + # return single number for entire graph + return float(coshA.diagonal().sum() / expA.diagonal().sum()) + else: + # contribution for individual nodes + index = dict(zip(nodelist, range(len(nodelist)))) + sb = {} + for n in nodes: + i = index[n] + sb[n] = coshA.item(i, i) / expA.item(i, i) + return sb diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/__pycache__/__init__.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/__pycache__/__init__.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..60eb0ad588d00a59d1b34732d7dfb7bc72d4d507 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/__pycache__/__init__.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/test_basic.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/test_basic.py new file mode 100644 index 0000000000000000000000000000000000000000..655506b4f74110b57cb37db277e2be50bb0be8f4 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/test_basic.py @@ -0,0 +1,125 @@ +import pytest + +import networkx as nx +from networkx.algorithms import bipartite + + +class TestBipartiteBasic: + def test_is_bipartite(self): + assert bipartite.is_bipartite(nx.path_graph(4)) + assert bipartite.is_bipartite(nx.DiGraph([(1, 0)])) + assert not bipartite.is_bipartite(nx.complete_graph(3)) + + def test_bipartite_color(self): + G = nx.path_graph(4) + c = bipartite.color(G) + assert c == {0: 1, 1: 0, 2: 1, 3: 0} + + def test_not_bipartite_color(self): + with pytest.raises(nx.NetworkXError): + c = bipartite.color(nx.complete_graph(4)) + + def test_bipartite_directed(self): + G = bipartite.random_graph(10, 10, 0.1, directed=True) + assert bipartite.is_bipartite(G) + + def test_bipartite_sets(self): + G = nx.path_graph(4) + X, Y = bipartite.sets(G) + assert X == {0, 2} + assert Y == {1, 3} + + def test_bipartite_sets_directed(self): + G = nx.path_graph(4) + D = G.to_directed() + X, Y = bipartite.sets(D) + assert X == {0, 2} + assert Y == {1, 3} + + def test_bipartite_sets_given_top_nodes(self): + G = nx.path_graph(4) + top_nodes = [0, 2] + X, Y = bipartite.sets(G, top_nodes) + assert X == {0, 2} + assert Y == {1, 3} + + def test_bipartite_sets_disconnected(self): + with pytest.raises(nx.AmbiguousSolution): + G = nx.path_graph(4) + G.add_edges_from([(5, 6), (6, 7)]) + X, Y = bipartite.sets(G) + + def test_is_bipartite_node_set(self): + G = nx.path_graph(4) + + with pytest.raises(nx.AmbiguousSolution): + bipartite.is_bipartite_node_set(G, [1, 1, 2, 3]) + + assert bipartite.is_bipartite_node_set(G, [0, 2]) + assert bipartite.is_bipartite_node_set(G, [1, 3]) + assert not bipartite.is_bipartite_node_set(G, [1, 2]) + G.add_edge(10, 20) + assert bipartite.is_bipartite_node_set(G, [0, 2, 10]) + assert bipartite.is_bipartite_node_set(G, [0, 2, 20]) + assert bipartite.is_bipartite_node_set(G, [1, 3, 10]) + assert bipartite.is_bipartite_node_set(G, [1, 3, 20]) + + def test_bipartite_density(self): + G = nx.path_graph(5) + X, Y = bipartite.sets(G) + density = len(list(G.edges())) / (len(X) * len(Y)) + assert bipartite.density(G, X) == density + D = nx.DiGraph(G.edges()) + assert bipartite.density(D, X) == density / 2.0 + assert bipartite.density(nx.Graph(), {}) == 0.0 + + def test_bipartite_degrees(self): + G = nx.path_graph(5) + X = {1, 3} + Y = {0, 2, 4} + u, d = bipartite.degrees(G, Y) + assert dict(u) == {1: 2, 3: 2} + assert dict(d) == {0: 1, 2: 2, 4: 1} + + def test_bipartite_weighted_degrees(self): + G = nx.path_graph(5) + G.add_edge(0, 1, weight=0.1, other=0.2) + X = {1, 3} + Y = {0, 2, 4} + u, d = bipartite.degrees(G, Y, weight="weight") + assert dict(u) == {1: 1.1, 3: 2} + assert dict(d) == {0: 0.1, 2: 2, 4: 1} + u, d = bipartite.degrees(G, Y, weight="other") + assert dict(u) == {1: 1.2, 3: 2} + assert dict(d) == {0: 0.2, 2: 2, 4: 1} + + def test_biadjacency_matrix_weight(self): + pytest.importorskip("scipy") + G = nx.path_graph(5) + G.add_edge(0, 1, weight=2, other=4) + X = [1, 3] + Y = [0, 2, 4] + M = bipartite.biadjacency_matrix(G, X, weight="weight") + assert M[0, 0] == 2 + M = bipartite.biadjacency_matrix(G, X, weight="other") + assert M[0, 0] == 4 + + def test_biadjacency_matrix(self): + pytest.importorskip("scipy") + tops = [2, 5, 10] + bots = [5, 10, 15] + for i in range(len(tops)): + G = bipartite.random_graph(tops[i], bots[i], 0.2) + top = [n for n, d in G.nodes(data=True) if d["bipartite"] == 0] + M = bipartite.biadjacency_matrix(G, top) + assert M.shape[0] == tops[i] + assert M.shape[1] == bots[i] + + def test_biadjacency_matrix_order(self): + pytest.importorskip("scipy") + G = nx.path_graph(5) + G.add_edge(0, 1, weight=2) + X = [3, 1] + Y = [4, 2, 0] + M = bipartite.biadjacency_matrix(G, X, Y, weight="weight") + assert M[1, 2] == 2 diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/test_edgelist.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/test_edgelist.py new file mode 100644 index 0000000000000000000000000000000000000000..66be8a2f5b3e1f9486594c63015295ad6a270efa --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/test_edgelist.py @@ -0,0 +1,240 @@ +""" +Unit tests for bipartite edgelists. +""" + +import io + +import pytest + +import networkx as nx +from networkx.algorithms import bipartite +from networkx.utils import edges_equal, graphs_equal, nodes_equal + + +class TestEdgelist: + @classmethod + def setup_class(cls): + cls.G = nx.Graph(name="test") + e = [("a", "b"), ("b", "c"), ("c", "d"), ("d", "e"), ("e", "f"), ("a", "f")] + cls.G.add_edges_from(e) + cls.G.add_nodes_from(["a", "c", "e"], bipartite=0) + cls.G.add_nodes_from(["b", "d", "f"], bipartite=1) + cls.G.add_node("g", bipartite=0) + cls.DG = nx.DiGraph(cls.G) + cls.MG = nx.MultiGraph() + cls.MG.add_edges_from([(1, 2), (1, 2), (1, 2)]) + cls.MG.add_node(1, bipartite=0) + cls.MG.add_node(2, bipartite=1) + + def test_read_edgelist_1(self): + s = b"""\ +# comment line +1 2 +# comment line +2 3 +""" + bytesIO = io.BytesIO(s) + G = bipartite.read_edgelist(bytesIO, nodetype=int) + assert edges_equal(G.edges(), [(1, 2), (2, 3)]) + + def test_read_edgelist_3(self): + s = b"""\ +# comment line +1 2 {'weight':2.0} +# comment line +2 3 {'weight':3.0} +""" + bytesIO = io.BytesIO(s) + G = bipartite.read_edgelist(bytesIO, nodetype=int, data=False) + assert edges_equal(G.edges(), [(1, 2), (2, 3)]) + + bytesIO = io.BytesIO(s) + G = bipartite.read_edgelist(bytesIO, nodetype=int, data=True) + assert edges_equal( + G.edges(data=True), [(1, 2, {"weight": 2.0}), (2, 3, {"weight": 3.0})] + ) + + def test_write_edgelist_1(self): + fh = io.BytesIO() + G = nx.Graph() + G.add_edges_from([(1, 2), (2, 3)]) + G.add_node(1, bipartite=0) + G.add_node(2, bipartite=1) + G.add_node(3, bipartite=0) + bipartite.write_edgelist(G, fh, data=False) + fh.seek(0) + assert fh.read() == b"1 2\n3 2\n" + + def test_write_edgelist_2(self): + fh = io.BytesIO() + G = nx.Graph() + G.add_edges_from([(1, 2), (2, 3)]) + G.add_node(1, bipartite=0) + G.add_node(2, bipartite=1) + G.add_node(3, bipartite=0) + bipartite.write_edgelist(G, fh, data=True) + fh.seek(0) + assert fh.read() == b"1 2 {}\n3 2 {}\n" + + def test_write_edgelist_3(self): + fh = io.BytesIO() + G = nx.Graph() + G.add_edge(1, 2, weight=2.0) + G.add_edge(2, 3, weight=3.0) + G.add_node(1, bipartite=0) + G.add_node(2, bipartite=1) + G.add_node(3, bipartite=0) + bipartite.write_edgelist(G, fh, data=True) + fh.seek(0) + assert fh.read() == b"1 2 {'weight': 2.0}\n3 2 {'weight': 3.0}\n" + + def test_write_edgelist_4(self): + fh = io.BytesIO() + G = nx.Graph() + G.add_edge(1, 2, weight=2.0) + G.add_edge(2, 3, weight=3.0) + G.add_node(1, bipartite=0) + G.add_node(2, bipartite=1) + G.add_node(3, bipartite=0) + bipartite.write_edgelist(G, fh, data=[("weight")]) + fh.seek(0) + assert fh.read() == b"1 2 2.0\n3 2 3.0\n" + + def test_unicode(self, tmp_path): + G = nx.Graph() + name1 = chr(2344) + chr(123) + chr(6543) + name2 = chr(5543) + chr(1543) + chr(324) + G.add_edge(name1, "Radiohead", **{name2: 3}) + G.add_node(name1, bipartite=0) + G.add_node("Radiohead", bipartite=1) + + fname = tmp_path / "edgelist.txt" + bipartite.write_edgelist(G, fname) + H = bipartite.read_edgelist(fname) + assert graphs_equal(G, H) + + def test_latin1_issue(self, tmp_path): + G = nx.Graph() + name1 = chr(2344) + chr(123) + chr(6543) + name2 = chr(5543) + chr(1543) + chr(324) + G.add_edge(name1, "Radiohead", **{name2: 3}) + G.add_node(name1, bipartite=0) + G.add_node("Radiohead", bipartite=1) + + fname = tmp_path / "edgelist.txt" + with pytest.raises(UnicodeEncodeError): + bipartite.write_edgelist(G, fname, encoding="latin-1") + + def test_latin1(self, tmp_path): + G = nx.Graph() + name1 = "Bj" + chr(246) + "rk" + name2 = chr(220) + "ber" + G.add_edge(name1, "Radiohead", **{name2: 3}) + G.add_node(name1, bipartite=0) + G.add_node("Radiohead", bipartite=1) + + fname = tmp_path / "edgelist.txt" + bipartite.write_edgelist(G, fname, encoding="latin-1") + H = bipartite.read_edgelist(fname, encoding="latin-1") + assert graphs_equal(G, H) + + def test_edgelist_graph(self, tmp_path): + G = self.G + fname = tmp_path / "edgelist.txt" + bipartite.write_edgelist(G, fname) + H = bipartite.read_edgelist(fname) + H2 = bipartite.read_edgelist(fname) + assert H is not H2 # they should be different graphs + G.remove_node("g") # isolated nodes are not written in edgelist + assert nodes_equal(list(H), list(G)) + assert edges_equal(list(H.edges()), list(G.edges())) + + def test_edgelist_integers(self, tmp_path): + G = nx.convert_node_labels_to_integers(self.G) + fname = tmp_path / "edgelist.txt" + bipartite.write_edgelist(G, fname) + H = bipartite.read_edgelist(fname, nodetype=int) + # isolated nodes are not written in edgelist + G.remove_nodes_from(list(nx.isolates(G))) + assert nodes_equal(list(H), list(G)) + assert edges_equal(list(H.edges()), list(G.edges())) + + def test_edgelist_multigraph(self, tmp_path): + G = self.MG + fname = tmp_path / "edgelist.txt" + bipartite.write_edgelist(G, fname) + H = bipartite.read_edgelist(fname, nodetype=int, create_using=nx.MultiGraph()) + H2 = bipartite.read_edgelist(fname, nodetype=int, create_using=nx.MultiGraph()) + assert H is not H2 # they should be different graphs + assert nodes_equal(list(H), list(G)) + assert edges_equal(list(H.edges()), list(G.edges())) + + def test_empty_digraph(self): + with pytest.raises(nx.NetworkXNotImplemented): + bytesIO = io.BytesIO() + bipartite.write_edgelist(nx.DiGraph(), bytesIO) + + def test_raise_attribute(self): + with pytest.raises(AttributeError): + G = nx.path_graph(4) + bytesIO = io.BytesIO() + bipartite.write_edgelist(G, bytesIO) + + def test_parse_edgelist(self): + """Tests for conditions specific to + parse_edge_list method""" + + # ignore strings of length less than 2 + lines = ["1 2", "2 3", "3 1", "4", " "] + G = bipartite.parse_edgelist(lines, nodetype=int) + assert list(G.nodes) == [1, 2, 3] + + # Exception raised when node is not convertible + # to specified data type + with pytest.raises(TypeError, match=".*Failed to convert nodes"): + lines = ["a b", "b c", "c a"] + G = bipartite.parse_edgelist(lines, nodetype=int) + + # Exception raised when format of data is not + # convertible to dictionary object + with pytest.raises(TypeError, match=".*Failed to convert edge data"): + lines = ["1 2 3", "2 3 4", "3 1 2"] + G = bipartite.parse_edgelist(lines, nodetype=int) + + # Exception raised when edge data and data + # keys are not of same length + with pytest.raises(IndexError): + lines = ["1 2 3 4", "2 3 4"] + G = bipartite.parse_edgelist( + lines, nodetype=int, data=[("weight", int), ("key", int)] + ) + + # Exception raised when edge data is not + # convertible to specified data type + with pytest.raises(TypeError, match=".*Failed to convert key data"): + lines = ["1 2 3 a", "2 3 4 b"] + G = bipartite.parse_edgelist( + lines, nodetype=int, data=[("weight", int), ("key", int)] + ) + + +def test_bipartite_edgelist_consistent_strip_handling(): + """See gh-7462 + + Input when printed looks like: + + A B interaction 2 + B C interaction 4 + C A interaction + + Note the trailing \\t in the last line, which indicates the existence of + an empty data field. + """ + lines = io.StringIO( + "A\tB\tinteraction\t2\nB\tC\tinteraction\t4\nC\tA\tinteraction\t" + ) + descr = [("type", str), ("weight", str)] + # Should not raise + G = nx.bipartite.parse_edgelist(lines, delimiter="\t", data=descr) + expected = [("A", "B", "2"), ("A", "C", ""), ("B", "C", "4")] + assert sorted(G.edges(data="weight")) == expected diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/test_matching.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/test_matching.py new file mode 100644 index 0000000000000000000000000000000000000000..c24659ea8fcf01ab4a26a6c6959c4935ab9aad2d --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/test_matching.py @@ -0,0 +1,327 @@ +"""Unit tests for the :mod:`networkx.algorithms.bipartite.matching` module.""" + +import itertools + +import pytest + +import networkx as nx +from networkx.algorithms.bipartite.matching import ( + eppstein_matching, + hopcroft_karp_matching, + maximum_matching, + minimum_weight_full_matching, + to_vertex_cover, +) + + +class TestMatching: + """Tests for bipartite matching algorithms.""" + + def setup_method(self): + """Creates a bipartite graph for use in testing matching algorithms. + + The bipartite graph has a maximum cardinality matching that leaves + vertex 1 and vertex 10 unmatched. The first six numbers are the left + vertices and the next six numbers are the right vertices. + + """ + self.simple_graph = nx.complete_bipartite_graph(2, 3) + self.simple_solution = {0: 2, 1: 3, 2: 0, 3: 1} + + edges = [(0, 7), (0, 8), (2, 6), (2, 9), (3, 8), (4, 8), (4, 9), (5, 11)] + self.top_nodes = set(range(6)) + self.graph = nx.Graph() + self.graph.add_nodes_from(range(12)) + self.graph.add_edges_from(edges) + + # Example bipartite graph from issue 2127 + G = nx.Graph() + G.add_nodes_from( + [ + (1, "C"), + (1, "B"), + (0, "G"), + (1, "F"), + (1, "E"), + (0, "C"), + (1, "D"), + (1, "I"), + (0, "A"), + (0, "D"), + (0, "F"), + (0, "E"), + (0, "H"), + (1, "G"), + (1, "A"), + (0, "I"), + (0, "B"), + (1, "H"), + ] + ) + G.add_edge((1, "C"), (0, "A")) + G.add_edge((1, "B"), (0, "A")) + G.add_edge((0, "G"), (1, "I")) + G.add_edge((0, "G"), (1, "H")) + G.add_edge((1, "F"), (0, "A")) + G.add_edge((1, "F"), (0, "C")) + G.add_edge((1, "F"), (0, "E")) + G.add_edge((1, "E"), (0, "A")) + G.add_edge((1, "E"), (0, "C")) + G.add_edge((0, "C"), (1, "D")) + G.add_edge((0, "C"), (1, "I")) + G.add_edge((0, "C"), (1, "G")) + G.add_edge((0, "C"), (1, "H")) + G.add_edge((1, "D"), (0, "A")) + G.add_edge((1, "I"), (0, "A")) + G.add_edge((1, "I"), (0, "E")) + G.add_edge((0, "A"), (1, "G")) + G.add_edge((0, "A"), (1, "H")) + G.add_edge((0, "E"), (1, "G")) + G.add_edge((0, "E"), (1, "H")) + self.disconnected_graph = G + + def check_match(self, matching): + """Asserts that the matching is what we expect from the bipartite graph + constructed in the :meth:`setup` fixture. + + """ + # For the sake of brevity, rename `matching` to `M`. + M = matching + matched_vertices = frozenset(itertools.chain(*M.items())) + # Assert that the maximum number of vertices (10) is matched. + assert matched_vertices == frozenset(range(12)) - {1, 10} + # Assert that no vertex appears in two edges, or in other words, that + # the matching (u, v) and (v, u) both appear in the matching + # dictionary. + assert all(u == M[M[u]] for u in range(12) if u in M) + + def check_vertex_cover(self, vertices): + """Asserts that the given set of vertices is the vertex cover we + expected from the bipartite graph constructed in the :meth:`setup` + fixture. + + """ + # By Konig's theorem, the number of edges in a maximum matching equals + # the number of vertices in a minimum vertex cover. + assert len(vertices) == 5 + # Assert that the set is truly a vertex cover. + for u, v in self.graph.edges(): + assert u in vertices or v in vertices + # TODO Assert that the vertices are the correct ones. + + def test_eppstein_matching(self): + """Tests that David Eppstein's implementation of the Hopcroft--Karp + algorithm produces a maximum cardinality matching. + + """ + self.check_match(eppstein_matching(self.graph, self.top_nodes)) + + def test_hopcroft_karp_matching(self): + """Tests that the Hopcroft--Karp algorithm produces a maximum + cardinality matching in a bipartite graph. + + """ + self.check_match(hopcroft_karp_matching(self.graph, self.top_nodes)) + + def test_to_vertex_cover(self): + """Test for converting a maximum matching to a minimum vertex cover.""" + matching = maximum_matching(self.graph, self.top_nodes) + vertex_cover = to_vertex_cover(self.graph, matching, self.top_nodes) + self.check_vertex_cover(vertex_cover) + + def test_eppstein_matching_simple(self): + match = eppstein_matching(self.simple_graph) + assert match == self.simple_solution + + def test_hopcroft_karp_matching_simple(self): + match = hopcroft_karp_matching(self.simple_graph) + assert match == self.simple_solution + + def test_eppstein_matching_disconnected(self): + with pytest.raises(nx.AmbiguousSolution): + match = eppstein_matching(self.disconnected_graph) + + def test_hopcroft_karp_matching_disconnected(self): + with pytest.raises(nx.AmbiguousSolution): + match = hopcroft_karp_matching(self.disconnected_graph) + + def test_issue_2127(self): + """Test from issue 2127""" + # Build the example DAG + G = nx.DiGraph() + G.add_edge("A", "C") + G.add_edge("A", "B") + G.add_edge("C", "E") + G.add_edge("C", "D") + G.add_edge("E", "G") + G.add_edge("E", "F") + G.add_edge("G", "I") + G.add_edge("G", "H") + + tc = nx.transitive_closure(G) + btc = nx.Graph() + + # Create a bipartite graph based on the transitive closure of G + for v in tc.nodes(): + btc.add_node((0, v)) + btc.add_node((1, v)) + + for u, v in tc.edges(): + btc.add_edge((0, u), (1, v)) + + top_nodes = {n for n in btc if n[0] == 0} + matching = hopcroft_karp_matching(btc, top_nodes) + vertex_cover = to_vertex_cover(btc, matching, top_nodes) + independent_set = set(G) - {v for _, v in vertex_cover} + assert {"B", "D", "F", "I", "H"} == independent_set + + def test_vertex_cover_issue_2384(self): + G = nx.Graph([(0, 3), (1, 3), (1, 4), (2, 3)]) + matching = maximum_matching(G) + vertex_cover = to_vertex_cover(G, matching) + for u, v in G.edges(): + assert u in vertex_cover or v in vertex_cover + + def test_vertex_cover_issue_3306(self): + G = nx.Graph() + edges = [(0, 2), (1, 0), (1, 1), (1, 2), (2, 2)] + G.add_edges_from([((i, "L"), (j, "R")) for i, j in edges]) + + matching = maximum_matching(G) + vertex_cover = to_vertex_cover(G, matching) + for u, v in G.edges(): + assert u in vertex_cover or v in vertex_cover + + def test_unorderable_nodes(self): + a = object() + b = object() + c = object() + d = object() + e = object() + G = nx.Graph([(a, d), (b, d), (b, e), (c, d)]) + matching = maximum_matching(G) + vertex_cover = to_vertex_cover(G, matching) + for u, v in G.edges(): + assert u in vertex_cover or v in vertex_cover + + +def test_eppstein_matching(): + """Test in accordance to issue #1927""" + G = nx.Graph() + G.add_nodes_from(["a", 2, 3, 4], bipartite=0) + G.add_nodes_from([1, "b", "c"], bipartite=1) + G.add_edges_from([("a", 1), ("a", "b"), (2, "b"), (2, "c"), (3, "c"), (4, 1)]) + matching = eppstein_matching(G) + assert len(matching) == len(maximum_matching(G)) + assert all(x in set(matching.keys()) for x in set(matching.values())) + + +class TestMinimumWeightFullMatching: + @classmethod + def setup_class(cls): + pytest.importorskip("scipy") + + def test_minimum_weight_full_matching_incomplete_graph(self): + B = nx.Graph() + B.add_nodes_from([1, 2], bipartite=0) + B.add_nodes_from([3, 4], bipartite=1) + B.add_edge(1, 4, weight=100) + B.add_edge(2, 3, weight=100) + B.add_edge(2, 4, weight=50) + matching = minimum_weight_full_matching(B) + assert matching == {1: 4, 2: 3, 4: 1, 3: 2} + + def test_minimum_weight_full_matching_with_no_full_matching(self): + B = nx.Graph() + B.add_nodes_from([1, 2, 3], bipartite=0) + B.add_nodes_from([4, 5, 6], bipartite=1) + B.add_edge(1, 4, weight=100) + B.add_edge(2, 4, weight=100) + B.add_edge(3, 4, weight=50) + B.add_edge(3, 5, weight=50) + B.add_edge(3, 6, weight=50) + with pytest.raises(ValueError): + minimum_weight_full_matching(B) + + def test_minimum_weight_full_matching_square(self): + G = nx.complete_bipartite_graph(3, 3) + G.add_edge(0, 3, weight=400) + G.add_edge(0, 4, weight=150) + G.add_edge(0, 5, weight=400) + G.add_edge(1, 3, weight=400) + G.add_edge(1, 4, weight=450) + G.add_edge(1, 5, weight=600) + G.add_edge(2, 3, weight=300) + G.add_edge(2, 4, weight=225) + G.add_edge(2, 5, weight=300) + matching = minimum_weight_full_matching(G) + assert matching == {0: 4, 1: 3, 2: 5, 4: 0, 3: 1, 5: 2} + + def test_minimum_weight_full_matching_smaller_left(self): + G = nx.complete_bipartite_graph(3, 4) + G.add_edge(0, 3, weight=400) + G.add_edge(0, 4, weight=150) + G.add_edge(0, 5, weight=400) + G.add_edge(0, 6, weight=1) + G.add_edge(1, 3, weight=400) + G.add_edge(1, 4, weight=450) + G.add_edge(1, 5, weight=600) + G.add_edge(1, 6, weight=2) + G.add_edge(2, 3, weight=300) + G.add_edge(2, 4, weight=225) + G.add_edge(2, 5, weight=290) + G.add_edge(2, 6, weight=3) + matching = minimum_weight_full_matching(G) + assert matching == {0: 4, 1: 6, 2: 5, 4: 0, 5: 2, 6: 1} + + def test_minimum_weight_full_matching_smaller_top_nodes_right(self): + G = nx.complete_bipartite_graph(3, 4) + G.add_edge(0, 3, weight=400) + G.add_edge(0, 4, weight=150) + G.add_edge(0, 5, weight=400) + G.add_edge(0, 6, weight=1) + G.add_edge(1, 3, weight=400) + G.add_edge(1, 4, weight=450) + G.add_edge(1, 5, weight=600) + G.add_edge(1, 6, weight=2) + G.add_edge(2, 3, weight=300) + G.add_edge(2, 4, weight=225) + G.add_edge(2, 5, weight=290) + G.add_edge(2, 6, weight=3) + matching = minimum_weight_full_matching(G, top_nodes=[3, 4, 5, 6]) + assert matching == {0: 4, 1: 6, 2: 5, 4: 0, 5: 2, 6: 1} + + def test_minimum_weight_full_matching_smaller_right(self): + G = nx.complete_bipartite_graph(4, 3) + G.add_edge(0, 4, weight=400) + G.add_edge(0, 5, weight=400) + G.add_edge(0, 6, weight=300) + G.add_edge(1, 4, weight=150) + G.add_edge(1, 5, weight=450) + G.add_edge(1, 6, weight=225) + G.add_edge(2, 4, weight=400) + G.add_edge(2, 5, weight=600) + G.add_edge(2, 6, weight=290) + G.add_edge(3, 4, weight=1) + G.add_edge(3, 5, weight=2) + G.add_edge(3, 6, weight=3) + matching = minimum_weight_full_matching(G) + assert matching == {1: 4, 2: 6, 3: 5, 4: 1, 5: 3, 6: 2} + + def test_minimum_weight_full_matching_negative_weights(self): + G = nx.complete_bipartite_graph(2, 2) + G.add_edge(0, 2, weight=-2) + G.add_edge(0, 3, weight=0.2) + G.add_edge(1, 2, weight=-2) + G.add_edge(1, 3, weight=0.3) + matching = minimum_weight_full_matching(G) + assert matching == {0: 3, 1: 2, 2: 1, 3: 0} + + def test_minimum_weight_full_matching_different_weight_key(self): + G = nx.complete_bipartite_graph(2, 2) + G.add_edge(0, 2, mass=2) + G.add_edge(0, 3, mass=0.2) + G.add_edge(1, 2, mass=1) + G.add_edge(1, 3, mass=2) + matching = minimum_weight_full_matching(G, weight="mass") + assert matching == {0: 3, 1: 2, 2: 1, 3: 0} diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/dispersion.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/dispersion.py new file mode 100644 index 0000000000000000000000000000000000000000..a3fa68583a9d18a40e6fbd4c8267e25f7a13c60a --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/dispersion.py @@ -0,0 +1,107 @@ +from itertools import combinations + +import networkx as nx + +__all__ = ["dispersion"] + + +@nx._dispatchable +def dispersion(G, u=None, v=None, normalized=True, alpha=1.0, b=0.0, c=0.0): + r"""Calculate dispersion between `u` and `v` in `G`. + + A link between two actors (`u` and `v`) has a high dispersion when their + mutual ties (`s` and `t`) are not well connected with each other. + + Parameters + ---------- + G : graph + A NetworkX graph. + u : node, optional + The source for the dispersion score (e.g. ego node of the network). + v : node, optional + The target of the dispersion score if specified. + normalized : bool + If True (default) normalize by the embeddedness of the nodes (u and v). + alpha, b, c : float + Parameters for the normalization procedure. When `normalized` is True, + the dispersion value is normalized by:: + + result = ((dispersion + b) ** alpha) / (embeddedness + c) + + as long as the denominator is nonzero. + + Returns + ------- + nodes : dictionary + If u (v) is specified, returns a dictionary of nodes with dispersion + score for all "target" ("source") nodes. If neither u nor v is + specified, returns a dictionary of dictionaries for all nodes 'u' in the + graph with a dispersion score for each node 'v'. + + Notes + ----- + This implementation follows Lars Backstrom and Jon Kleinberg [1]_. Typical + usage would be to run dispersion on the ego network $G_u$ if $u$ were + specified. Running :func:`dispersion` with neither $u$ nor $v$ specified + can take some time to complete. + + References + ---------- + .. [1] Romantic Partnerships and the Dispersion of Social Ties: + A Network Analysis of Relationship Status on Facebook. + Lars Backstrom, Jon Kleinberg. + https://arxiv.org/pdf/1310.6753v1.pdf + + """ + + def _dispersion(G_u, u, v): + """dispersion for all nodes 'v' in a ego network G_u of node 'u'""" + u_nbrs = set(G_u[u]) + ST = {n for n in G_u[v] if n in u_nbrs} + set_uv = {u, v} + # all possible ties of connections that u and b share + possib = combinations(ST, 2) + total = 0 + for s, t in possib: + # neighbors of s that are in G_u, not including u and v + nbrs_s = u_nbrs.intersection(G_u[s]) - set_uv + # s and t are not directly connected + if t not in nbrs_s: + # s and t do not share a connection + if nbrs_s.isdisjoint(G_u[t]): + # tick for disp(u, v) + total += 1 + # neighbors that u and v share + embeddedness = len(ST) + + dispersion_val = total + if normalized: + dispersion_val = (total + b) ** alpha + if embeddedness + c != 0: + dispersion_val /= embeddedness + c + + return dispersion_val + + if u is None: + # v and u are not specified + if v is None: + results = {n: {} for n in G} + for u in G: + for v in G[u]: + results[u][v] = _dispersion(G, u, v) + # u is not specified, but v is + else: + results = dict.fromkeys(G[v], {}) + for u in G[v]: + results[u] = _dispersion(G, v, u) + else: + # u is specified with no target v + if v is None: + results = dict.fromkeys(G[u], {}) + for v in G[u]: + results[v] = _dispersion(G, u, v) + # both u and v are specified + else: + results = _dispersion(G, u, v) + + return results diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/flow_matrix.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/flow_matrix.py new file mode 100644 index 0000000000000000000000000000000000000000..e72b5e976c003c9e870f0c17e0fea25bb6e0596a --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/flow_matrix.py @@ -0,0 +1,130 @@ +# Helpers for current-flow betweenness and current-flow closeness +# Lazy computations for inverse Laplacian and flow-matrix rows. +import networkx as nx + + +@nx._dispatchable(edge_attrs="weight") +def flow_matrix_row(G, weight=None, dtype=float, solver="lu"): + # Generate a row of the current-flow matrix + import numpy as np + + solvername = { + "full": FullInverseLaplacian, + "lu": SuperLUInverseLaplacian, + "cg": CGInverseLaplacian, + } + n = G.number_of_nodes() + L = nx.laplacian_matrix(G, nodelist=range(n), weight=weight).asformat("csc") + L = L.astype(dtype) + C = solvername[solver](L, dtype=dtype) # initialize solver + w = C.w # w is the Laplacian matrix width + # row-by-row flow matrix + for u, v in sorted(sorted((u, v)) for u, v in G.edges()): + B = np.zeros(w, dtype=dtype) + c = G[u][v].get(weight, 1.0) + B[u % w] = c + B[v % w] = -c + # get only the rows needed in the inverse laplacian + # and multiply to get the flow matrix row + row = B @ C.get_rows(u, v) + yield row, (u, v) + + +# Class to compute the inverse laplacian only for specified rows +# Allows computation of the current-flow matrix without storing entire +# inverse laplacian matrix +class InverseLaplacian: + def __init__(self, L, width=None, dtype=None): + global np + import numpy as np + + (n, n) = L.shape + self.dtype = dtype + self.n = n + if width is None: + self.w = self.width(L) + else: + self.w = width + self.C = np.zeros((self.w, n), dtype=dtype) + self.L1 = L[1:, 1:] + self.init_solver(L) + + def init_solver(self, L): + pass + + def solve(self, r): + raise nx.NetworkXError("Implement solver") + + def solve_inverse(self, r): + raise nx.NetworkXError("Implement solver") + + def get_rows(self, r1, r2): + for r in range(r1, r2 + 1): + self.C[r % self.w, 1:] = self.solve_inverse(r) + return self.C + + def get_row(self, r): + self.C[r % self.w, 1:] = self.solve_inverse(r) + return self.C[r % self.w] + + def width(self, L): + m = 0 + for i, row in enumerate(L): + w = 0 + y = np.nonzero(row)[-1] + if len(y) > 0: + v = y - i + w = v.max() - v.min() + 1 + m = max(w, m) + return m + + +class FullInverseLaplacian(InverseLaplacian): + def init_solver(self, L): + self.IL = np.zeros(L.shape, dtype=self.dtype) + self.IL[1:, 1:] = np.linalg.inv(self.L1.todense()) + + def solve(self, rhs): + s = np.zeros(rhs.shape, dtype=self.dtype) + s = self.IL @ rhs + return s + + def solve_inverse(self, r): + return self.IL[r, 1:] + + +class SuperLUInverseLaplacian(InverseLaplacian): + def init_solver(self, L): + import scipy as sp + + self.lusolve = sp.sparse.linalg.factorized(self.L1.tocsc()) + + def solve_inverse(self, r): + rhs = np.zeros(self.n, dtype=self.dtype) + rhs[r] = 1 + return self.lusolve(rhs[1:]) + + def solve(self, rhs): + s = np.zeros(rhs.shape, dtype=self.dtype) + s[1:] = self.lusolve(rhs[1:]) + return s + + +class CGInverseLaplacian(InverseLaplacian): + def init_solver(self, L): + global sp + import scipy as sp + + ilu = sp.sparse.linalg.spilu(self.L1.tocsc()) + n = self.n - 1 + self.M = sp.sparse.linalg.LinearOperator(shape=(n, n), matvec=ilu.solve) + + def solve(self, rhs): + s = np.zeros(rhs.shape, dtype=self.dtype) + s[1:] = sp.sparse.linalg.cg(self.L1, rhs[1:], M=self.M, atol=0)[0] + return s + + def solve_inverse(self, r): + rhs = np.zeros(self.n, self.dtype) + rhs[r] = 1 + return sp.sparse.linalg.cg(self.L1, rhs[1:], M=self.M, atol=0)[0] diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/laplacian.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/laplacian.py new file mode 100644 index 0000000000000000000000000000000000000000..efb6e8f67b6a0980381dd121051ce62608b8a984 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/laplacian.py @@ -0,0 +1,150 @@ +""" +Laplacian centrality measures. +""" + +import networkx as nx + +__all__ = ["laplacian_centrality"] + + +@nx._dispatchable(edge_attrs="weight") +def laplacian_centrality( + G, normalized=True, nodelist=None, weight="weight", walk_type=None, alpha=0.95 +): + r"""Compute the Laplacian centrality for nodes in the graph `G`. + + The Laplacian Centrality of a node ``i`` is measured by the drop in the + Laplacian Energy after deleting node ``i`` from the graph. The Laplacian Energy + is the sum of the squared eigenvalues of a graph's Laplacian matrix. + + .. math:: + + C_L(u_i,G) = \frac{(\Delta E)_i}{E_L (G)} = \frac{E_L (G)-E_L (G_i)}{E_L (G)} + + E_L (G) = \sum_{i=0}^n \lambda_i^2 + + Where $E_L (G)$ is the Laplacian energy of graph `G`, + E_L (G_i) is the Laplacian energy of graph `G` after deleting node ``i`` + and $\lambda_i$ are the eigenvalues of `G`'s Laplacian matrix. + This formula shows the normalized value. Without normalization, + the numerator on the right side is returned. + + Parameters + ---------- + G : graph + A networkx graph + + normalized : bool (default = True) + If True the centrality score is scaled so the sum over all nodes is 1. + If False the centrality score for each node is the drop in Laplacian + energy when that node is removed. + + nodelist : list, optional (default = None) + The rows and columns are ordered according to the nodes in nodelist. + If nodelist is None, then the ordering is produced by G.nodes(). + + weight: string or None, optional (default=`weight`) + Optional parameter `weight` to compute the Laplacian matrix. + The edge data key used to compute each value in the matrix. + If None, then each edge has weight 1. + + walk_type : string or None, optional (default=None) + Optional parameter `walk_type` used when calling + :func:`directed_laplacian_matrix `. + One of ``"random"``, ``"lazy"``, or ``"pagerank"``. If ``walk_type=None`` + (the default), then a value is selected according to the properties of `G`: + - ``walk_type="random"`` if `G` is strongly connected and aperiodic + - ``walk_type="lazy"`` if `G` is strongly connected but not aperiodic + - ``walk_type="pagerank"`` for all other cases. + + alpha : real (default = 0.95) + Optional parameter `alpha` used when calling + :func:`directed_laplacian_matrix `. + (1 - alpha) is the teleportation probability used with pagerank. + + Returns + ------- + nodes : dictionary + Dictionary of nodes with Laplacian centrality as the value. + + Examples + -------- + >>> G = nx.Graph() + >>> edges = [(0, 1, 4), (0, 2, 2), (2, 1, 1), (1, 3, 2), (1, 4, 2), (4, 5, 1)] + >>> G.add_weighted_edges_from(edges) + >>> sorted((v, f"{c:0.2f}") for v, c in laplacian_centrality(G).items()) + [(0, '0.70'), (1, '0.90'), (2, '0.28'), (3, '0.22'), (4, '0.26'), (5, '0.04')] + + Notes + ----- + The algorithm is implemented based on [1]_ with an extension to directed graphs + using the ``directed_laplacian_matrix`` function. + + Raises + ------ + NetworkXPointlessConcept + If the graph `G` is the null graph. + ZeroDivisionError + If the graph `G` has no edges (is empty) and normalization is requested. + + References + ---------- + .. [1] Qi, X., Fuller, E., Wu, Q., Wu, Y., and Zhang, C.-Q. (2012). + Laplacian centrality: A new centrality measure for weighted networks. + Information Sciences, 194:240-253. + https://math.wvu.edu/~cqzhang/Publication-files/my-paper/INS-2012-Laplacian-W.pdf + + See Also + -------- + :func:`~networkx.linalg.laplacianmatrix.directed_laplacian_matrix` + :func:`~networkx.linalg.laplacianmatrix.laplacian_matrix` + """ + import numpy as np + import scipy as sp + + if len(G) == 0: + raise nx.NetworkXPointlessConcept("null graph has no centrality defined") + if G.size(weight=weight) == 0: + if normalized: + raise ZeroDivisionError("graph with no edges has zero full energy") + return {n: 0 for n in G} + + if nodelist is not None: + nodeset = set(G.nbunch_iter(nodelist)) + if len(nodeset) != len(nodelist): + raise nx.NetworkXError("nodelist has duplicate nodes or nodes not in G") + nodes = nodelist + [n for n in G if n not in nodeset] + else: + nodelist = nodes = list(G) + + if G.is_directed(): + lap_matrix = nx.directed_laplacian_matrix(G, nodes, weight, walk_type, alpha) + else: + lap_matrix = nx.laplacian_matrix(G, nodes, weight).toarray() + + full_energy = np.power(sp.linalg.eigh(lap_matrix, eigvals_only=True), 2).sum() + + # calculate laplacian centrality + laplace_centralities_dict = {} + for i, node in enumerate(nodelist): + # remove row and col i from lap_matrix + all_but_i = list(np.arange(lap_matrix.shape[0])) + all_but_i.remove(i) + A_2 = lap_matrix[all_but_i, :][:, all_but_i] + + # Adjust diagonal for removed row + new_diag = lap_matrix.diagonal() - abs(lap_matrix[:, i]) + np.fill_diagonal(A_2, new_diag[all_but_i]) + + if len(all_but_i) > 0: # catches degenerate case of single node + new_energy = np.power(sp.linalg.eigh(A_2, eigvals_only=True), 2).sum() + else: + new_energy = 0.0 + + lapl_cent = full_energy - new_energy + if normalized: + lapl_cent = lapl_cent / full_energy + + laplace_centralities_dict[node] = float(lapl_cent) + + return laplace_centralities_dict diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/tests/__init__.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/tests/test_closeness_centrality.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/tests/test_closeness_centrality.py new file mode 100644 index 0000000000000000000000000000000000000000..7bdb7e7c38bbfe644ca914ea071e54308cf8c76e --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/tests/test_closeness_centrality.py @@ -0,0 +1,307 @@ +""" +Tests for closeness centrality. +""" + +import pytest + +import networkx as nx + + +class TestClosenessCentrality: + @classmethod + def setup_class(cls): + cls.K = nx.krackhardt_kite_graph() + cls.P3 = nx.path_graph(3) + cls.P4 = nx.path_graph(4) + cls.K5 = nx.complete_graph(5) + + cls.C4 = nx.cycle_graph(4) + cls.T = nx.balanced_tree(r=2, h=2) + cls.Gb = nx.Graph() + cls.Gb.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (4, 5), (3, 5)]) + + F = nx.florentine_families_graph() + cls.F = F + + cls.LM = nx.les_miserables_graph() + + # Create random undirected, unweighted graph for testing incremental version + cls.undirected_G = nx.fast_gnp_random_graph(n=100, p=0.6, seed=123) + cls.undirected_G_cc = nx.closeness_centrality(cls.undirected_G) + + def test_wf_improved(self): + G = nx.union(self.P4, nx.path_graph([4, 5, 6])) + c = nx.closeness_centrality(G) + cwf = nx.closeness_centrality(G, wf_improved=False) + res = {0: 0.25, 1: 0.375, 2: 0.375, 3: 0.25, 4: 0.222, 5: 0.333, 6: 0.222} + wf_res = {0: 0.5, 1: 0.75, 2: 0.75, 3: 0.5, 4: 0.667, 5: 1.0, 6: 0.667} + for n in G: + assert c[n] == pytest.approx(res[n], abs=1e-3) + assert cwf[n] == pytest.approx(wf_res[n], abs=1e-3) + + def test_digraph(self): + G = nx.path_graph(3, create_using=nx.DiGraph()) + c = nx.closeness_centrality(G) + cr = nx.closeness_centrality(G.reverse()) + d = {0: 0.0, 1: 0.500, 2: 0.667} + dr = {0: 0.667, 1: 0.500, 2: 0.0} + for n in sorted(self.P3): + assert c[n] == pytest.approx(d[n], abs=1e-3) + assert cr[n] == pytest.approx(dr[n], abs=1e-3) + + def test_k5_closeness(self): + c = nx.closeness_centrality(self.K5) + d = {0: 1.000, 1: 1.000, 2: 1.000, 3: 1.000, 4: 1.000} + for n in sorted(self.K5): + assert c[n] == pytest.approx(d[n], abs=1e-3) + + def test_p3_closeness(self): + c = nx.closeness_centrality(self.P3) + d = {0: 0.667, 1: 1.000, 2: 0.667} + for n in sorted(self.P3): + assert c[n] == pytest.approx(d[n], abs=1e-3) + + def test_krackhardt_closeness(self): + c = nx.closeness_centrality(self.K) + d = { + 0: 0.529, + 1: 0.529, + 2: 0.500, + 3: 0.600, + 4: 0.500, + 5: 0.643, + 6: 0.643, + 7: 0.600, + 8: 0.429, + 9: 0.310, + } + for n in sorted(self.K): + assert c[n] == pytest.approx(d[n], abs=1e-3) + + def test_florentine_families_closeness(self): + c = nx.closeness_centrality(self.F) + d = { + "Acciaiuoli": 0.368, + "Albizzi": 0.483, + "Barbadori": 0.4375, + "Bischeri": 0.400, + "Castellani": 0.389, + "Ginori": 0.333, + "Guadagni": 0.467, + "Lamberteschi": 0.326, + "Medici": 0.560, + "Pazzi": 0.286, + "Peruzzi": 0.368, + "Ridolfi": 0.500, + "Salviati": 0.389, + "Strozzi": 0.4375, + "Tornabuoni": 0.483, + } + for n in sorted(self.F): + assert c[n] == pytest.approx(d[n], abs=1e-3) + + def test_les_miserables_closeness(self): + c = nx.closeness_centrality(self.LM) + d = { + "Napoleon": 0.302, + "Myriel": 0.429, + "MlleBaptistine": 0.413, + "MmeMagloire": 0.413, + "CountessDeLo": 0.302, + "Geborand": 0.302, + "Champtercier": 0.302, + "Cravatte": 0.302, + "Count": 0.302, + "OldMan": 0.302, + "Valjean": 0.644, + "Labarre": 0.394, + "Marguerite": 0.413, + "MmeDeR": 0.394, + "Isabeau": 0.394, + "Gervais": 0.394, + "Listolier": 0.341, + "Tholomyes": 0.392, + "Fameuil": 0.341, + "Blacheville": 0.341, + "Favourite": 0.341, + "Dahlia": 0.341, + "Zephine": 0.341, + "Fantine": 0.461, + "MmeThenardier": 0.461, + "Thenardier": 0.517, + "Cosette": 0.478, + "Javert": 0.517, + "Fauchelevent": 0.402, + "Bamatabois": 0.427, + "Perpetue": 0.318, + "Simplice": 0.418, + "Scaufflaire": 0.394, + "Woman1": 0.396, + "Judge": 0.404, + "Champmathieu": 0.404, + "Brevet": 0.404, + "Chenildieu": 0.404, + "Cochepaille": 0.404, + "Pontmercy": 0.373, + "Boulatruelle": 0.342, + "Eponine": 0.396, + "Anzelma": 0.352, + "Woman2": 0.402, + "MotherInnocent": 0.398, + "Gribier": 0.288, + "MmeBurgon": 0.344, + "Jondrette": 0.257, + "Gavroche": 0.514, + "Gillenormand": 0.442, + "Magnon": 0.335, + "MlleGillenormand": 0.442, + "MmePontmercy": 0.315, + "MlleVaubois": 0.308, + "LtGillenormand": 0.365, + "Marius": 0.531, + "BaronessT": 0.352, + "Mabeuf": 0.396, + "Enjolras": 0.481, + "Combeferre": 0.392, + "Prouvaire": 0.357, + "Feuilly": 0.392, + "Courfeyrac": 0.400, + "Bahorel": 0.394, + "Bossuet": 0.475, + "Joly": 0.394, + "Grantaire": 0.358, + "MotherPlutarch": 0.285, + "Gueulemer": 0.463, + "Babet": 0.463, + "Claquesous": 0.452, + "Montparnasse": 0.458, + "Toussaint": 0.402, + "Child1": 0.342, + "Child2": 0.342, + "Brujon": 0.380, + "MmeHucheloup": 0.353, + } + for n in sorted(self.LM): + assert c[n] == pytest.approx(d[n], abs=1e-3) + + def test_weighted_closeness(self): + edges = [ + ("s", "u", 10), + ("s", "x", 5), + ("u", "v", 1), + ("u", "x", 2), + ("v", "y", 1), + ("x", "u", 3), + ("x", "v", 5), + ("x", "y", 2), + ("y", "s", 7), + ("y", "v", 6), + ] + XG = nx.Graph() + XG.add_weighted_edges_from(edges) + c = nx.closeness_centrality(XG, distance="weight") + d = {"y": 0.200, "x": 0.286, "s": 0.138, "u": 0.235, "v": 0.200} + for n in sorted(XG): + assert c[n] == pytest.approx(d[n], abs=1e-3) + + # + # Tests for incremental closeness centrality. + # + @staticmethod + def pick_add_edge(g): + u = nx.utils.arbitrary_element(g) + possible_nodes = set(g.nodes()) + neighbors = list(g.neighbors(u)) + [u] + possible_nodes.difference_update(neighbors) + v = nx.utils.arbitrary_element(possible_nodes) + return (u, v) + + @staticmethod + def pick_remove_edge(g): + u = nx.utils.arbitrary_element(g) + possible_nodes = list(g.neighbors(u)) + v = nx.utils.arbitrary_element(possible_nodes) + return (u, v) + + def test_directed_raises(self): + with pytest.raises(nx.NetworkXNotImplemented): + dir_G = nx.gn_graph(n=5) + prev_cc = None + edge = self.pick_add_edge(dir_G) + insert = True + nx.incremental_closeness_centrality(dir_G, edge, prev_cc, insert) + + def test_wrong_size_prev_cc_raises(self): + with pytest.raises(nx.NetworkXError): + G = self.undirected_G.copy() + edge = self.pick_add_edge(G) + insert = True + prev_cc = self.undirected_G_cc.copy() + prev_cc.pop(0) + nx.incremental_closeness_centrality(G, edge, prev_cc, insert) + + def test_wrong_nodes_prev_cc_raises(self): + with pytest.raises(nx.NetworkXError): + G = self.undirected_G.copy() + edge = self.pick_add_edge(G) + insert = True + prev_cc = self.undirected_G_cc.copy() + num_nodes = len(prev_cc) + prev_cc.pop(0) + prev_cc[num_nodes] = 0.5 + nx.incremental_closeness_centrality(G, edge, prev_cc, insert) + + def test_zero_centrality(self): + G = nx.path_graph(3) + prev_cc = nx.closeness_centrality(G) + edge = self.pick_remove_edge(G) + test_cc = nx.incremental_closeness_centrality(G, edge, prev_cc, insertion=False) + G.remove_edges_from([edge]) + real_cc = nx.closeness_centrality(G) + shared_items = set(test_cc.items()) & set(real_cc.items()) + assert len(shared_items) == len(real_cc) + assert 0 in test_cc.values() + + def test_incremental(self): + # Check that incremental and regular give same output + G = self.undirected_G.copy() + prev_cc = None + for i in range(5): + if i % 2 == 0: + # Remove an edge + insert = False + edge = self.pick_remove_edge(G) + else: + # Add an edge + insert = True + edge = self.pick_add_edge(G) + + # start = timeit.default_timer() + test_cc = nx.incremental_closeness_centrality(G, edge, prev_cc, insert) + # inc_elapsed = (timeit.default_timer() - start) + # print(f"incremental time: {inc_elapsed}") + + if insert: + G.add_edges_from([edge]) + else: + G.remove_edges_from([edge]) + + # start = timeit.default_timer() + real_cc = nx.closeness_centrality(G) + # reg_elapsed = (timeit.default_timer() - start) + # print(f"regular time: {reg_elapsed}") + # Example output: + # incremental time: 0.208 + # regular time: 0.276 + # incremental time: 0.00683 + # regular time: 0.260 + # incremental time: 0.0224 + # regular time: 0.278 + # incremental time: 0.00804 + # regular time: 0.208 + # incremental time: 0.00947 + # regular time: 0.188 + + assert set(test_cc.items()) == set(real_cc.items()) + + prev_cc = test_cc diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/tests/test_laplacian_centrality.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/tests/test_laplacian_centrality.py new file mode 100644 index 0000000000000000000000000000000000000000..21aa28b0b7c155078ab9c1a25e14d9aafa65683d --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/tests/test_laplacian_centrality.py @@ -0,0 +1,221 @@ +import pytest + +import networkx as nx + +np = pytest.importorskip("numpy") +sp = pytest.importorskip("scipy") + + +def test_laplacian_centrality_null_graph(): + G = nx.Graph() + with pytest.raises(nx.NetworkXPointlessConcept): + d = nx.laplacian_centrality(G, normalized=False) + + +def test_laplacian_centrality_single_node(): + """See gh-6571""" + G = nx.empty_graph(1) + assert nx.laplacian_centrality(G, normalized=False) == {0: 0} + with pytest.raises(ZeroDivisionError): + nx.laplacian_centrality(G, normalized=True) + + +def test_laplacian_centrality_unconnected_nodes(): + """laplacian_centrality on a unconnected node graph should return 0 + + For graphs without edges, the Laplacian energy is 0 and is unchanged with + node removal, so:: + + LC(v) = LE(G) - LE(G - v) = 0 - 0 = 0 + """ + G = nx.empty_graph(3) + assert nx.laplacian_centrality(G, normalized=False) == {0: 0, 1: 0, 2: 0} + + +def test_laplacian_centrality_empty_graph(): + G = nx.empty_graph(3) + with pytest.raises(ZeroDivisionError): + d = nx.laplacian_centrality(G, normalized=True) + + +def test_laplacian_centrality_E(): + E = nx.Graph() + E.add_weighted_edges_from( + [(0, 1, 4), (4, 5, 1), (0, 2, 2), (2, 1, 1), (1, 3, 2), (1, 4, 2)] + ) + d = nx.laplacian_centrality(E) + exact = { + 0: 0.700000, + 1: 0.900000, + 2: 0.280000, + 3: 0.220000, + 4: 0.260000, + 5: 0.040000, + } + + for n, dc in d.items(): + assert exact[n] == pytest.approx(dc, abs=1e-7) + + # Check not normalized + full_energy = 200 + dnn = nx.laplacian_centrality(E, normalized=False) + for n, dc in dnn.items(): + assert exact[n] * full_energy == pytest.approx(dc, abs=1e-7) + + # Check unweighted not-normalized version + duw_nn = nx.laplacian_centrality(E, normalized=False, weight=None) + print(duw_nn) + exact_uw_nn = { + 0: 18, + 1: 34, + 2: 18, + 3: 10, + 4: 16, + 5: 6, + } + for n, dc in duw_nn.items(): + assert exact_uw_nn[n] == pytest.approx(dc, abs=1e-7) + + # Check unweighted version + duw = nx.laplacian_centrality(E, weight=None) + full_energy = 42 + for n, dc in duw.items(): + assert exact_uw_nn[n] / full_energy == pytest.approx(dc, abs=1e-7) + + +def test_laplacian_centrality_KC(): + KC = nx.karate_club_graph() + d = nx.laplacian_centrality(KC) + exact = { + 0: 0.2543593, + 1: 0.1724524, + 2: 0.2166053, + 3: 0.0964646, + 4: 0.0350344, + 5: 0.0571109, + 6: 0.0540713, + 7: 0.0788674, + 8: 0.1222204, + 9: 0.0217565, + 10: 0.0308751, + 11: 0.0215965, + 12: 0.0174372, + 13: 0.118861, + 14: 0.0366341, + 15: 0.0548712, + 16: 0.0172772, + 17: 0.0191969, + 18: 0.0225564, + 19: 0.0331147, + 20: 0.0279955, + 21: 0.0246361, + 22: 0.0382339, + 23: 0.1294193, + 24: 0.0227164, + 25: 0.0644697, + 26: 0.0281555, + 27: 0.075188, + 28: 0.0364742, + 29: 0.0707087, + 30: 0.0708687, + 31: 0.131019, + 32: 0.2370821, + 33: 0.3066709, + } + for n, dc in d.items(): + assert exact[n] == pytest.approx(dc, abs=1e-7) + + # Check not normalized + full_energy = 12502 + dnn = nx.laplacian_centrality(KC, normalized=False) + for n, dc in dnn.items(): + assert exact[n] * full_energy == pytest.approx(dc, abs=1e-3) + + +def test_laplacian_centrality_K(): + K = nx.krackhardt_kite_graph() + d = nx.laplacian_centrality(K) + exact = { + 0: 0.3010753, + 1: 0.3010753, + 2: 0.2258065, + 3: 0.483871, + 4: 0.2258065, + 5: 0.3870968, + 6: 0.3870968, + 7: 0.1935484, + 8: 0.0752688, + 9: 0.0322581, + } + for n, dc in d.items(): + assert exact[n] == pytest.approx(dc, abs=1e-7) + + # Check not normalized + full_energy = 186 + dnn = nx.laplacian_centrality(K, normalized=False) + for n, dc in dnn.items(): + assert exact[n] * full_energy == pytest.approx(dc, abs=1e-3) + + +def test_laplacian_centrality_P3(): + P3 = nx.path_graph(3) + d = nx.laplacian_centrality(P3) + exact = {0: 0.6, 1: 1.0, 2: 0.6} + for n, dc in d.items(): + assert exact[n] == pytest.approx(dc, abs=1e-7) + + +def test_laplacian_centrality_K5(): + K5 = nx.complete_graph(5) + d = nx.laplacian_centrality(K5) + exact = {0: 0.52, 1: 0.52, 2: 0.52, 3: 0.52, 4: 0.52} + for n, dc in d.items(): + assert exact[n] == pytest.approx(dc, abs=1e-7) + + +def test_laplacian_centrality_FF(): + FF = nx.florentine_families_graph() + d = nx.laplacian_centrality(FF) + exact = { + "Acciaiuoli": 0.0804598, + "Medici": 0.4022989, + "Castellani": 0.1724138, + "Peruzzi": 0.183908, + "Strozzi": 0.2528736, + "Barbadori": 0.137931, + "Ridolfi": 0.2183908, + "Tornabuoni": 0.2183908, + "Albizzi": 0.1954023, + "Salviati": 0.1149425, + "Pazzi": 0.0344828, + "Bischeri": 0.1954023, + "Guadagni": 0.2298851, + "Ginori": 0.045977, + "Lamberteschi": 0.0574713, + } + for n, dc in d.items(): + assert exact[n] == pytest.approx(dc, abs=1e-7) + + +def test_laplacian_centrality_DG(): + DG = nx.DiGraph([(0, 5), (1, 5), (2, 5), (3, 5), (4, 5), (5, 6), (5, 7), (5, 8)]) + d = nx.laplacian_centrality(DG) + exact = { + 0: 0.2123352, + 5: 0.515391, + 1: 0.2123352, + 2: 0.2123352, + 3: 0.2123352, + 4: 0.2123352, + 6: 0.2952031, + 7: 0.2952031, + 8: 0.2952031, + } + for n, dc in d.items(): + assert exact[n] == pytest.approx(dc, abs=1e-7) + + # Check not normalized + full_energy = 9.50704 + dnn = nx.laplacian_centrality(DG, normalized=False) + for n, dc in dnn.items(): + assert exact[n] * full_energy == pytest.approx(dc, abs=1e-4) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/clique.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/clique.py new file mode 100644 index 0000000000000000000000000000000000000000..57b588ae350943636d7c0648c2d1b7d327f0d071 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/clique.py @@ -0,0 +1,755 @@ +"""Functions for finding and manipulating cliques. + +Finding the largest clique in a graph is NP-complete problem, so most of +these algorithms have an exponential running time; for more information, +see the Wikipedia article on the clique problem [1]_. + +.. [1] clique problem:: https://en.wikipedia.org/wiki/Clique_problem + +""" + +from collections import defaultdict, deque +from itertools import chain, combinations, islice + +import networkx as nx +from networkx.utils import not_implemented_for + +__all__ = [ + "find_cliques", + "find_cliques_recursive", + "make_max_clique_graph", + "make_clique_bipartite", + "node_clique_number", + "number_of_cliques", + "enumerate_all_cliques", + "max_weight_clique", +] + + +@not_implemented_for("directed") +@nx._dispatchable +def enumerate_all_cliques(G): + """Returns all cliques in an undirected graph. + + This function returns an iterator over cliques, each of which is a + list of nodes. The iteration is ordered by cardinality of the + cliques: first all cliques of size one, then all cliques of size + two, etc. + + Parameters + ---------- + G : NetworkX graph + An undirected graph. + + Returns + ------- + iterator + An iterator over cliques, each of which is a list of nodes in + `G`. The cliques are ordered according to size. + + Notes + ----- + To obtain a list of all cliques, use + `list(enumerate_all_cliques(G))`. However, be aware that in the + worst-case, the length of this list can be exponential in the number + of nodes in the graph (for example, when the graph is the complete + graph). This function avoids storing all cliques in memory by only + keeping current candidate node lists in memory during its search. + + The implementation is adapted from the algorithm by Zhang, et + al. (2005) [1]_ to output all cliques discovered. + + This algorithm ignores self-loops and parallel edges, since cliques + are not conventionally defined with such edges. + + References + ---------- + .. [1] Yun Zhang, Abu-Khzam, F.N., Baldwin, N.E., Chesler, E.J., + Langston, M.A., Samatova, N.F., + "Genome-Scale Computational Approaches to Memory-Intensive + Applications in Systems Biology". + *Supercomputing*, 2005. Proceedings of the ACM/IEEE SC 2005 + Conference, pp. 12, 12--18 Nov. 2005. + . + + """ + index = {} + nbrs = {} + for u in G: + index[u] = len(index) + # Neighbors of u that appear after u in the iteration order of G. + nbrs[u] = {v for v in G[u] if v not in index} + + queue = deque(([u], sorted(nbrs[u], key=index.__getitem__)) for u in G) + # Loop invariants: + # 1. len(base) is nondecreasing. + # 2. (base + cnbrs) is sorted with respect to the iteration order of G. + # 3. cnbrs is a set of common neighbors of nodes in base. + while queue: + base, cnbrs = map(list, queue.popleft()) + yield base + for i, u in enumerate(cnbrs): + # Use generators to reduce memory consumption. + queue.append( + ( + chain(base, [u]), + filter(nbrs[u].__contains__, islice(cnbrs, i + 1, None)), + ) + ) + + +@not_implemented_for("directed") +@nx._dispatchable +def find_cliques(G, nodes=None): + """Returns all maximal cliques in an undirected graph. + + For each node *n*, a *maximal clique for n* is a largest complete + subgraph containing *n*. The largest maximal clique is sometimes + called the *maximum clique*. + + This function returns an iterator over cliques, each of which is a + list of nodes. It is an iterative implementation, so should not + suffer from recursion depth issues. + + This function accepts a list of `nodes` and only the maximal cliques + containing all of these `nodes` are returned. It can considerably speed up + the running time if some specific cliques are desired. + + Parameters + ---------- + G : NetworkX graph + An undirected graph. + + nodes : list, optional (default=None) + If provided, only yield *maximal cliques* containing all nodes in `nodes`. + If `nodes` isn't a clique itself, a ValueError is raised. + + Returns + ------- + iterator + An iterator over maximal cliques, each of which is a list of + nodes in `G`. If `nodes` is provided, only the maximal cliques + containing all the nodes in `nodes` are returned. The order of + cliques is arbitrary. + + Raises + ------ + ValueError + If `nodes` is not a clique. + + Examples + -------- + >>> from pprint import pprint # For nice dict formatting + >>> G = nx.karate_club_graph() + >>> sum(1 for c in nx.find_cliques(G)) # The number of maximal cliques in G + 36 + >>> max(nx.find_cliques(G), key=len) # The largest maximal clique in G + [0, 1, 2, 3, 13] + + The size of the largest maximal clique is known as the *clique number* of + the graph, which can be found directly with: + + >>> max(len(c) for c in nx.find_cliques(G)) + 5 + + One can also compute the number of maximal cliques in `G` that contain a given + node. The following produces a dictionary keyed by node whose + values are the number of maximal cliques in `G` that contain the node: + + >>> pprint({n: sum(1 for c in nx.find_cliques(G) if n in c) for n in G}) + {0: 13, + 1: 6, + 2: 7, + 3: 3, + 4: 2, + 5: 3, + 6: 3, + 7: 1, + 8: 3, + 9: 2, + 10: 2, + 11: 1, + 12: 1, + 13: 2, + 14: 1, + 15: 1, + 16: 1, + 17: 1, + 18: 1, + 19: 2, + 20: 1, + 21: 1, + 22: 1, + 23: 3, + 24: 2, + 25: 2, + 26: 1, + 27: 3, + 28: 2, + 29: 2, + 30: 2, + 31: 4, + 32: 9, + 33: 14} + + Or, similarly, the maximal cliques in `G` that contain a given node. + For example, the 4 maximal cliques that contain node 31: + + >>> [c for c in nx.find_cliques(G) if 31 in c] + [[0, 31], [33, 32, 31], [33, 28, 31], [24, 25, 31]] + + See Also + -------- + find_cliques_recursive + A recursive version of the same algorithm. + + Notes + ----- + To obtain a list of all maximal cliques, use + `list(find_cliques(G))`. However, be aware that in the worst-case, + the length of this list can be exponential in the number of nodes in + the graph. This function avoids storing all cliques in memory by + only keeping current candidate node lists in memory during its search. + + This implementation is based on the algorithm published by Bron and + Kerbosch (1973) [1]_, as adapted by Tomita, Tanaka and Takahashi + (2006) [2]_ and discussed in Cazals and Karande (2008) [3]_. It + essentially unrolls the recursion used in the references to avoid + issues of recursion stack depth (for a recursive implementation, see + :func:`find_cliques_recursive`). + + This algorithm ignores self-loops and parallel edges, since cliques + are not conventionally defined with such edges. + + References + ---------- + .. [1] Bron, C. and Kerbosch, J. + "Algorithm 457: finding all cliques of an undirected graph". + *Communications of the ACM* 16, 9 (Sep. 1973), 575--577. + + + .. [2] Etsuji Tomita, Akira Tanaka, Haruhisa Takahashi, + "The worst-case time complexity for generating all maximal + cliques and computational experiments", + *Theoretical Computer Science*, Volume 363, Issue 1, + Computing and Combinatorics, + 10th Annual International Conference on + Computing and Combinatorics (COCOON 2004), 25 October 2006, Pages 28--42 + + + .. [3] F. Cazals, C. Karande, + "A note on the problem of reporting maximal cliques", + *Theoretical Computer Science*, + Volume 407, Issues 1--3, 6 November 2008, Pages 564--568, + + + """ + if len(G) == 0: + return + + adj = {u: {v for v in G[u] if v != u} for u in G} + + # Initialize Q with the given nodes and subg, cand with their nbrs + Q = nodes[:] if nodes is not None else [] + cand = set(G) + for node in Q: + if node not in cand: + raise ValueError(f"The given `nodes` {nodes} do not form a clique") + cand &= adj[node] + + if not cand: + yield Q[:] + return + + subg = cand.copy() + stack = [] + Q.append(None) + + u = max(subg, key=lambda u: len(cand & adj[u])) + ext_u = cand - adj[u] + + try: + while True: + if ext_u: + q = ext_u.pop() + cand.remove(q) + Q[-1] = q + adj_q = adj[q] + subg_q = subg & adj_q + if not subg_q: + yield Q[:] + else: + cand_q = cand & adj_q + if cand_q: + stack.append((subg, cand, ext_u)) + Q.append(None) + subg = subg_q + cand = cand_q + u = max(subg, key=lambda u: len(cand & adj[u])) + ext_u = cand - adj[u] + else: + Q.pop() + subg, cand, ext_u = stack.pop() + except IndexError: + pass + + +# TODO Should this also be not implemented for directed graphs? +@nx._dispatchable +def find_cliques_recursive(G, nodes=None): + """Returns all maximal cliques in a graph. + + For each node *v*, a *maximal clique for v* is a largest complete + subgraph containing *v*. The largest maximal clique is sometimes + called the *maximum clique*. + + This function returns an iterator over cliques, each of which is a + list of nodes. It is a recursive implementation, so may suffer from + recursion depth issues, but is included for pedagogical reasons. + For a non-recursive implementation, see :func:`find_cliques`. + + This function accepts a list of `nodes` and only the maximal cliques + containing all of these `nodes` are returned. It can considerably speed up + the running time if some specific cliques are desired. + + Parameters + ---------- + G : NetworkX graph + + nodes : list, optional (default=None) + If provided, only yield *maximal cliques* containing all nodes in `nodes`. + If `nodes` isn't a clique itself, a ValueError is raised. + + Returns + ------- + iterator + An iterator over maximal cliques, each of which is a list of + nodes in `G`. If `nodes` is provided, only the maximal cliques + containing all the nodes in `nodes` are yielded. The order of + cliques is arbitrary. + + Raises + ------ + ValueError + If `nodes` is not a clique. + + See Also + -------- + find_cliques + An iterative version of the same algorithm. See docstring for examples. + + Notes + ----- + To obtain a list of all maximal cliques, use + `list(find_cliques_recursive(G))`. However, be aware that in the + worst-case, the length of this list can be exponential in the number + of nodes in the graph. This function avoids storing all cliques in memory + by only keeping current candidate node lists in memory during its search. + + This implementation is based on the algorithm published by Bron and + Kerbosch (1973) [1]_, as adapted by Tomita, Tanaka and Takahashi + (2006) [2]_ and discussed in Cazals and Karande (2008) [3]_. For a + non-recursive implementation, see :func:`find_cliques`. + + This algorithm ignores self-loops and parallel edges, since cliques + are not conventionally defined with such edges. + + References + ---------- + .. [1] Bron, C. and Kerbosch, J. + "Algorithm 457: finding all cliques of an undirected graph". + *Communications of the ACM* 16, 9 (Sep. 1973), 575--577. + + + .. [2] Etsuji Tomita, Akira Tanaka, Haruhisa Takahashi, + "The worst-case time complexity for generating all maximal + cliques and computational experiments", + *Theoretical Computer Science*, Volume 363, Issue 1, + Computing and Combinatorics, + 10th Annual International Conference on + Computing and Combinatorics (COCOON 2004), 25 October 2006, Pages 28--42 + + + .. [3] F. Cazals, C. Karande, + "A note on the problem of reporting maximal cliques", + *Theoretical Computer Science*, + Volume 407, Issues 1--3, 6 November 2008, Pages 564--568, + + + """ + if len(G) == 0: + return iter([]) + + adj = {u: {v for v in G[u] if v != u} for u in G} + + # Initialize Q with the given nodes and subg, cand with their nbrs + Q = nodes[:] if nodes is not None else [] + cand_init = set(G) + for node in Q: + if node not in cand_init: + raise ValueError(f"The given `nodes` {nodes} do not form a clique") + cand_init &= adj[node] + + if not cand_init: + return iter([Q]) + + subg_init = cand_init.copy() + + def expand(subg, cand): + u = max(subg, key=lambda u: len(cand & adj[u])) + for q in cand - adj[u]: + cand.remove(q) + Q.append(q) + adj_q = adj[q] + subg_q = subg & adj_q + if not subg_q: + yield Q[:] + else: + cand_q = cand & adj_q + if cand_q: + yield from expand(subg_q, cand_q) + Q.pop() + + return expand(subg_init, cand_init) + + +@nx._dispatchable(returns_graph=True) +def make_max_clique_graph(G, create_using=None): + """Returns the maximal clique graph of the given graph. + + The nodes of the maximal clique graph of `G` are the cliques of + `G` and an edge joins two cliques if the cliques are not disjoint. + + Parameters + ---------- + G : NetworkX graph + + create_using : NetworkX graph constructor, optional (default=nx.Graph) + Graph type to create. If graph instance, then cleared before populated. + + Returns + ------- + NetworkX graph + A graph whose nodes are the cliques of `G` and whose edges + join two cliques if they are not disjoint. + + Notes + ----- + This function behaves like the following code:: + + import networkx as nx + + G = nx.make_clique_bipartite(G) + cliques = [v for v in G.nodes() if G.nodes[v]["bipartite"] == 0] + G = nx.bipartite.projected_graph(G, cliques) + G = nx.relabel_nodes(G, {-v: v - 1 for v in G}) + + It should be faster, though, since it skips all the intermediate + steps. + + """ + if create_using is None: + B = G.__class__() + else: + B = nx.empty_graph(0, create_using) + cliques = list(enumerate(set(c) for c in find_cliques(G))) + # Add a numbered node for each clique. + B.add_nodes_from(i for i, c in cliques) + # Join cliques by an edge if they share a node. + clique_pairs = combinations(cliques, 2) + B.add_edges_from((i, j) for (i, c1), (j, c2) in clique_pairs if c1 & c2) + return B + + +@nx._dispatchable(returns_graph=True) +def make_clique_bipartite(G, fpos=None, create_using=None, name=None): + """Returns the bipartite clique graph corresponding to `G`. + + In the returned bipartite graph, the "bottom" nodes are the nodes of + `G` and the "top" nodes represent the maximal cliques of `G`. + There is an edge from node *v* to clique *C* in the returned graph + if and only if *v* is an element of *C*. + + Parameters + ---------- + G : NetworkX graph + An undirected graph. + + fpos : bool + If True or not None, the returned graph will have an + additional attribute, `pos`, a dictionary mapping node to + position in the Euclidean plane. + + create_using : NetworkX graph constructor, optional (default=nx.Graph) + Graph type to create. If graph instance, then cleared before populated. + + Returns + ------- + NetworkX graph + A bipartite graph whose "bottom" set is the nodes of the graph + `G`, whose "top" set is the cliques of `G`, and whose edges + join nodes of `G` to the cliques that contain them. + + The nodes of the graph `G` have the node attribute + 'bipartite' set to 1 and the nodes representing cliques + have the node attribute 'bipartite' set to 0, as is the + convention for bipartite graphs in NetworkX. + + """ + B = nx.empty_graph(0, create_using) + B.clear() + # The "bottom" nodes in the bipartite graph are the nodes of the + # original graph, G. + B.add_nodes_from(G, bipartite=1) + for i, cl in enumerate(find_cliques(G)): + # The "top" nodes in the bipartite graph are the cliques. These + # nodes get negative numbers as labels. + name = -i - 1 + B.add_node(name, bipartite=0) + B.add_edges_from((v, name) for v in cl) + return B + + +@nx._dispatchable +def node_clique_number(G, nodes=None, cliques=None, separate_nodes=False): + """Returns the size of the largest maximal clique containing each given node. + + Returns a single or list depending on input nodes. + An optional list of cliques can be input if already computed. + + Parameters + ---------- + G : NetworkX graph + An undirected graph. + + cliques : list, optional (default=None) + A list of cliques, each of which is itself a list of nodes. + If not specified, the list of all cliques will be computed + using :func:`find_cliques`. + + Returns + ------- + int or dict + If `nodes` is a single node, returns the size of the + largest maximal clique in `G` containing that node. + Otherwise return a dict keyed by node to the size + of the largest maximal clique containing that node. + + See Also + -------- + find_cliques + find_cliques yields the maximal cliques of G. + It accepts a `nodes` argument which restricts consideration to + maximal cliques containing all the given `nodes`. + The search for the cliques is optimized for `nodes`. + """ + if cliques is None: + if nodes is not None: + # Use ego_graph to decrease size of graph + # check for single node + if nodes in G: + return max(len(c) for c in find_cliques(nx.ego_graph(G, nodes))) + # handle multiple nodes + return { + n: max(len(c) for c in find_cliques(nx.ego_graph(G, n))) for n in nodes + } + + # nodes is None--find all cliques + cliques = list(find_cliques(G)) + + # single node requested + if nodes in G: + return max(len(c) for c in cliques if nodes in c) + + # multiple nodes requested + # preprocess all nodes (faster than one at a time for even 2 nodes) + size_for_n = defaultdict(int) + for c in cliques: + size_of_c = len(c) + for n in c: + if size_for_n[n] < size_of_c: + size_for_n[n] = size_of_c + if nodes is None: + return size_for_n + return {n: size_for_n[n] for n in nodes} + + +def number_of_cliques(G, nodes=None, cliques=None): + """Returns the number of maximal cliques for each node. + + Returns a single or list depending on input nodes. + Optional list of cliques can be input if already computed. + """ + if cliques is None: + cliques = list(find_cliques(G)) + + if nodes is None: + nodes = list(G.nodes()) # none, get entire graph + + if not isinstance(nodes, list): # check for a list + v = nodes + # assume it is a single value + numcliq = len([1 for c in cliques if v in c]) + else: + numcliq = {} + for v in nodes: + numcliq[v] = len([1 for c in cliques if v in c]) + return numcliq + + +class MaxWeightClique: + """A class for the maximum weight clique algorithm. + + This class is a helper for the `max_weight_clique` function. The class + should not normally be used directly. + + Parameters + ---------- + G : NetworkX graph + The undirected graph for which a maximum weight clique is sought + weight : string or None, optional (default='weight') + The node attribute that holds the integer value used as a weight. + If None, then each node has weight 1. + + Attributes + ---------- + G : NetworkX graph + The undirected graph for which a maximum weight clique is sought + node_weights: dict + The weight of each node + incumbent_nodes : list + The nodes of the incumbent clique (the best clique found so far) + incumbent_weight: int + The weight of the incumbent clique + """ + + def __init__(self, G, weight): + self.G = G + self.incumbent_nodes = [] + self.incumbent_weight = 0 + + if weight is None: + self.node_weights = {v: 1 for v in G.nodes()} + else: + for v in G.nodes(): + if weight not in G.nodes[v]: + errmsg = f"Node {v!r} does not have the requested weight field." + raise KeyError(errmsg) + if not isinstance(G.nodes[v][weight], int): + errmsg = f"The {weight!r} field of node {v!r} is not an integer." + raise ValueError(errmsg) + self.node_weights = {v: G.nodes[v][weight] for v in G.nodes()} + + def update_incumbent_if_improved(self, C, C_weight): + """Update the incumbent if the node set C has greater weight. + + C is assumed to be a clique. + """ + if C_weight > self.incumbent_weight: + self.incumbent_nodes = C[:] + self.incumbent_weight = C_weight + + def greedily_find_independent_set(self, P): + """Greedily find an independent set of nodes from a set of + nodes P.""" + independent_set = [] + P = P[:] + while P: + v = P[0] + independent_set.append(v) + P = [w for w in P if v != w and not self.G.has_edge(v, w)] + return independent_set + + def find_branching_nodes(self, P, target): + """Find a set of nodes to branch on.""" + residual_wt = {v: self.node_weights[v] for v in P} + total_wt = 0 + P = P[:] + while P: + independent_set = self.greedily_find_independent_set(P) + min_wt_in_class = min(residual_wt[v] for v in independent_set) + total_wt += min_wt_in_class + if total_wt > target: + break + for v in independent_set: + residual_wt[v] -= min_wt_in_class + P = [v for v in P if residual_wt[v] != 0] + return P + + def expand(self, C, C_weight, P): + """Look for the best clique that contains all the nodes in C and zero or + more of the nodes in P, backtracking if it can be shown that no such + clique has greater weight than the incumbent. + """ + self.update_incumbent_if_improved(C, C_weight) + branching_nodes = self.find_branching_nodes(P, self.incumbent_weight - C_weight) + while branching_nodes: + v = branching_nodes.pop() + P.remove(v) + new_C = C + [v] + new_C_weight = C_weight + self.node_weights[v] + new_P = [w for w in P if self.G.has_edge(v, w)] + self.expand(new_C, new_C_weight, new_P) + + def find_max_weight_clique(self): + """Find a maximum weight clique.""" + # Sort nodes in reverse order of degree for speed + nodes = sorted(self.G.nodes(), key=lambda v: self.G.degree(v), reverse=True) + nodes = [v for v in nodes if self.node_weights[v] > 0] + self.expand([], 0, nodes) + + +@not_implemented_for("directed") +@nx._dispatchable(node_attrs="weight") +def max_weight_clique(G, weight="weight"): + """Find a maximum weight clique in G. + + A *clique* in a graph is a set of nodes such that every two distinct nodes + are adjacent. The *weight* of a clique is the sum of the weights of its + nodes. A *maximum weight clique* of graph G is a clique C in G such that + no clique in G has weight greater than the weight of C. + + Parameters + ---------- + G : NetworkX graph + Undirected graph + weight : string or None, optional (default='weight') + The node attribute that holds the integer value used as a weight. + If None, then each node has weight 1. + + Returns + ------- + clique : list + the nodes of a maximum weight clique + weight : int + the weight of a maximum weight clique + + Notes + ----- + The implementation is recursive, and therefore it may run into recursion + depth issues if G contains a clique whose number of nodes is close to the + recursion depth limit. + + At each search node, the algorithm greedily constructs a weighted + independent set cover of part of the graph in order to find a small set of + nodes on which to branch. The algorithm is very similar to the algorithm + of Tavares et al. [1]_, other than the fact that the NetworkX version does + not use bitsets. This style of algorithm for maximum weight clique (and + maximum weight independent set, which is the same problem but on the + complement graph) has a decades-long history. See Algorithm B of Warren + and Hicks [2]_ and the references in that paper. + + References + ---------- + .. [1] Tavares, W.A., Neto, M.B.C., Rodrigues, C.D., Michelon, P.: Um + algoritmo de branch and bound para o problema da clique máxima + ponderada. Proceedings of XLVII SBPO 1 (2015). + + .. [2] Warren, Jeffrey S, Hicks, Illya V.: Combinatorial Branch-and-Bound + for the Maximum Weight Independent Set Problem. Technical Report, + Texas A&M University (2016). + """ + + mwc = MaxWeightClique(G, weight) + mwc.find_max_weight_clique() + return mwc.incumbent_nodes, mwc.incumbent_weight diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/cycles.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/cycles.py new file mode 100644 index 0000000000000000000000000000000000000000..975462a73312ad456abbbfaf419295628d02910c --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/cycles.py @@ -0,0 +1,1230 @@ +""" +======================== +Cycle finding algorithms +======================== +""" + +from collections import Counter, defaultdict +from itertools import combinations, product +from math import inf + +import networkx as nx +from networkx.utils import not_implemented_for, pairwise + +__all__ = [ + "cycle_basis", + "simple_cycles", + "recursive_simple_cycles", + "find_cycle", + "minimum_cycle_basis", + "chordless_cycles", + "girth", +] + + +@not_implemented_for("directed") +@not_implemented_for("multigraph") +@nx._dispatchable +def cycle_basis(G, root=None): + """Returns a list of cycles which form a basis for cycles of G. + + A basis for cycles of a network is a minimal collection of + cycles such that any cycle in the network can be written + as a sum of cycles in the basis. Here summation of cycles + is defined as "exclusive or" of the edges. Cycle bases are + useful, e.g. when deriving equations for electric circuits + using Kirchhoff's Laws. + + Parameters + ---------- + G : NetworkX Graph + root : node, optional + Specify starting node for basis. + + Returns + ------- + A list of cycle lists. Each cycle list is a list of nodes + which forms a cycle (loop) in G. + + Examples + -------- + >>> G = nx.Graph() + >>> nx.add_cycle(G, [0, 1, 2, 3]) + >>> nx.add_cycle(G, [0, 3, 4, 5]) + >>> nx.cycle_basis(G, 0) + [[3, 4, 5, 0], [1, 2, 3, 0]] + + Notes + ----- + This is adapted from algorithm CACM 491 [1]_. + + References + ---------- + .. [1] Paton, K. An algorithm for finding a fundamental set of + cycles of a graph. Comm. ACM 12, 9 (Sept 1969), 514-518. + + See Also + -------- + simple_cycles + minimum_cycle_basis + """ + gnodes = dict.fromkeys(G) # set-like object that maintains node order + cycles = [] + while gnodes: # loop over connected components + if root is None: + root = gnodes.popitem()[0] + stack = [root] + pred = {root: root} + used = {root: set()} + while stack: # walk the spanning tree finding cycles + z = stack.pop() # use last-in so cycles easier to find + zused = used[z] + for nbr in G[z]: + if nbr not in used: # new node + pred[nbr] = z + stack.append(nbr) + used[nbr] = {z} + elif nbr == z: # self loops + cycles.append([z]) + elif nbr not in zused: # found a cycle + pn = used[nbr] + cycle = [nbr, z] + p = pred[z] + while p not in pn: + cycle.append(p) + p = pred[p] + cycle.append(p) + cycles.append(cycle) + used[nbr].add(z) + for node in pred: + gnodes.pop(node, None) + root = None + return cycles + + +@nx._dispatchable +def simple_cycles(G, length_bound=None): + """Find simple cycles (elementary circuits) of a graph. + + A "simple cycle", or "elementary circuit", is a closed path where + no node appears twice. In a directed graph, two simple cycles are distinct + if they are not cyclic permutations of each other. In an undirected graph, + two simple cycles are distinct if they are not cyclic permutations of each + other nor of the other's reversal. + + Optionally, the cycles are bounded in length. In the unbounded case, we use + a nonrecursive, iterator/generator version of Johnson's algorithm [1]_. In + the bounded case, we use a version of the algorithm of Gupta and + Suzumura [2]_. There may be better algorithms for some cases [3]_ [4]_ [5]_. + + The algorithms of Johnson, and Gupta and Suzumura, are enhanced by some + well-known preprocessing techniques. When `G` is directed, we restrict our + attention to strongly connected components of `G`, generate all simple cycles + containing a certain node, remove that node, and further decompose the + remainder into strongly connected components. When `G` is undirected, we + restrict our attention to biconnected components, generate all simple cycles + containing a particular edge, remove that edge, and further decompose the + remainder into biconnected components. + + Note that multigraphs are supported by this function -- and in undirected + multigraphs, a pair of parallel edges is considered a cycle of length 2. + Likewise, self-loops are considered to be cycles of length 1. We define + cycles as sequences of nodes; so the presence of loops and parallel edges + does not change the number of simple cycles in a graph. + + Parameters + ---------- + G : NetworkX Graph + A networkx graph. Undirected, directed, and multigraphs are all supported. + + length_bound : int or None, optional (default=None) + If `length_bound` is an int, generate all simple cycles of `G` with length at + most `length_bound`. Otherwise, generate all simple cycles of `G`. + + Yields + ------ + list of nodes + Each cycle is represented by a list of nodes along the cycle. + + Examples + -------- + >>> G = nx.DiGraph([(0, 0), (0, 1), (0, 2), (1, 2), (2, 0), (2, 1), (2, 2)]) + >>> sorted(nx.simple_cycles(G)) + [[0], [0, 1, 2], [0, 2], [1, 2], [2]] + + To filter the cycles so that they don't include certain nodes or edges, + copy your graph and eliminate those nodes or edges before calling. + For example, to exclude self-loops from the above example: + + >>> H = G.copy() + >>> H.remove_edges_from(nx.selfloop_edges(G)) + >>> sorted(nx.simple_cycles(H)) + [[0, 1, 2], [0, 2], [1, 2]] + + Notes + ----- + When `length_bound` is None, the time complexity is $O((n+e)(c+1))$ for $n$ + nodes, $e$ edges and $c$ simple circuits. Otherwise, when ``length_bound > 1``, + the time complexity is $O((c+n)(k-1)d^k)$ where $d$ is the average degree of + the nodes of `G` and $k$ = `length_bound`. + + Raises + ------ + ValueError + when ``length_bound < 0``. + + References + ---------- + .. [1] Finding all the elementary circuits of a directed graph. + D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975. + https://doi.org/10.1137/0204007 + .. [2] Finding All Bounded-Length Simple Cycles in a Directed Graph + A. Gupta and T. Suzumura https://arxiv.org/abs/2105.10094 + .. [3] Enumerating the cycles of a digraph: a new preprocessing strategy. + G. Loizou and P. Thanish, Information Sciences, v. 27, 163-182, 1982. + .. [4] A search strategy for the elementary cycles of a directed graph. + J.L. Szwarcfiter and P.E. Lauer, BIT NUMERICAL MATHEMATICS, + v. 16, no. 2, 192-204, 1976. + .. [5] Optimal Listing of Cycles and st-Paths in Undirected Graphs + R. Ferreira and R. Grossi and A. Marino and N. Pisanti and R. Rizzi and + G. Sacomoto https://arxiv.org/abs/1205.2766 + + See Also + -------- + cycle_basis + chordless_cycles + """ + + if length_bound is not None: + if length_bound == 0: + return + elif length_bound < 0: + raise ValueError("length bound must be non-negative") + + directed = G.is_directed() + yield from ([v] for v, Gv in G.adj.items() if v in Gv) + + if length_bound is not None and length_bound == 1: + return + + if G.is_multigraph() and not directed: + visited = set() + for u, Gu in G.adj.items(): + multiplicity = ((v, len(Guv)) for v, Guv in Gu.items() if v in visited) + yield from ([u, v] for v, m in multiplicity if m > 1) + visited.add(u) + + # explicitly filter out loops; implicitly filter out parallel edges + if directed: + G = nx.DiGraph((u, v) for u, Gu in G.adj.items() for v in Gu if v != u) + else: + G = nx.Graph((u, v) for u, Gu in G.adj.items() for v in Gu if v != u) + + # this case is not strictly necessary but improves performance + if length_bound is not None and length_bound == 2: + if directed: + visited = set() + for u, Gu in G.adj.items(): + yield from ( + [v, u] for v in visited.intersection(Gu) if G.has_edge(v, u) + ) + visited.add(u) + return + + if directed: + yield from _directed_cycle_search(G, length_bound) + else: + yield from _undirected_cycle_search(G, length_bound) + + +def _directed_cycle_search(G, length_bound): + """A dispatch function for `simple_cycles` for directed graphs. + + We generate all cycles of G through binary partition. + + 1. Pick a node v in G which belongs to at least one cycle + a. Generate all cycles of G which contain the node v. + b. Recursively generate all cycles of G \\ v. + + This is accomplished through the following: + + 1. Compute the strongly connected components SCC of G. + 2. Select and remove a biconnected component C from BCC. Select a + non-tree edge (u, v) of a depth-first search of G[C]. + 3. For each simple cycle P containing v in G[C], yield P. + 4. Add the biconnected components of G[C \\ v] to BCC. + + If the parameter length_bound is not None, then step 3 will be limited to + simple cycles of length at most length_bound. + + Parameters + ---------- + G : NetworkX DiGraph + A directed graph + + length_bound : int or None + If length_bound is an int, generate all simple cycles of G with length at most length_bound. + Otherwise, generate all simple cycles of G. + + Yields + ------ + list of nodes + Each cycle is represented by a list of nodes along the cycle. + """ + + scc = nx.strongly_connected_components + components = [c for c in scc(G) if len(c) >= 2] + while components: + c = components.pop() + Gc = G.subgraph(c) + v = next(iter(c)) + if length_bound is None: + yield from _johnson_cycle_search(Gc, [v]) + else: + yield from _bounded_cycle_search(Gc, [v], length_bound) + # delete v after searching G, to make sure we can find v + G.remove_node(v) + components.extend(c for c in scc(Gc) if len(c) >= 2) + + +def _undirected_cycle_search(G, length_bound): + """A dispatch function for `simple_cycles` for undirected graphs. + + We generate all cycles of G through binary partition. + + 1. Pick an edge (u, v) in G which belongs to at least one cycle + a. Generate all cycles of G which contain the edge (u, v) + b. Recursively generate all cycles of G \\ (u, v) + + This is accomplished through the following: + + 1. Compute the biconnected components BCC of G. + 2. Select and remove a biconnected component C from BCC. Select a + non-tree edge (u, v) of a depth-first search of G[C]. + 3. For each (v -> u) path P remaining in G[C] \\ (u, v), yield P. + 4. Add the biconnected components of G[C] \\ (u, v) to BCC. + + If the parameter length_bound is not None, then step 3 will be limited to simple paths + of length at most length_bound. + + Parameters + ---------- + G : NetworkX Graph + An undirected graph + + length_bound : int or None + If length_bound is an int, generate all simple cycles of G with length at most length_bound. + Otherwise, generate all simple cycles of G. + + Yields + ------ + list of nodes + Each cycle is represented by a list of nodes along the cycle. + """ + + bcc = nx.biconnected_components + components = [c for c in bcc(G) if len(c) >= 3] + while components: + c = components.pop() + Gc = G.subgraph(c) + uv = list(next(iter(Gc.edges))) + G.remove_edge(*uv) + # delete (u, v) before searching G, to avoid fake 3-cycles [u, v, u] + if length_bound is None: + yield from _johnson_cycle_search(Gc, uv) + else: + yield from _bounded_cycle_search(Gc, uv, length_bound) + components.extend(c for c in bcc(Gc) if len(c) >= 3) + + +class _NeighborhoodCache(dict): + """Very lightweight graph wrapper which caches neighborhoods as list. + + This dict subclass uses the __missing__ functionality to query graphs for + their neighborhoods, and store the result as a list. This is used to avoid + the performance penalty incurred by subgraph views. + """ + + def __init__(self, G): + self.G = G + + def __missing__(self, v): + Gv = self[v] = list(self.G[v]) + return Gv + + +def _johnson_cycle_search(G, path): + """The main loop of the cycle-enumeration algorithm of Johnson. + + Parameters + ---------- + G : NetworkX Graph or DiGraph + A graph + + path : list + A cycle prefix. All cycles generated will begin with this prefix. + + Yields + ------ + list of nodes + Each cycle is represented by a list of nodes along the cycle. + + References + ---------- + .. [1] Finding all the elementary circuits of a directed graph. + D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975. + https://doi.org/10.1137/0204007 + + """ + + G = _NeighborhoodCache(G) + blocked = set(path) + B = defaultdict(set) # graph portions that yield no elementary circuit + start = path[0] + stack = [iter(G[path[-1]])] + closed = [False] + while stack: + nbrs = stack[-1] + for w in nbrs: + if w == start: + yield path[:] + closed[-1] = True + elif w not in blocked: + path.append(w) + closed.append(False) + stack.append(iter(G[w])) + blocked.add(w) + break + else: # no more nbrs + stack.pop() + v = path.pop() + if closed.pop(): + if closed: + closed[-1] = True + unblock_stack = {v} + while unblock_stack: + u = unblock_stack.pop() + if u in blocked: + blocked.remove(u) + unblock_stack.update(B[u]) + B[u].clear() + else: + for w in G[v]: + B[w].add(v) + + +def _bounded_cycle_search(G, path, length_bound): + """The main loop of the cycle-enumeration algorithm of Gupta and Suzumura. + + Parameters + ---------- + G : NetworkX Graph or DiGraph + A graph + + path : list + A cycle prefix. All cycles generated will begin with this prefix. + + length_bound: int + A length bound. All cycles generated will have length at most length_bound. + + Yields + ------ + list of nodes + Each cycle is represented by a list of nodes along the cycle. + + References + ---------- + .. [1] Finding All Bounded-Length Simple Cycles in a Directed Graph + A. Gupta and T. Suzumura https://arxiv.org/abs/2105.10094 + + """ + G = _NeighborhoodCache(G) + lock = {v: 0 for v in path} + B = defaultdict(set) + start = path[0] + stack = [iter(G[path[-1]])] + blen = [length_bound] + while stack: + nbrs = stack[-1] + for w in nbrs: + if w == start: + yield path[:] + blen[-1] = 1 + elif len(path) < lock.get(w, length_bound): + path.append(w) + blen.append(length_bound) + lock[w] = len(path) + stack.append(iter(G[w])) + break + else: + stack.pop() + v = path.pop() + bl = blen.pop() + if blen: + blen[-1] = min(blen[-1], bl) + if bl < length_bound: + relax_stack = [(bl, v)] + while relax_stack: + bl, u = relax_stack.pop() + if lock.get(u, length_bound) < length_bound - bl + 1: + lock[u] = length_bound - bl + 1 + relax_stack.extend((bl + 1, w) for w in B[u].difference(path)) + else: + for w in G[v]: + B[w].add(v) + + +@nx._dispatchable +def chordless_cycles(G, length_bound=None): + """Find simple chordless cycles of a graph. + + A `simple cycle` is a closed path where no node appears twice. In a simple + cycle, a `chord` is an additional edge between two nodes in the cycle. A + `chordless cycle` is a simple cycle without chords. Said differently, a + chordless cycle is a cycle C in a graph G where the number of edges in the + induced graph G[C] is equal to the length of `C`. + + Note that some care must be taken in the case that G is not a simple graph + nor a simple digraph. Some authors limit the definition of chordless cycles + to have a prescribed minimum length; we do not. + + 1. We interpret self-loops to be chordless cycles, except in multigraphs + with multiple loops in parallel. Likewise, in a chordless cycle of + length greater than 1, there can be no nodes with self-loops. + + 2. We interpret directed two-cycles to be chordless cycles, except in + multi-digraphs when any edge in a two-cycle has a parallel copy. + + 3. We interpret parallel pairs of undirected edges as two-cycles, except + when a third (or more) parallel edge exists between the two nodes. + + 4. Generalizing the above, edges with parallel clones may not occur in + chordless cycles. + + In a directed graph, two chordless cycles are distinct if they are not + cyclic permutations of each other. In an undirected graph, two chordless + cycles are distinct if they are not cyclic permutations of each other nor of + the other's reversal. + + Optionally, the cycles are bounded in length. + + We use an algorithm strongly inspired by that of Dias et al [1]_. It has + been modified in the following ways: + + 1. Recursion is avoided, per Python's limitations + + 2. The labeling function is not necessary, because the starting paths + are chosen (and deleted from the host graph) to prevent multiple + occurrences of the same path + + 3. The search is optionally bounded at a specified length + + 4. Support for directed graphs is provided by extending cycles along + forward edges, and blocking nodes along forward and reverse edges + + 5. Support for multigraphs is provided by omitting digons from the set + of forward edges + + Parameters + ---------- + G : NetworkX DiGraph + A directed graph + + length_bound : int or None, optional (default=None) + If length_bound is an int, generate all simple cycles of G with length at + most length_bound. Otherwise, generate all simple cycles of G. + + Yields + ------ + list of nodes + Each cycle is represented by a list of nodes along the cycle. + + Examples + -------- + >>> sorted(list(nx.chordless_cycles(nx.complete_graph(4)))) + [[1, 0, 2], [1, 0, 3], [2, 0, 3], [2, 1, 3]] + + Notes + ----- + When length_bound is None, and the graph is simple, the time complexity is + $O((n+e)(c+1))$ for $n$ nodes, $e$ edges and $c$ chordless cycles. + + Raises + ------ + ValueError + when length_bound < 0. + + References + ---------- + .. [1] Efficient enumeration of chordless cycles + E. Dias and D. Castonguay and H. Longo and W.A.R. Jradi + https://arxiv.org/abs/1309.1051 + + See Also + -------- + simple_cycles + """ + + if length_bound is not None: + if length_bound == 0: + return + elif length_bound < 0: + raise ValueError("length bound must be non-negative") + + directed = G.is_directed() + multigraph = G.is_multigraph() + + if multigraph: + yield from ([v] for v, Gv in G.adj.items() if len(Gv.get(v, ())) == 1) + else: + yield from ([v] for v, Gv in G.adj.items() if v in Gv) + + if length_bound is not None and length_bound == 1: + return + + # Nodes with loops cannot belong to longer cycles. Let's delete them here. + # also, we implicitly reduce the multiplicity of edges down to 1 in the case + # of multiedges. + if directed: + F = nx.DiGraph((u, v) for u, Gu in G.adj.items() if u not in Gu for v in Gu) + B = F.to_undirected(as_view=False) + else: + F = nx.Graph((u, v) for u, Gu in G.adj.items() if u not in Gu for v in Gu) + B = None + + # If we're given a multigraph, we have a few cases to consider with parallel + # edges. + # + # 1. If we have 2 or more edges in parallel between the nodes (u, v), we + # must not construct longer cycles along (u, v). + # 2. If G is not directed, then a pair of parallel edges between (u, v) is a + # chordless cycle unless there exists a third (or more) parallel edge. + # 3. If G is directed, then parallel edges do not form cycles, but do + # preclude back-edges from forming cycles (handled in the next section), + # Thus, if an edge (u, v) is duplicated and the reverse (v, u) is also + # present, then we remove both from F. + # + # In directed graphs, we need to consider both directions that edges can + # take, so iterate over all edges (u, v) and possibly (v, u). In undirected + # graphs, we need to be a little careful to only consider every edge once, + # so we use a "visited" set to emulate node-order comparisons. + + if multigraph: + if not directed: + B = F.copy() + visited = set() + for u, Gu in G.adj.items(): + if directed: + multiplicity = ((v, len(Guv)) for v, Guv in Gu.items()) + for v, m in multiplicity: + if m > 1: + F.remove_edges_from(((u, v), (v, u))) + else: + multiplicity = ((v, len(Guv)) for v, Guv in Gu.items() if v in visited) + for v, m in multiplicity: + if m == 2: + yield [u, v] + if m > 1: + F.remove_edge(u, v) + visited.add(u) + + # If we're given a directed graphs, we need to think about digons. If we + # have two edges (u, v) and (v, u), then that's a two-cycle. If either edge + # was duplicated above, then we removed both from F. So, any digons we find + # here are chordless. After finding digons, we remove their edges from F + # to avoid traversing them in the search for chordless cycles. + if directed: + for u, Fu in F.adj.items(): + digons = [[u, v] for v in Fu if F.has_edge(v, u)] + yield from digons + F.remove_edges_from(digons) + F.remove_edges_from(e[::-1] for e in digons) + + if length_bound is not None and length_bound == 2: + return + + # Now, we prepare to search for cycles. We have removed all cycles of + # lengths 1 and 2, so F is a simple graph or simple digraph. We repeatedly + # separate digraphs into their strongly connected components, and undirected + # graphs into their biconnected components. For each component, we pick a + # node v, search for chordless cycles based at each "stem" (u, v, w), and + # then remove v from that component before separating the graph again. + if directed: + separate = nx.strongly_connected_components + + # Directed stems look like (u -> v -> w), so we use the product of + # predecessors of v with successors of v. + def stems(C, v): + for u, w in product(C.pred[v], C.succ[v]): + if not G.has_edge(u, w): # omit stems with acyclic chords + yield [u, v, w], F.has_edge(w, u) + + else: + separate = nx.biconnected_components + + # Undirected stems look like (u ~ v ~ w), but we must not also search + # (w ~ v ~ u), so we use combinations of v's neighbors of length 2. + def stems(C, v): + yield from (([u, v, w], F.has_edge(w, u)) for u, w in combinations(C[v], 2)) + + components = [c for c in separate(F) if len(c) > 2] + while components: + c = components.pop() + v = next(iter(c)) + Fc = F.subgraph(c) + Fcc = Bcc = None + for S, is_triangle in stems(Fc, v): + if is_triangle: + yield S + else: + if Fcc is None: + Fcc = _NeighborhoodCache(Fc) + Bcc = Fcc if B is None else _NeighborhoodCache(B.subgraph(c)) + yield from _chordless_cycle_search(Fcc, Bcc, S, length_bound) + + components.extend(c for c in separate(F.subgraph(c - {v})) if len(c) > 2) + + +def _chordless_cycle_search(F, B, path, length_bound): + """The main loop for chordless cycle enumeration. + + This algorithm is strongly inspired by that of Dias et al [1]_. It has been + modified in the following ways: + + 1. Recursion is avoided, per Python's limitations + + 2. The labeling function is not necessary, because the starting paths + are chosen (and deleted from the host graph) to prevent multiple + occurrences of the same path + + 3. The search is optionally bounded at a specified length + + 4. Support for directed graphs is provided by extending cycles along + forward edges, and blocking nodes along forward and reverse edges + + 5. Support for multigraphs is provided by omitting digons from the set + of forward edges + + Parameters + ---------- + F : _NeighborhoodCache + A graph of forward edges to follow in constructing cycles + + B : _NeighborhoodCache + A graph of blocking edges to prevent the production of chordless cycles + + path : list + A cycle prefix. All cycles generated will begin with this prefix. + + length_bound : int + A length bound. All cycles generated will have length at most length_bound. + + + Yields + ------ + list of nodes + Each cycle is represented by a list of nodes along the cycle. + + References + ---------- + .. [1] Efficient enumeration of chordless cycles + E. Dias and D. Castonguay and H. Longo and W.A.R. Jradi + https://arxiv.org/abs/1309.1051 + + """ + blocked = defaultdict(int) + target = path[0] + blocked[path[1]] = 1 + for w in path[1:]: + for v in B[w]: + blocked[v] += 1 + + stack = [iter(F[path[2]])] + while stack: + nbrs = stack[-1] + for w in nbrs: + if blocked[w] == 1 and (length_bound is None or len(path) < length_bound): + Fw = F[w] + if target in Fw: + yield path + [w] + else: + Bw = B[w] + if target in Bw: + continue + for v in Bw: + blocked[v] += 1 + path.append(w) + stack.append(iter(Fw)) + break + else: + stack.pop() + for v in B[path.pop()]: + blocked[v] -= 1 + + +@not_implemented_for("undirected") +@nx._dispatchable(mutates_input=True) +def recursive_simple_cycles(G): + """Find simple cycles (elementary circuits) of a directed graph. + + A `simple cycle`, or `elementary circuit`, is a closed path where + no node appears twice. Two elementary circuits are distinct if they + are not cyclic permutations of each other. + + This version uses a recursive algorithm to build a list of cycles. + You should probably use the iterator version called simple_cycles(). + Warning: This recursive version uses lots of RAM! + It appears in NetworkX for pedagogical value. + + Parameters + ---------- + G : NetworkX DiGraph + A directed graph + + Returns + ------- + A list of cycles, where each cycle is represented by a list of nodes + along the cycle. + + Example: + + >>> edges = [(0, 0), (0, 1), (0, 2), (1, 2), (2, 0), (2, 1), (2, 2)] + >>> G = nx.DiGraph(edges) + >>> nx.recursive_simple_cycles(G) + [[0], [2], [0, 1, 2], [0, 2], [1, 2]] + + Notes + ----- + The implementation follows pp. 79-80 in [1]_. + + The time complexity is $O((n+e)(c+1))$ for $n$ nodes, $e$ edges and $c$ + elementary circuits. + + References + ---------- + .. [1] Finding all the elementary circuits of a directed graph. + D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975. + https://doi.org/10.1137/0204007 + + See Also + -------- + simple_cycles, cycle_basis + """ + + # Jon Olav Vik, 2010-08-09 + def _unblock(thisnode): + """Recursively unblock and remove nodes from B[thisnode].""" + if blocked[thisnode]: + blocked[thisnode] = False + while B[thisnode]: + _unblock(B[thisnode].pop()) + + def circuit(thisnode, startnode, component): + closed = False # set to True if elementary path is closed + path.append(thisnode) + blocked[thisnode] = True + for nextnode in component[thisnode]: # direct successors of thisnode + if nextnode == startnode: + result.append(path[:]) + closed = True + elif not blocked[nextnode]: + if circuit(nextnode, startnode, component): + closed = True + if closed: + _unblock(thisnode) + else: + for nextnode in component[thisnode]: + if thisnode not in B[nextnode]: # TODO: use set for speedup? + B[nextnode].append(thisnode) + path.pop() # remove thisnode from path + return closed + + path = [] # stack of nodes in current path + blocked = defaultdict(bool) # vertex: blocked from search? + B = defaultdict(list) # graph portions that yield no elementary circuit + result = [] # list to accumulate the circuits found + + # Johnson's algorithm exclude self cycle edges like (v, v) + # To be backward compatible, we record those cycles in advance + # and then remove from subG + for v in G: + if G.has_edge(v, v): + result.append([v]) + G.remove_edge(v, v) + + # Johnson's algorithm requires some ordering of the nodes. + # They might not be sortable so we assign an arbitrary ordering. + ordering = dict(zip(G, range(len(G)))) + for s in ordering: + # Build the subgraph induced by s and following nodes in the ordering + subgraph = G.subgraph(node for node in G if ordering[node] >= ordering[s]) + # Find the strongly connected component in the subgraph + # that contains the least node according to the ordering + strongcomp = nx.strongly_connected_components(subgraph) + mincomp = min(strongcomp, key=lambda ns: min(ordering[n] for n in ns)) + component = G.subgraph(mincomp) + if len(component) > 1: + # smallest node in the component according to the ordering + startnode = min(component, key=ordering.__getitem__) + for node in component: + blocked[node] = False + B[node][:] = [] + dummy = circuit(startnode, startnode, component) + return result + + +@nx._dispatchable +def find_cycle(G, source=None, orientation=None): + """Returns a cycle found via depth-first traversal. + + The cycle is a list of edges indicating the cyclic path. + Orientation of directed edges is controlled by `orientation`. + + Parameters + ---------- + G : graph + A directed/undirected graph/multigraph. + + source : node, list of nodes + The node from which the traversal begins. If None, then a source + is chosen arbitrarily and repeatedly until all edges from each node in + the graph are searched. + + orientation : None | 'original' | 'reverse' | 'ignore' (default: None) + For directed graphs and directed multigraphs, edge traversals need not + respect the original orientation of the edges. + When set to 'reverse' every edge is traversed in the reverse direction. + When set to 'ignore', every edge is treated as undirected. + When set to 'original', every edge is treated as directed. + In all three cases, the yielded edge tuples add a last entry to + indicate the direction in which that edge was traversed. + If orientation is None, the yielded edge has no direction indicated. + The direction is respected, but not reported. + + Returns + ------- + edges : directed edges + A list of directed edges indicating the path taken for the loop. + If no cycle is found, then an exception is raised. + For graphs, an edge is of the form `(u, v)` where `u` and `v` + are the tail and head of the edge as determined by the traversal. + For multigraphs, an edge is of the form `(u, v, key)`, where `key` is + the key of the edge. When the graph is directed, then `u` and `v` + are always in the order of the actual directed edge. + If orientation is not None then the edge tuple is extended to include + the direction of traversal ('forward' or 'reverse') on that edge. + + Raises + ------ + NetworkXNoCycle + If no cycle was found. + + Examples + -------- + In this example, we construct a DAG and find, in the first call, that there + are no directed cycles, and so an exception is raised. In the second call, + we ignore edge orientations and find that there is an undirected cycle. + Note that the second call finds a directed cycle while effectively + traversing an undirected graph, and so, we found an "undirected cycle". + This means that this DAG structure does not form a directed tree (which + is also known as a polytree). + + >>> G = nx.DiGraph([(0, 1), (0, 2), (1, 2)]) + >>> nx.find_cycle(G, orientation="original") + Traceback (most recent call last): + ... + networkx.exception.NetworkXNoCycle: No cycle found. + >>> list(nx.find_cycle(G, orientation="ignore")) + [(0, 1, 'forward'), (1, 2, 'forward'), (0, 2, 'reverse')] + + See Also + -------- + simple_cycles + """ + if not G.is_directed() or orientation in (None, "original"): + + def tailhead(edge): + return edge[:2] + + elif orientation == "reverse": + + def tailhead(edge): + return edge[1], edge[0] + + elif orientation == "ignore": + + def tailhead(edge): + if edge[-1] == "reverse": + return edge[1], edge[0] + return edge[:2] + + explored = set() + cycle = [] + final_node = None + for start_node in G.nbunch_iter(source): + if start_node in explored: + # No loop is possible. + continue + + edges = [] + # All nodes seen in this iteration of edge_dfs + seen = {start_node} + # Nodes in active path. + active_nodes = {start_node} + previous_head = None + + for edge in nx.edge_dfs(G, start_node, orientation): + # Determine if this edge is a continuation of the active path. + tail, head = tailhead(edge) + if head in explored: + # Then we've already explored it. No loop is possible. + continue + if previous_head is not None and tail != previous_head: + # This edge results from backtracking. + # Pop until we get a node whose head equals the current tail. + # So for example, we might have: + # (0, 1), (1, 2), (2, 3), (1, 4) + # which must become: + # (0, 1), (1, 4) + while True: + try: + popped_edge = edges.pop() + except IndexError: + edges = [] + active_nodes = {tail} + break + else: + popped_head = tailhead(popped_edge)[1] + active_nodes.remove(popped_head) + + if edges: + last_head = tailhead(edges[-1])[1] + if tail == last_head: + break + edges.append(edge) + + if head in active_nodes: + # We have a loop! + cycle.extend(edges) + final_node = head + break + else: + seen.add(head) + active_nodes.add(head) + previous_head = head + + if cycle: + break + else: + explored.update(seen) + + else: + assert len(cycle) == 0 + raise nx.exception.NetworkXNoCycle("No cycle found.") + + # We now have a list of edges which ends on a cycle. + # So we need to remove from the beginning edges that are not relevant. + + for i, edge in enumerate(cycle): + tail, head = tailhead(edge) + if tail == final_node: + break + + return cycle[i:] + + +@not_implemented_for("directed") +@not_implemented_for("multigraph") +@nx._dispatchable(edge_attrs="weight") +def minimum_cycle_basis(G, weight=None): + """Returns a minimum weight cycle basis for G + + Minimum weight means a cycle basis for which the total weight + (length for unweighted graphs) of all the cycles is minimum. + + Parameters + ---------- + G : NetworkX Graph + weight: string + name of the edge attribute to use for edge weights + + Returns + ------- + A list of cycle lists. Each cycle list is a list of nodes + which forms a cycle (loop) in G. Note that the nodes are not + necessarily returned in a order by which they appear in the cycle + + Examples + -------- + >>> G = nx.Graph() + >>> nx.add_cycle(G, [0, 1, 2, 3]) + >>> nx.add_cycle(G, [0, 3, 4, 5]) + >>> nx.minimum_cycle_basis(G) + [[5, 4, 3, 0], [3, 2, 1, 0]] + + References: + [1] Kavitha, Telikepalli, et al. "An O(m^2n) Algorithm for + Minimum Cycle Basis of Graphs." + http://link.springer.com/article/10.1007/s00453-007-9064-z + [2] de Pina, J. 1995. Applications of shortest path methods. + Ph.D. thesis, University of Amsterdam, Netherlands + + See Also + -------- + simple_cycles, cycle_basis + """ + # We first split the graph in connected subgraphs + return sum( + (_min_cycle_basis(G.subgraph(c), weight) for c in nx.connected_components(G)), + [], + ) + + +def _min_cycle_basis(G, weight): + cb = [] + # We extract the edges not in a spanning tree. We do not really need a + # *minimum* spanning tree. That is why we call the next function with + # weight=None. Depending on implementation, it may be faster as well + tree_edges = list(nx.minimum_spanning_edges(G, weight=None, data=False)) + chords = G.edges - tree_edges - {(v, u) for u, v in tree_edges} + + # We maintain a set of vectors orthogonal to sofar found cycles + set_orth = [{edge} for edge in chords] + while set_orth: + base = set_orth.pop() + # kth cycle is "parallel" to kth vector in set_orth + cycle_edges = _min_cycle(G, base, weight) + cb.append([v for u, v in cycle_edges]) + + # now update set_orth so that k+1,k+2... th elements are + # orthogonal to the newly found cycle, as per [p. 336, 1] + set_orth = [ + ( + {e for e in orth if e not in base if e[::-1] not in base} + | {e for e in base if e not in orth if e[::-1] not in orth} + ) + if sum((e in orth or e[::-1] in orth) for e in cycle_edges) % 2 + else orth + for orth in set_orth + ] + return cb + + +def _min_cycle(G, orth, weight): + """ + Computes the minimum weight cycle in G, + orthogonal to the vector orth as per [p. 338, 1] + Use (u, 1) to indicate the lifted copy of u (denoted u' in paper). + """ + Gi = nx.Graph() + + # Add 2 copies of each edge in G to Gi. + # If edge is in orth, add cross edge; otherwise in-plane edge + for u, v, wt in G.edges(data=weight, default=1): + if (u, v) in orth or (v, u) in orth: + Gi.add_edges_from([(u, (v, 1)), ((u, 1), v)], Gi_weight=wt) + else: + Gi.add_edges_from([(u, v), ((u, 1), (v, 1))], Gi_weight=wt) + + # find the shortest length in Gi between n and (n, 1) for each n + # Note: Use "Gi_weight" for name of weight attribute + spl = nx.shortest_path_length + lift = {n: spl(Gi, source=n, target=(n, 1), weight="Gi_weight") for n in G} + + # Now compute that short path in Gi, which translates to a cycle in G + start = min(lift, key=lift.get) + end = (start, 1) + min_path_i = nx.shortest_path(Gi, source=start, target=end, weight="Gi_weight") + + # Now we obtain the actual path, re-map nodes in Gi to those in G + min_path = [n if n in G else n[0] for n in min_path_i] + + # Now remove the edges that occur two times + # two passes: flag which edges get kept, then build it + edgelist = list(pairwise(min_path)) + edgeset = set() + for e in edgelist: + if e in edgeset: + edgeset.remove(e) + elif e[::-1] in edgeset: + edgeset.remove(e[::-1]) + else: + edgeset.add(e) + + min_edgelist = [] + for e in edgelist: + if e in edgeset: + min_edgelist.append(e) + edgeset.remove(e) + elif e[::-1] in edgeset: + min_edgelist.append(e[::-1]) + edgeset.remove(e[::-1]) + + return min_edgelist + + +@not_implemented_for("directed") +@not_implemented_for("multigraph") +@nx._dispatchable +def girth(G): + """Returns the girth of the graph. + + The girth of a graph is the length of its shortest cycle, or infinity if + the graph is acyclic. The algorithm follows the description given on the + Wikipedia page [1]_, and runs in time O(mn) on a graph with m edges and n + nodes. + + Parameters + ---------- + G : NetworkX Graph + + Returns + ------- + int or math.inf + + Examples + -------- + All examples below (except P_5) can easily be checked using Wikipedia, + which has a page for each of these famous graphs. + + >>> nx.girth(nx.chvatal_graph()) + 4 + >>> nx.girth(nx.tutte_graph()) + 4 + >>> nx.girth(nx.petersen_graph()) + 5 + >>> nx.girth(nx.heawood_graph()) + 6 + >>> nx.girth(nx.pappus_graph()) + 6 + >>> nx.girth(nx.path_graph(5)) + inf + + References + ---------- + .. [1] `Wikipedia: Girth `_ + + """ + girth = depth_limit = inf + tree_edge = nx.algorithms.traversal.breadth_first_search.TREE_EDGE + level_edge = nx.algorithms.traversal.breadth_first_search.LEVEL_EDGE + for n in G: + # run a BFS from source n, keeping track of distances; since we want + # the shortest cycle, no need to explore beyond the current minimum length + depth = {n: 0} + for u, v, label in nx.bfs_labeled_edges(G, n): + du = depth[u] + if du > depth_limit: + break + if label is tree_edge: + depth[v] = du + 1 + else: + # if (u, v) is a level edge, the length is du + du + 1 (odd) + # otherwise, it's a forward edge; length is du + (du + 1) + 1 (even) + delta = label is level_edge + length = du + du + 2 - delta + if length < girth: + girth = length + depth_limit = du - delta + + return girth diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/distance_regular.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/distance_regular.py new file mode 100644 index 0000000000000000000000000000000000000000..27b4d0216e427a03f6cc0b90d15f4debb2d52b56 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/distance_regular.py @@ -0,0 +1,238 @@ +""" +======================= +Distance-regular graphs +======================= +""" + +import networkx as nx +from networkx.utils import not_implemented_for + +from .distance_measures import diameter + +__all__ = [ + "is_distance_regular", + "is_strongly_regular", + "intersection_array", + "global_parameters", +] + + +@nx._dispatchable +def is_distance_regular(G): + """Returns True if the graph is distance regular, False otherwise. + + A connected graph G is distance-regular if for any nodes x,y + and any integers i,j=0,1,...,d (where d is the graph + diameter), the number of vertices at distance i from x and + distance j from y depends only on i,j and the graph distance + between x and y, independently of the choice of x and y. + + Parameters + ---------- + G: Networkx graph (undirected) + + Returns + ------- + bool + True if the graph is Distance Regular, False otherwise + + Examples + -------- + >>> G = nx.hypercube_graph(6) + >>> nx.is_distance_regular(G) + True + + See Also + -------- + intersection_array, global_parameters + + Notes + ----- + For undirected and simple graphs only + + References + ---------- + .. [1] Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. + Distance-Regular Graphs. New York: Springer-Verlag, 1989. + .. [2] Weisstein, Eric W. "Distance-Regular Graph." + http://mathworld.wolfram.com/Distance-RegularGraph.html + + """ + try: + intersection_array(G) + return True + except nx.NetworkXError: + return False + + +def global_parameters(b, c): + """Returns global parameters for a given intersection array. + + Given a distance-regular graph G with integers b_i, c_i,i = 0,....,d + such that for any 2 vertices x,y in G at a distance i=d(x,y), there + are exactly c_i neighbors of y at a distance of i-1 from x and b_i + neighbors of y at a distance of i+1 from x. + + Thus, a distance regular graph has the global parameters, + [[c_0,a_0,b_0],[c_1,a_1,b_1],......,[c_d,a_d,b_d]] for the + intersection array [b_0,b_1,.....b_{d-1};c_1,c_2,.....c_d] + where a_i+b_i+c_i=k , k= degree of every vertex. + + Parameters + ---------- + b : list + + c : list + + Returns + ------- + iterable + An iterable over three tuples. + + Examples + -------- + >>> G = nx.dodecahedral_graph() + >>> b, c = nx.intersection_array(G) + >>> list(nx.global_parameters(b, c)) + [(0, 0, 3), (1, 0, 2), (1, 1, 1), (1, 1, 1), (2, 0, 1), (3, 0, 0)] + + References + ---------- + .. [1] Weisstein, Eric W. "Global Parameters." + From MathWorld--A Wolfram Web Resource. + http://mathworld.wolfram.com/GlobalParameters.html + + See Also + -------- + intersection_array + """ + return ((y, b[0] - x - y, x) for x, y in zip(b + [0], [0] + c)) + + +@not_implemented_for("directed") +@not_implemented_for("multigraph") +@nx._dispatchable +def intersection_array(G): + """Returns the intersection array of a distance-regular graph. + + Given a distance-regular graph G with integers b_i, c_i,i = 0,....,d + such that for any 2 vertices x,y in G at a distance i=d(x,y), there + are exactly c_i neighbors of y at a distance of i-1 from x and b_i + neighbors of y at a distance of i+1 from x. + + A distance regular graph's intersection array is given by, + [b_0,b_1,.....b_{d-1};c_1,c_2,.....c_d] + + Parameters + ---------- + G: Networkx graph (undirected) + + Returns + ------- + b,c: tuple of lists + + Examples + -------- + >>> G = nx.icosahedral_graph() + >>> nx.intersection_array(G) + ([5, 2, 1], [1, 2, 5]) + + References + ---------- + .. [1] Weisstein, Eric W. "Intersection Array." + From MathWorld--A Wolfram Web Resource. + http://mathworld.wolfram.com/IntersectionArray.html + + See Also + -------- + global_parameters + """ + # test for regular graph (all degrees must be equal) + if len(G) == 0: + raise nx.NetworkXPointlessConcept("Graph has no nodes.") + degree = iter(G.degree()) + (_, k) = next(degree) + for _, knext in degree: + if knext != k: + raise nx.NetworkXError("Graph is not distance regular.") + k = knext + path_length = dict(nx.all_pairs_shortest_path_length(G)) + diameter = max(max(path_length[n].values()) for n in path_length) + bint = {} # 'b' intersection array + cint = {} # 'c' intersection array + for u in G: + for v in G: + try: + i = path_length[u][v] + except KeyError as err: # graph must be connected + raise nx.NetworkXError("Graph is not distance regular.") from err + # number of neighbors of v at a distance of i-1 from u + c = len([n for n in G[v] if path_length[n][u] == i - 1]) + # number of neighbors of v at a distance of i+1 from u + b = len([n for n in G[v] if path_length[n][u] == i + 1]) + # b,c are independent of u and v + if cint.get(i, c) != c or bint.get(i, b) != b: + raise nx.NetworkXError("Graph is not distance regular") + bint[i] = b + cint[i] = c + return ( + [bint.get(j, 0) for j in range(diameter)], + [cint.get(j + 1, 0) for j in range(diameter)], + ) + + +# TODO There is a definition for directed strongly regular graphs. +@not_implemented_for("directed") +@not_implemented_for("multigraph") +@nx._dispatchable +def is_strongly_regular(G): + """Returns True if and only if the given graph is strongly + regular. + + An undirected graph is *strongly regular* if + + * it is regular, + * each pair of adjacent vertices has the same number of neighbors in + common, + * each pair of nonadjacent vertices has the same number of neighbors + in common. + + Each strongly regular graph is a distance-regular graph. + Conversely, if a distance-regular graph has diameter two, then it is + a strongly regular graph. For more information on distance-regular + graphs, see :func:`is_distance_regular`. + + Parameters + ---------- + G : NetworkX graph + An undirected graph. + + Returns + ------- + bool + Whether `G` is strongly regular. + + Examples + -------- + + The cycle graph on five vertices is strongly regular. It is + two-regular, each pair of adjacent vertices has no shared neighbors, + and each pair of nonadjacent vertices has one shared neighbor:: + + >>> G = nx.cycle_graph(5) + >>> nx.is_strongly_regular(G) + True + + """ + # Here is an alternate implementation based directly on the + # definition of strongly regular graphs: + # + # return (all_equal(G.degree().values()) + # and all_equal(len(common_neighbors(G, u, v)) + # for u, v in G.edges()) + # and all_equal(len(common_neighbors(G, u, v)) + # for u, v in non_edges(G))) + # + # We instead use the fact that a distance-regular graph of diameter + # two is strongly regular. + return is_distance_regular(G) and diameter(G) == 2 diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/dominating.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/dominating.py new file mode 100644 index 0000000000000000000000000000000000000000..ff956f74d8d07b0ec4814c66aa1e9d7ea8dc08fd --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/dominating.py @@ -0,0 +1,95 @@ +"""Functions for computing dominating sets in a graph.""" + +from itertools import chain + +import networkx as nx +from networkx.utils import arbitrary_element + +__all__ = ["dominating_set", "is_dominating_set"] + + +@nx._dispatchable +def dominating_set(G, start_with=None): + r"""Finds a dominating set for the graph G. + + A *dominating set* for a graph with node set *V* is a subset *D* of + *V* such that every node not in *D* is adjacent to at least one + member of *D* [1]_. + + Parameters + ---------- + G : NetworkX graph + + start_with : node (default=None) + Node to use as a starting point for the algorithm. + + Returns + ------- + D : set + A dominating set for G. + + Notes + ----- + This function is an implementation of algorithm 7 in [2]_ which + finds some dominating set, not necessarily the smallest one. + + See also + -------- + is_dominating_set + + References + ---------- + .. [1] https://en.wikipedia.org/wiki/Dominating_set + + .. [2] Abdol-Hossein Esfahanian. Connectivity Algorithms. + http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf + + """ + all_nodes = set(G) + if start_with is None: + start_with = arbitrary_element(all_nodes) + if start_with not in G: + raise nx.NetworkXError(f"node {start_with} is not in G") + dominating_set = {start_with} + dominated_nodes = set(G[start_with]) + remaining_nodes = all_nodes - dominated_nodes - dominating_set + while remaining_nodes: + # Choose an arbitrary node and determine its undominated neighbors. + v = remaining_nodes.pop() + undominated_nbrs = set(G[v]) - dominating_set + # Add the node to the dominating set and the neighbors to the + # dominated set. Finally, remove all of those nodes from the set + # of remaining nodes. + dominating_set.add(v) + dominated_nodes |= undominated_nbrs + remaining_nodes -= undominated_nbrs + return dominating_set + + +@nx._dispatchable +def is_dominating_set(G, nbunch): + """Checks if `nbunch` is a dominating set for `G`. + + A *dominating set* for a graph with node set *V* is a subset *D* of + *V* such that every node not in *D* is adjacent to at least one + member of *D* [1]_. + + Parameters + ---------- + G : NetworkX graph + + nbunch : iterable + An iterable of nodes in the graph `G`. + + See also + -------- + dominating_set + + References + ---------- + .. [1] https://en.wikipedia.org/wiki/Dominating_set + + """ + testset = {n for n in nbunch if n in G} + nbrs = set(chain.from_iterable(G[n] for n in testset)) + return len(set(G) - testset - nbrs) == 0 diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/euler.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/euler.py new file mode 100644 index 0000000000000000000000000000000000000000..2c308e380c774a6450d4ce275118ccffd65defaa --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/euler.py @@ -0,0 +1,470 @@ +""" +Eulerian circuits and graphs. +""" + +from itertools import combinations + +import networkx as nx + +from ..utils import arbitrary_element, not_implemented_for + +__all__ = [ + "is_eulerian", + "eulerian_circuit", + "eulerize", + "is_semieulerian", + "has_eulerian_path", + "eulerian_path", +] + + +@nx._dispatchable +def is_eulerian(G): + """Returns True if and only if `G` is Eulerian. + + A graph is *Eulerian* if it has an Eulerian circuit. An *Eulerian + circuit* is a closed walk that includes each edge of a graph exactly + once. + + Graphs with isolated vertices (i.e. vertices with zero degree) are not + considered to have Eulerian circuits. Therefore, if the graph is not + connected (or not strongly connected, for directed graphs), this function + returns False. + + Parameters + ---------- + G : NetworkX graph + A graph, either directed or undirected. + + Examples + -------- + >>> nx.is_eulerian(nx.DiGraph({0: [3], 1: [2], 2: [3], 3: [0, 1]})) + True + >>> nx.is_eulerian(nx.complete_graph(5)) + True + >>> nx.is_eulerian(nx.petersen_graph()) + False + + If you prefer to allow graphs with isolated vertices to have Eulerian circuits, + you can first remove such vertices and then call `is_eulerian` as below example shows. + + >>> G = nx.Graph([(0, 1), (1, 2), (0, 2)]) + >>> G.add_node(3) + >>> nx.is_eulerian(G) + False + + >>> G.remove_nodes_from(list(nx.isolates(G))) + >>> nx.is_eulerian(G) + True + + + """ + if G.is_directed(): + # Every node must have equal in degree and out degree and the + # graph must be strongly connected + return all( + G.in_degree(n) == G.out_degree(n) for n in G + ) and nx.is_strongly_connected(G) + # An undirected Eulerian graph has no vertices of odd degree and + # must be connected. + return all(d % 2 == 0 for v, d in G.degree()) and nx.is_connected(G) + + +@nx._dispatchable +def is_semieulerian(G): + """Return True iff `G` is semi-Eulerian. + + G is semi-Eulerian if it has an Eulerian path but no Eulerian circuit. + + See Also + -------- + has_eulerian_path + is_eulerian + """ + return has_eulerian_path(G) and not is_eulerian(G) + + +def _find_path_start(G): + """Return a suitable starting vertex for an Eulerian path. + + If no path exists, return None. + """ + if not has_eulerian_path(G): + return None + + if is_eulerian(G): + return arbitrary_element(G) + + if G.is_directed(): + v1, v2 = (v for v in G if G.in_degree(v) != G.out_degree(v)) + # Determines which is the 'start' node (as opposed to the 'end') + if G.out_degree(v1) > G.in_degree(v1): + return v1 + else: + return v2 + + else: + # In an undirected graph randomly choose one of the possibilities + start = [v for v in G if G.degree(v) % 2 != 0][0] + return start + + +def _simplegraph_eulerian_circuit(G, source): + if G.is_directed(): + degree = G.out_degree + edges = G.out_edges + else: + degree = G.degree + edges = G.edges + vertex_stack = [source] + last_vertex = None + while vertex_stack: + current_vertex = vertex_stack[-1] + if degree(current_vertex) == 0: + if last_vertex is not None: + yield (last_vertex, current_vertex) + last_vertex = current_vertex + vertex_stack.pop() + else: + _, next_vertex = arbitrary_element(edges(current_vertex)) + vertex_stack.append(next_vertex) + G.remove_edge(current_vertex, next_vertex) + + +def _multigraph_eulerian_circuit(G, source): + if G.is_directed(): + degree = G.out_degree + edges = G.out_edges + else: + degree = G.degree + edges = G.edges + vertex_stack = [(source, None)] + last_vertex = None + last_key = None + while vertex_stack: + current_vertex, current_key = vertex_stack[-1] + if degree(current_vertex) == 0: + if last_vertex is not None: + yield (last_vertex, current_vertex, last_key) + last_vertex, last_key = current_vertex, current_key + vertex_stack.pop() + else: + triple = arbitrary_element(edges(current_vertex, keys=True)) + _, next_vertex, next_key = triple + vertex_stack.append((next_vertex, next_key)) + G.remove_edge(current_vertex, next_vertex, next_key) + + +@nx._dispatchable +def eulerian_circuit(G, source=None, keys=False): + """Returns an iterator over the edges of an Eulerian circuit in `G`. + + An *Eulerian circuit* is a closed walk that includes each edge of a + graph exactly once. + + Parameters + ---------- + G : NetworkX graph + A graph, either directed or undirected. + + source : node, optional + Starting node for circuit. + + keys : bool + If False, edges generated by this function will be of the form + ``(u, v)``. Otherwise, edges will be of the form ``(u, v, k)``. + This option is ignored unless `G` is a multigraph. + + Returns + ------- + edges : iterator + An iterator over edges in the Eulerian circuit. + + Raises + ------ + NetworkXError + If the graph is not Eulerian. + + See Also + -------- + is_eulerian + + Notes + ----- + This is a linear time implementation of an algorithm adapted from [1]_. + + For general information about Euler tours, see [2]_. + + References + ---------- + .. [1] J. Edmonds, E. L. Johnson. + Matching, Euler tours and the Chinese postman. + Mathematical programming, Volume 5, Issue 1 (1973), 111-114. + .. [2] https://en.wikipedia.org/wiki/Eulerian_path + + Examples + -------- + To get an Eulerian circuit in an undirected graph:: + + >>> G = nx.complete_graph(3) + >>> list(nx.eulerian_circuit(G)) + [(0, 2), (2, 1), (1, 0)] + >>> list(nx.eulerian_circuit(G, source=1)) + [(1, 2), (2, 0), (0, 1)] + + To get the sequence of vertices in an Eulerian circuit:: + + >>> [u for u, v in nx.eulerian_circuit(G)] + [0, 2, 1] + + """ + if not is_eulerian(G): + raise nx.NetworkXError("G is not Eulerian.") + if G.is_directed(): + G = G.reverse() + else: + G = G.copy() + if source is None: + source = arbitrary_element(G) + if G.is_multigraph(): + for u, v, k in _multigraph_eulerian_circuit(G, source): + if keys: + yield u, v, k + else: + yield u, v + else: + yield from _simplegraph_eulerian_circuit(G, source) + + +@nx._dispatchable +def has_eulerian_path(G, source=None): + """Return True iff `G` has an Eulerian path. + + An Eulerian path is a path in a graph which uses each edge of a graph + exactly once. If `source` is specified, then this function checks + whether an Eulerian path that starts at node `source` exists. + + A directed graph has an Eulerian path iff: + - at most one vertex has out_degree - in_degree = 1, + - at most one vertex has in_degree - out_degree = 1, + - every other vertex has equal in_degree and out_degree, + - and all of its vertices belong to a single connected + component of the underlying undirected graph. + + If `source` is not None, an Eulerian path starting at `source` exists if no + other node has out_degree - in_degree = 1. This is equivalent to either + there exists an Eulerian circuit or `source` has out_degree - in_degree = 1 + and the conditions above hold. + + An undirected graph has an Eulerian path iff: + - exactly zero or two vertices have odd degree, + - and all of its vertices belong to a single connected component. + + If `source` is not None, an Eulerian path starting at `source` exists if + either there exists an Eulerian circuit or `source` has an odd degree and the + conditions above hold. + + Graphs with isolated vertices (i.e. vertices with zero degree) are not considered + to have an Eulerian path. Therefore, if the graph is not connected (or not strongly + connected, for directed graphs), this function returns False. + + Parameters + ---------- + G : NetworkX Graph + The graph to find an euler path in. + + source : node, optional + Starting node for path. + + Returns + ------- + Bool : True if G has an Eulerian path. + + Examples + -------- + If you prefer to allow graphs with isolated vertices to have Eulerian path, + you can first remove such vertices and then call `has_eulerian_path` as below example shows. + + >>> G = nx.Graph([(0, 1), (1, 2), (0, 2)]) + >>> G.add_node(3) + >>> nx.has_eulerian_path(G) + False + + >>> G.remove_nodes_from(list(nx.isolates(G))) + >>> nx.has_eulerian_path(G) + True + + See Also + -------- + is_eulerian + eulerian_path + """ + if nx.is_eulerian(G): + return True + + if G.is_directed(): + ins = G.in_degree + outs = G.out_degree + # Since we know it is not eulerian, outs - ins must be 1 for source + if source is not None and outs[source] - ins[source] != 1: + return False + + unbalanced_ins = 0 + unbalanced_outs = 0 + for v in G: + if ins[v] - outs[v] == 1: + unbalanced_ins += 1 + elif outs[v] - ins[v] == 1: + unbalanced_outs += 1 + elif ins[v] != outs[v]: + return False + + return ( + unbalanced_ins <= 1 and unbalanced_outs <= 1 and nx.is_weakly_connected(G) + ) + else: + # We know it is not eulerian, so degree of source must be odd. + if source is not None and G.degree[source] % 2 != 1: + return False + + # Sum is 2 since we know it is not eulerian (which implies sum is 0) + return sum(d % 2 == 1 for v, d in G.degree()) == 2 and nx.is_connected(G) + + +@nx._dispatchable +def eulerian_path(G, source=None, keys=False): + """Return an iterator over the edges of an Eulerian path in `G`. + + Parameters + ---------- + G : NetworkX Graph + The graph in which to look for an eulerian path. + source : node or None (default: None) + The node at which to start the search. None means search over all + starting nodes. + keys : Bool (default: False) + Indicates whether to yield edge 3-tuples (u, v, edge_key). + The default yields edge 2-tuples + + Yields + ------ + Edge tuples along the eulerian path. + + Warning: If `source` provided is not the start node of an Euler path + will raise error even if an Euler Path exists. + """ + if not has_eulerian_path(G, source): + raise nx.NetworkXError("Graph has no Eulerian paths.") + if G.is_directed(): + G = G.reverse() + if source is None or nx.is_eulerian(G) is False: + source = _find_path_start(G) + if G.is_multigraph(): + for u, v, k in _multigraph_eulerian_circuit(G, source): + if keys: + yield u, v, k + else: + yield u, v + else: + yield from _simplegraph_eulerian_circuit(G, source) + else: + G = G.copy() + if source is None: + source = _find_path_start(G) + if G.is_multigraph(): + if keys: + yield from reversed( + [(v, u, k) for u, v, k in _multigraph_eulerian_circuit(G, source)] + ) + else: + yield from reversed( + [(v, u) for u, v, k in _multigraph_eulerian_circuit(G, source)] + ) + else: + yield from reversed( + [(v, u) for u, v in _simplegraph_eulerian_circuit(G, source)] + ) + + +@not_implemented_for("directed") +@nx._dispatchable(returns_graph=True) +def eulerize(G): + """Transforms a graph into an Eulerian graph. + + If `G` is Eulerian the result is `G` as a MultiGraph, otherwise the result is a smallest + (in terms of the number of edges) multigraph whose underlying simple graph is `G`. + + Parameters + ---------- + G : NetworkX graph + An undirected graph + + Returns + ------- + G : NetworkX multigraph + + Raises + ------ + NetworkXError + If the graph is not connected. + + See Also + -------- + is_eulerian + eulerian_circuit + + References + ---------- + .. [1] J. Edmonds, E. L. Johnson. + Matching, Euler tours and the Chinese postman. + Mathematical programming, Volume 5, Issue 1 (1973), 111-114. + .. [2] https://en.wikipedia.org/wiki/Eulerian_path + .. [3] http://web.math.princeton.edu/math_alive/5/Notes1.pdf + + Examples + -------- + >>> G = nx.complete_graph(10) + >>> H = nx.eulerize(G) + >>> nx.is_eulerian(H) + True + + """ + if G.order() == 0: + raise nx.NetworkXPointlessConcept("Cannot Eulerize null graph") + if not nx.is_connected(G): + raise nx.NetworkXError("G is not connected") + odd_degree_nodes = [n for n, d in G.degree() if d % 2 == 1] + G = nx.MultiGraph(G) + if len(odd_degree_nodes) == 0: + return G + + # get all shortest paths between vertices of odd degree + odd_deg_pairs_paths = [ + (m, {n: nx.shortest_path(G, source=m, target=n)}) + for m, n in combinations(odd_degree_nodes, 2) + ] + + # use the number of vertices in a graph + 1 as an upper bound on + # the maximum length of a path in G + upper_bound_on_max_path_length = len(G) + 1 + + # use "len(G) + 1 - len(P)", + # where P is a shortest path between vertices n and m, + # as edge-weights in a new graph + # store the paths in the graph for easy indexing later + Gp = nx.Graph() + for n, Ps in odd_deg_pairs_paths: + for m, P in Ps.items(): + if n != m: + Gp.add_edge( + m, n, weight=upper_bound_on_max_path_length - len(P), path=P + ) + + # find the minimum weight matching of edges in the weighted graph + best_matching = nx.Graph(list(nx.max_weight_matching(Gp))) + + # duplicate each edge along each path in the set of paths in Gp + for m, n in best_matching.edges(): + path = Gp[m][n]["path"] + G.add_edges_from(nx.utils.pairwise(path)) + return G diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__init__.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..58c22688660073a6abb59f7639871f711d1bd6ac --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__init__.py @@ -0,0 +1,7 @@ +from networkx.algorithms.isomorphism.isomorph import * +from networkx.algorithms.isomorphism.vf2userfunc import * +from networkx.algorithms.isomorphism.matchhelpers import * +from networkx.algorithms.isomorphism.temporalisomorphvf2 import * +from networkx.algorithms.isomorphism.ismags import * +from networkx.algorithms.isomorphism.tree_isomorphism import * +from networkx.algorithms.isomorphism.vf2pp import * diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/__init__.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/__init__.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..f6f35e605729671f7b49974c3beafc4957d6eaa4 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/__init__.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/ismags.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/ismags.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..f5dd57f392988609afb1e5bd42d86acba4e55905 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/ismags.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/isomorph.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/isomorph.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..4e65a679f2c7afcf21a8e67d1d16fa84603981ca Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/isomorph.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/isomorphvf2.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/isomorphvf2.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..fc8a66c7b59586cf8bdcc154540b5cd58bb10d58 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/isomorphvf2.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/temporalisomorphvf2.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/temporalisomorphvf2.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..9046b4f72499bc4afe79ba134983363cb21cf87c Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/temporalisomorphvf2.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/tree_isomorphism.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/tree_isomorphism.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..f350be611a6148ab1464bda772cf129b5d1b54fa Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__pycache__/tree_isomorphism.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/ismags.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/ismags.py new file mode 100644 index 0000000000000000000000000000000000000000..24819faf95cf42f8264960a4a6a27754301fc661 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/ismags.py @@ -0,0 +1,1163 @@ +""" +ISMAGS Algorithm +================ + +Provides a Python implementation of the ISMAGS algorithm. [1]_ + +It is capable of finding (subgraph) isomorphisms between two graphs, taking the +symmetry of the subgraph into account. In most cases the VF2 algorithm is +faster (at least on small graphs) than this implementation, but in some cases +there is an exponential number of isomorphisms that are symmetrically +equivalent. In that case, the ISMAGS algorithm will provide only one solution +per symmetry group. + +>>> petersen = nx.petersen_graph() +>>> ismags = nx.isomorphism.ISMAGS(petersen, petersen) +>>> isomorphisms = list(ismags.isomorphisms_iter(symmetry=False)) +>>> len(isomorphisms) +120 +>>> isomorphisms = list(ismags.isomorphisms_iter(symmetry=True)) +>>> answer = [{0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9}] +>>> answer == isomorphisms +True + +In addition, this implementation also provides an interface to find the +largest common induced subgraph [2]_ between any two graphs, again taking +symmetry into account. Given `graph` and `subgraph` the algorithm will remove +nodes from the `subgraph` until `subgraph` is isomorphic to a subgraph of +`graph`. Since only the symmetry of `subgraph` is taken into account it is +worth thinking about how you provide your graphs: + +>>> graph1 = nx.path_graph(4) +>>> graph2 = nx.star_graph(3) +>>> ismags = nx.isomorphism.ISMAGS(graph1, graph2) +>>> ismags.is_isomorphic() +False +>>> largest_common_subgraph = list(ismags.largest_common_subgraph()) +>>> answer = [{1: 0, 0: 1, 2: 2}, {2: 0, 1: 1, 3: 2}] +>>> answer == largest_common_subgraph +True +>>> ismags2 = nx.isomorphism.ISMAGS(graph2, graph1) +>>> largest_common_subgraph = list(ismags2.largest_common_subgraph()) +>>> answer = [ +... {1: 0, 0: 1, 2: 2}, +... {1: 0, 0: 1, 3: 2}, +... {2: 0, 0: 1, 1: 2}, +... {2: 0, 0: 1, 3: 2}, +... {3: 0, 0: 1, 1: 2}, +... {3: 0, 0: 1, 2: 2}, +... ] +>>> answer == largest_common_subgraph +True + +However, when not taking symmetry into account, it doesn't matter: + +>>> largest_common_subgraph = list(ismags.largest_common_subgraph(symmetry=False)) +>>> answer = [ +... {1: 0, 0: 1, 2: 2}, +... {1: 0, 2: 1, 0: 2}, +... {2: 0, 1: 1, 3: 2}, +... {2: 0, 3: 1, 1: 2}, +... {1: 0, 0: 1, 2: 3}, +... {1: 0, 2: 1, 0: 3}, +... {2: 0, 1: 1, 3: 3}, +... {2: 0, 3: 1, 1: 3}, +... {1: 0, 0: 2, 2: 3}, +... {1: 0, 2: 2, 0: 3}, +... {2: 0, 1: 2, 3: 3}, +... {2: 0, 3: 2, 1: 3}, +... ] +>>> answer == largest_common_subgraph +True +>>> largest_common_subgraph = list(ismags2.largest_common_subgraph(symmetry=False)) +>>> answer = [ +... {1: 0, 0: 1, 2: 2}, +... {1: 0, 0: 1, 3: 2}, +... {2: 0, 0: 1, 1: 2}, +... {2: 0, 0: 1, 3: 2}, +... {3: 0, 0: 1, 1: 2}, +... {3: 0, 0: 1, 2: 2}, +... {1: 1, 0: 2, 2: 3}, +... {1: 1, 0: 2, 3: 3}, +... {2: 1, 0: 2, 1: 3}, +... {2: 1, 0: 2, 3: 3}, +... {3: 1, 0: 2, 1: 3}, +... {3: 1, 0: 2, 2: 3}, +... ] +>>> answer == largest_common_subgraph +True + +Notes +----- +- The current implementation works for undirected graphs only. The algorithm + in general should work for directed graphs as well though. +- Node keys for both provided graphs need to be fully orderable as well as + hashable. +- Node and edge equality is assumed to be transitive: if A is equal to B, and + B is equal to C, then A is equal to C. + +References +---------- +.. [1] M. Houbraken, S. Demeyer, T. Michoel, P. Audenaert, D. Colle, + M. Pickavet, "The Index-Based Subgraph Matching Algorithm with General + Symmetries (ISMAGS): Exploiting Symmetry for Faster Subgraph + Enumeration", PLoS One 9(5): e97896, 2014. + https://doi.org/10.1371/journal.pone.0097896 +.. [2] https://en.wikipedia.org/wiki/Maximum_common_induced_subgraph +""" + +__all__ = ["ISMAGS"] + +import itertools +from collections import Counter, defaultdict +from functools import reduce, wraps + + +def are_all_equal(iterable): + """ + Returns ``True`` if and only if all elements in `iterable` are equal; and + ``False`` otherwise. + + Parameters + ---------- + iterable: collections.abc.Iterable + The container whose elements will be checked. + + Returns + ------- + bool + ``True`` iff all elements in `iterable` compare equal, ``False`` + otherwise. + """ + try: + shape = iterable.shape + except AttributeError: + pass + else: + if len(shape) > 1: + message = "The function does not works on multidimensional arrays." + raise NotImplementedError(message) from None + + iterator = iter(iterable) + first = next(iterator, None) + return all(item == first for item in iterator) + + +def make_partitions(items, test): + """ + Partitions items into sets based on the outcome of ``test(item1, item2)``. + Pairs of items for which `test` returns `True` end up in the same set. + + Parameters + ---------- + items : collections.abc.Iterable[collections.abc.Hashable] + Items to partition + test : collections.abc.Callable[collections.abc.Hashable, collections.abc.Hashable] + A function that will be called with 2 arguments, taken from items. + Should return `True` if those 2 items need to end up in the same + partition, and `False` otherwise. + + Returns + ------- + list[set] + A list of sets, with each set containing part of the items in `items`, + such that ``all(test(*pair) for pair in itertools.combinations(set, 2)) + == True`` + + Notes + ----- + The function `test` is assumed to be transitive: if ``test(a, b)`` and + ``test(b, c)`` return ``True``, then ``test(a, c)`` must also be ``True``. + """ + partitions = [] + for item in items: + for partition in partitions: + p_item = next(iter(partition)) + if test(item, p_item): + partition.add(item) + break + else: # No break + partitions.append({item}) + return partitions + + +def partition_to_color(partitions): + """ + Creates a dictionary that maps each item in each partition to the index of + the partition to which it belongs. + + Parameters + ---------- + partitions: collections.abc.Sequence[collections.abc.Iterable] + As returned by :func:`make_partitions`. + + Returns + ------- + dict + """ + colors = {} + for color, keys in enumerate(partitions): + for key in keys: + colors[key] = color + return colors + + +def intersect(collection_of_sets): + """ + Given an collection of sets, returns the intersection of those sets. + + Parameters + ---------- + collection_of_sets: collections.abc.Collection[set] + A collection of sets. + + Returns + ------- + set + An intersection of all sets in `collection_of_sets`. Will have the same + type as the item initially taken from `collection_of_sets`. + """ + collection_of_sets = list(collection_of_sets) + first = collection_of_sets.pop() + out = reduce(set.intersection, collection_of_sets, set(first)) + return type(first)(out) + + +class ISMAGS: + """ + Implements the ISMAGS subgraph matching algorithm. [1]_ ISMAGS stands for + "Index-based Subgraph Matching Algorithm with General Symmetries". As the + name implies, it is symmetry aware and will only generate non-symmetric + isomorphisms. + + Notes + ----- + The implementation imposes additional conditions compared to the VF2 + algorithm on the graphs provided and the comparison functions + (:attr:`node_equality` and :attr:`edge_equality`): + + - Node keys in both graphs must be orderable as well as hashable. + - Equality must be transitive: if A is equal to B, and B is equal to C, + then A must be equal to C. + + Attributes + ---------- + graph: networkx.Graph + subgraph: networkx.Graph + node_equality: collections.abc.Callable + The function called to see if two nodes should be considered equal. + It's signature looks like this: + ``f(graph1: networkx.Graph, node1, graph2: networkx.Graph, node2) -> bool``. + `node1` is a node in `graph1`, and `node2` a node in `graph2`. + Constructed from the argument `node_match`. + edge_equality: collections.abc.Callable + The function called to see if two edges should be considered equal. + It's signature looks like this: + ``f(graph1: networkx.Graph, edge1, graph2: networkx.Graph, edge2) -> bool``. + `edge1` is an edge in `graph1`, and `edge2` an edge in `graph2`. + Constructed from the argument `edge_match`. + + References + ---------- + .. [1] M. Houbraken, S. Demeyer, T. Michoel, P. Audenaert, D. Colle, + M. Pickavet, "The Index-Based Subgraph Matching Algorithm with General + Symmetries (ISMAGS): Exploiting Symmetry for Faster Subgraph + Enumeration", PLoS One 9(5): e97896, 2014. + https://doi.org/10.1371/journal.pone.0097896 + """ + + def __init__(self, graph, subgraph, node_match=None, edge_match=None, cache=None): + """ + Parameters + ---------- + graph: networkx.Graph + subgraph: networkx.Graph + node_match: collections.abc.Callable or None + Function used to determine whether two nodes are equivalent. Its + signature should look like ``f(n1: dict, n2: dict) -> bool``, with + `n1` and `n2` node property dicts. See also + :func:`~networkx.algorithms.isomorphism.categorical_node_match` and + friends. + If `None`, all nodes are considered equal. + edge_match: collections.abc.Callable or None + Function used to determine whether two edges are equivalent. Its + signature should look like ``f(e1: dict, e2: dict) -> bool``, with + `e1` and `e2` edge property dicts. See also + :func:`~networkx.algorithms.isomorphism.categorical_edge_match` and + friends. + If `None`, all edges are considered equal. + cache: collections.abc.Mapping + A cache used for caching graph symmetries. + """ + # TODO: graph and subgraph setter methods that invalidate the caches. + # TODO: allow for precomputed partitions and colors + self.graph = graph + self.subgraph = subgraph + self._symmetry_cache = cache + # Naming conventions are taken from the original paper. For your + # sanity: + # sg: subgraph + # g: graph + # e: edge(s) + # n: node(s) + # So: sgn means "subgraph nodes". + self._sgn_partitions_ = None + self._sge_partitions_ = None + + self._sgn_colors_ = None + self._sge_colors_ = None + + self._gn_partitions_ = None + self._ge_partitions_ = None + + self._gn_colors_ = None + self._ge_colors_ = None + + self._node_compat_ = None + self._edge_compat_ = None + + if node_match is None: + self.node_equality = self._node_match_maker(lambda n1, n2: True) + self._sgn_partitions_ = [set(self.subgraph.nodes)] + self._gn_partitions_ = [set(self.graph.nodes)] + self._node_compat_ = {0: 0} + else: + self.node_equality = self._node_match_maker(node_match) + if edge_match is None: + self.edge_equality = self._edge_match_maker(lambda e1, e2: True) + self._sge_partitions_ = [set(self.subgraph.edges)] + self._ge_partitions_ = [set(self.graph.edges)] + self._edge_compat_ = {0: 0} + else: + self.edge_equality = self._edge_match_maker(edge_match) + + @property + def _sgn_partitions(self): + if self._sgn_partitions_ is None: + + def nodematch(node1, node2): + return self.node_equality(self.subgraph, node1, self.subgraph, node2) + + self._sgn_partitions_ = make_partitions(self.subgraph.nodes, nodematch) + return self._sgn_partitions_ + + @property + def _sge_partitions(self): + if self._sge_partitions_ is None: + + def edgematch(edge1, edge2): + return self.edge_equality(self.subgraph, edge1, self.subgraph, edge2) + + self._sge_partitions_ = make_partitions(self.subgraph.edges, edgematch) + return self._sge_partitions_ + + @property + def _gn_partitions(self): + if self._gn_partitions_ is None: + + def nodematch(node1, node2): + return self.node_equality(self.graph, node1, self.graph, node2) + + self._gn_partitions_ = make_partitions(self.graph.nodes, nodematch) + return self._gn_partitions_ + + @property + def _ge_partitions(self): + if self._ge_partitions_ is None: + + def edgematch(edge1, edge2): + return self.edge_equality(self.graph, edge1, self.graph, edge2) + + self._ge_partitions_ = make_partitions(self.graph.edges, edgematch) + return self._ge_partitions_ + + @property + def _sgn_colors(self): + if self._sgn_colors_ is None: + self._sgn_colors_ = partition_to_color(self._sgn_partitions) + return self._sgn_colors_ + + @property + def _sge_colors(self): + if self._sge_colors_ is None: + self._sge_colors_ = partition_to_color(self._sge_partitions) + return self._sge_colors_ + + @property + def _gn_colors(self): + if self._gn_colors_ is None: + self._gn_colors_ = partition_to_color(self._gn_partitions) + return self._gn_colors_ + + @property + def _ge_colors(self): + if self._ge_colors_ is None: + self._ge_colors_ = partition_to_color(self._ge_partitions) + return self._ge_colors_ + + @property + def _node_compatibility(self): + if self._node_compat_ is not None: + return self._node_compat_ + self._node_compat_ = {} + for sgn_part_color, gn_part_color in itertools.product( + range(len(self._sgn_partitions)), range(len(self._gn_partitions)) + ): + sgn = next(iter(self._sgn_partitions[sgn_part_color])) + gn = next(iter(self._gn_partitions[gn_part_color])) + if self.node_equality(self.subgraph, sgn, self.graph, gn): + self._node_compat_[sgn_part_color] = gn_part_color + return self._node_compat_ + + @property + def _edge_compatibility(self): + if self._edge_compat_ is not None: + return self._edge_compat_ + self._edge_compat_ = {} + for sge_part_color, ge_part_color in itertools.product( + range(len(self._sge_partitions)), range(len(self._ge_partitions)) + ): + sge = next(iter(self._sge_partitions[sge_part_color])) + ge = next(iter(self._ge_partitions[ge_part_color])) + if self.edge_equality(self.subgraph, sge, self.graph, ge): + self._edge_compat_[sge_part_color] = ge_part_color + return self._edge_compat_ + + @staticmethod + def _node_match_maker(cmp): + @wraps(cmp) + def comparer(graph1, node1, graph2, node2): + return cmp(graph1.nodes[node1], graph2.nodes[node2]) + + return comparer + + @staticmethod + def _edge_match_maker(cmp): + @wraps(cmp) + def comparer(graph1, edge1, graph2, edge2): + return cmp(graph1.edges[edge1], graph2.edges[edge2]) + + return comparer + + def find_isomorphisms(self, symmetry=True): + """Find all subgraph isomorphisms between subgraph and graph + + Finds isomorphisms where :attr:`subgraph` <= :attr:`graph`. + + Parameters + ---------- + symmetry: bool + Whether symmetry should be taken into account. If False, found + isomorphisms may be symmetrically equivalent. + + Yields + ------ + dict + The found isomorphism mappings of {graph_node: subgraph_node}. + """ + # The networkx VF2 algorithm is slightly funny in when it yields an + # empty dict and when not. + if not self.subgraph: + yield {} + return + elif not self.graph: + return + elif len(self.graph) < len(self.subgraph): + return + + if symmetry: + _, cosets = self.analyze_symmetry( + self.subgraph, self._sgn_partitions, self._sge_colors + ) + constraints = self._make_constraints(cosets) + else: + constraints = [] + + candidates = self._find_nodecolor_candidates() + la_candidates = self._get_lookahead_candidates() + for sgn in self.subgraph: + extra_candidates = la_candidates[sgn] + if extra_candidates: + candidates[sgn] = candidates[sgn] | {frozenset(extra_candidates)} + + if any(candidates.values()): + start_sgn = min(candidates, key=lambda n: min(candidates[n], key=len)) + candidates[start_sgn] = (intersect(candidates[start_sgn]),) + yield from self._map_nodes(start_sgn, candidates, constraints) + else: + return + + @staticmethod + def _find_neighbor_color_count(graph, node, node_color, edge_color): + """ + For `node` in `graph`, count the number of edges of a specific color + it has to nodes of a specific color. + """ + counts = Counter() + neighbors = graph[node] + for neighbor in neighbors: + n_color = node_color[neighbor] + if (node, neighbor) in edge_color: + e_color = edge_color[node, neighbor] + else: + e_color = edge_color[neighbor, node] + counts[e_color, n_color] += 1 + return counts + + def _get_lookahead_candidates(self): + """ + Returns a mapping of {subgraph node: collection of graph nodes} for + which the graph nodes are feasible candidates for the subgraph node, as + determined by looking ahead one edge. + """ + g_counts = {} + for gn in self.graph: + g_counts[gn] = self._find_neighbor_color_count( + self.graph, gn, self._gn_colors, self._ge_colors + ) + candidates = defaultdict(set) + for sgn in self.subgraph: + sg_count = self._find_neighbor_color_count( + self.subgraph, sgn, self._sgn_colors, self._sge_colors + ) + new_sg_count = Counter() + for (sge_color, sgn_color), count in sg_count.items(): + try: + ge_color = self._edge_compatibility[sge_color] + gn_color = self._node_compatibility[sgn_color] + except KeyError: + pass + else: + new_sg_count[ge_color, gn_color] = count + + for gn, g_count in g_counts.items(): + if all(new_sg_count[x] <= g_count[x] for x in new_sg_count): + # Valid candidate + candidates[sgn].add(gn) + return candidates + + def largest_common_subgraph(self, symmetry=True): + """ + Find the largest common induced subgraphs between :attr:`subgraph` and + :attr:`graph`. + + Parameters + ---------- + symmetry: bool + Whether symmetry should be taken into account. If False, found + largest common subgraphs may be symmetrically equivalent. + + Yields + ------ + dict + The found isomorphism mappings of {graph_node: subgraph_node}. + """ + # The networkx VF2 algorithm is slightly funny in when it yields an + # empty dict and when not. + if not self.subgraph: + yield {} + return + elif not self.graph: + return + + if symmetry: + _, cosets = self.analyze_symmetry( + self.subgraph, self._sgn_partitions, self._sge_colors + ) + constraints = self._make_constraints(cosets) + else: + constraints = [] + + candidates = self._find_nodecolor_candidates() + + if any(candidates.values()): + yield from self._largest_common_subgraph(candidates, constraints) + else: + return + + def analyze_symmetry(self, graph, node_partitions, edge_colors): + """ + Find a minimal set of permutations and corresponding co-sets that + describe the symmetry of `graph`, given the node and edge equalities + given by `node_partitions` and `edge_colors`, respectively. + + Parameters + ---------- + graph : networkx.Graph + The graph whose symmetry should be analyzed. + node_partitions : list of sets + A list of sets containing node keys. Node keys in the same set + are considered equivalent. Every node key in `graph` should be in + exactly one of the sets. If all nodes are equivalent, this should + be ``[set(graph.nodes)]``. + edge_colors : dict mapping edges to their colors + A dict mapping every edge in `graph` to its corresponding color. + Edges with the same color are considered equivalent. If all edges + are equivalent, this should be ``{e: 0 for e in graph.edges}``. + + + Returns + ------- + set[frozenset] + The found permutations. This is a set of frozensets of pairs of node + keys which can be exchanged without changing :attr:`subgraph`. + dict[collections.abc.Hashable, set[collections.abc.Hashable]] + The found co-sets. The co-sets is a dictionary of + ``{node key: set of node keys}``. + Every key-value pair describes which ``values`` can be interchanged + without changing nodes less than ``key``. + """ + if self._symmetry_cache is not None: + key = hash( + ( + tuple(graph.nodes), + tuple(graph.edges), + tuple(map(tuple, node_partitions)), + tuple(edge_colors.items()), + ) + ) + if key in self._symmetry_cache: + return self._symmetry_cache[key] + node_partitions = list( + self._refine_node_partitions(graph, node_partitions, edge_colors) + ) + assert len(node_partitions) == 1 + node_partitions = node_partitions[0] + permutations, cosets = self._process_ordered_pair_partitions( + graph, node_partitions, node_partitions, edge_colors + ) + if self._symmetry_cache is not None: + self._symmetry_cache[key] = permutations, cosets + return permutations, cosets + + def is_isomorphic(self, symmetry=False): + """ + Returns True if :attr:`graph` is isomorphic to :attr:`subgraph` and + False otherwise. + + Returns + ------- + bool + """ + return len(self.subgraph) == len(self.graph) and self.subgraph_is_isomorphic( + symmetry + ) + + def subgraph_is_isomorphic(self, symmetry=False): + """ + Returns True if a subgraph of :attr:`graph` is isomorphic to + :attr:`subgraph` and False otherwise. + + Returns + ------- + bool + """ + # symmetry=False, since we only need to know whether there is any + # example; figuring out all symmetry elements probably costs more time + # than it gains. + isom = next(self.subgraph_isomorphisms_iter(symmetry=symmetry), None) + return isom is not None + + def isomorphisms_iter(self, symmetry=True): + """ + Does the same as :meth:`find_isomorphisms` if :attr:`graph` and + :attr:`subgraph` have the same number of nodes. + """ + if len(self.graph) == len(self.subgraph): + yield from self.subgraph_isomorphisms_iter(symmetry=symmetry) + + def subgraph_isomorphisms_iter(self, symmetry=True): + """Alternative name for :meth:`find_isomorphisms`.""" + return self.find_isomorphisms(symmetry) + + def _find_nodecolor_candidates(self): + """ + Per node in subgraph find all nodes in graph that have the same color. + """ + candidates = defaultdict(set) + for sgn in self.subgraph.nodes: + sgn_color = self._sgn_colors[sgn] + if sgn_color in self._node_compatibility: + gn_color = self._node_compatibility[sgn_color] + candidates[sgn].add(frozenset(self._gn_partitions[gn_color])) + else: + candidates[sgn].add(frozenset()) + candidates = dict(candidates) + for sgn, options in candidates.items(): + candidates[sgn] = frozenset(options) + return candidates + + @staticmethod + def _make_constraints(cosets): + """ + Turn cosets into constraints. + """ + constraints = [] + for node_i, node_ts in cosets.items(): + for node_t in node_ts: + if node_i != node_t: + # Node i must be smaller than node t. + constraints.append((node_i, node_t)) + return constraints + + @staticmethod + def _find_node_edge_color(graph, node_colors, edge_colors): + """ + For every node in graph, come up with a color that combines 1) the + color of the node, and 2) the number of edges of a color to each type + of node. + """ + counts = defaultdict(lambda: defaultdict(int)) + for node1, node2 in graph.edges: + if (node1, node2) in edge_colors: + # FIXME directed graphs + ecolor = edge_colors[node1, node2] + else: + ecolor = edge_colors[node2, node1] + # Count per node how many edges it has of what color to nodes of + # what color + counts[node1][ecolor, node_colors[node2]] += 1 + counts[node2][ecolor, node_colors[node1]] += 1 + + node_edge_colors = {} + for node in graph.nodes: + node_edge_colors[node] = node_colors[node], set(counts[node].items()) + + return node_edge_colors + + @staticmethod + def _get_permutations_by_length(items): + """ + Get all permutations of items, but only permute items with the same + length. + + >>> found = list(ISMAGS._get_permutations_by_length([[1], [2], [3, 4], [4, 5]])) + >>> answer = [ + ... (([1], [2]), ([3, 4], [4, 5])), + ... (([1], [2]), ([4, 5], [3, 4])), + ... (([2], [1]), ([3, 4], [4, 5])), + ... (([2], [1]), ([4, 5], [3, 4])), + ... ] + >>> found == answer + True + """ + by_len = defaultdict(list) + for item in items: + by_len[len(item)].append(item) + + yield from itertools.product( + *(itertools.permutations(by_len[l]) for l in sorted(by_len)) + ) + + @classmethod + def _refine_node_partitions(cls, graph, node_partitions, edge_colors, branch=False): + """ + Given a partition of nodes in graph, make the partitions smaller such + that all nodes in a partition have 1) the same color, and 2) the same + number of edges to specific other partitions. + """ + + def equal_color(node1, node2): + return node_edge_colors[node1] == node_edge_colors[node2] + + node_partitions = list(node_partitions) + node_colors = partition_to_color(node_partitions) + node_edge_colors = cls._find_node_edge_color(graph, node_colors, edge_colors) + if all( + are_all_equal(node_edge_colors[node] for node in partition) + for partition in node_partitions + ): + yield node_partitions + return + + new_partitions = [] + output = [new_partitions] + for partition in node_partitions: + if not are_all_equal(node_edge_colors[node] for node in partition): + refined = make_partitions(partition, equal_color) + if ( + branch + and len(refined) != 1 + and len({len(r) for r in refined}) != len([len(r) for r in refined]) + ): + # This is where it breaks. There are multiple new cells + # in refined with the same length, and their order + # matters. + # So option 1) Hit it with a big hammer and simply make all + # orderings. + permutations = cls._get_permutations_by_length(refined) + new_output = [] + for n_p in output: + for permutation in permutations: + new_output.append(n_p + list(permutation[0])) + output = new_output + else: + for n_p in output: + n_p.extend(sorted(refined, key=len)) + else: + for n_p in output: + n_p.append(partition) + for n_p in output: + yield from cls._refine_node_partitions(graph, n_p, edge_colors, branch) + + def _edges_of_same_color(self, sgn1, sgn2): + """ + Returns all edges in :attr:`graph` that have the same colour as the + edge between sgn1 and sgn2 in :attr:`subgraph`. + """ + if (sgn1, sgn2) in self._sge_colors: + # FIXME directed graphs + sge_color = self._sge_colors[sgn1, sgn2] + else: + sge_color = self._sge_colors[sgn2, sgn1] + if sge_color in self._edge_compatibility: + ge_color = self._edge_compatibility[sge_color] + g_edges = self._ge_partitions[ge_color] + else: + g_edges = [] + return g_edges + + def _map_nodes(self, sgn, candidates, constraints, mapping=None, to_be_mapped=None): + """ + Find all subgraph isomorphisms honoring constraints. + """ + if mapping is None: + mapping = {} + else: + mapping = mapping.copy() + if to_be_mapped is None: + to_be_mapped = set(self.subgraph.nodes) + + # Note, we modify candidates here. Doesn't seem to affect results, but + # remember this. + # candidates = candidates.copy() + sgn_candidates = intersect(candidates[sgn]) + candidates[sgn] = frozenset([sgn_candidates]) + for gn in sgn_candidates: + # We're going to try to map sgn to gn. + if gn in mapping.values() or sgn not in to_be_mapped: + # gn is already mapped to something + continue # pragma: no cover + + # REDUCTION and COMBINATION + mapping[sgn] = gn + # BASECASE + if to_be_mapped == set(mapping.keys()): + yield {v: k for k, v in mapping.items()} + continue + left_to_map = to_be_mapped - set(mapping.keys()) + + new_candidates = candidates.copy() + sgn_nbrs = set(self.subgraph[sgn]) + not_gn_nbrs = set(self.graph.nodes) - set(self.graph[gn]) + for sgn2 in left_to_map: + if sgn2 not in sgn_nbrs: + gn2_options = not_gn_nbrs + else: + # Get all edges to gn of the right color: + g_edges = self._edges_of_same_color(sgn, sgn2) + # FIXME directed graphs + # And all nodes involved in those which are connected to gn + gn2_options = {n for e in g_edges for n in e if gn in e} + # Node color compatibility should be taken care of by the + # initial candidate lists made by find_subgraphs + + # Add gn2_options to the right collection. Since new_candidates + # is a dict of frozensets of frozensets of node indices it's + # a bit clunky. We can't do .add, and + also doesn't work. We + # could do |, but I deem union to be clearer. + new_candidates[sgn2] = new_candidates[sgn2].union( + [frozenset(gn2_options)] + ) + + if (sgn, sgn2) in constraints: + gn2_options = {gn2 for gn2 in self.graph if gn2 > gn} + elif (sgn2, sgn) in constraints: + gn2_options = {gn2 for gn2 in self.graph if gn2 < gn} + else: + continue # pragma: no cover + new_candidates[sgn2] = new_candidates[sgn2].union( + [frozenset(gn2_options)] + ) + + # The next node is the one that is unmapped and has fewest + # candidates + next_sgn = min(left_to_map, key=lambda n: min(new_candidates[n], key=len)) + yield from self._map_nodes( + next_sgn, + new_candidates, + constraints, + mapping=mapping, + to_be_mapped=to_be_mapped, + ) + # Unmap sgn-gn. Strictly not necessary since it'd get overwritten + # when making a new mapping for sgn. + # del mapping[sgn] + + def _largest_common_subgraph(self, candidates, constraints, to_be_mapped=None): + """ + Find all largest common subgraphs honoring constraints. + """ + if to_be_mapped is None: + to_be_mapped = {frozenset(self.subgraph.nodes)} + + # The LCS problem is basically a repeated subgraph isomorphism problem + # with smaller and smaller subgraphs. We store the nodes that are + # "part of" the subgraph in to_be_mapped, and we make it a little + # smaller every iteration. + + current_size = len(next(iter(to_be_mapped), [])) + + found_iso = False + if current_size <= len(self.graph): + # There's no point in trying to find isomorphisms of + # graph >= subgraph if subgraph has more nodes than graph. + + # Try the isomorphism first with the nodes with lowest ID. So sort + # them. Those are more likely to be part of the final + # correspondence. This makes finding the first answer(s) faster. In + # theory. + for nodes in sorted(to_be_mapped, key=sorted): + # Find the isomorphism between subgraph[to_be_mapped] <= graph + next_sgn = min(nodes, key=lambda n: min(candidates[n], key=len)) + isomorphs = self._map_nodes( + next_sgn, candidates, constraints, to_be_mapped=nodes + ) + + # This is effectively `yield from isomorphs`, except that we look + # whether an item was yielded. + try: + item = next(isomorphs) + except StopIteration: + pass + else: + yield item + yield from isomorphs + found_iso = True + + # BASECASE + if found_iso or current_size == 1: + # Shrinking has no point because either 1) we end up with a smaller + # common subgraph (and we want the largest), or 2) there'll be no + # more subgraph. + return + + left_to_be_mapped = set() + for nodes in to_be_mapped: + for sgn in nodes: + # We're going to remove sgn from to_be_mapped, but subject to + # symmetry constraints. We know that for every constraint we + # have those subgraph nodes are equal. So whenever we would + # remove the lower part of a constraint, remove the higher + # instead. This is all dealth with by _remove_node. And because + # left_to_be_mapped is a set, we don't do double work. + + # And finally, make the subgraph one node smaller. + # REDUCTION + new_nodes = self._remove_node(sgn, nodes, constraints) + left_to_be_mapped.add(new_nodes) + # COMBINATION + yield from self._largest_common_subgraph( + candidates, constraints, to_be_mapped=left_to_be_mapped + ) + + @staticmethod + def _remove_node(node, nodes, constraints): + """ + Returns a new set where node has been removed from nodes, subject to + symmetry constraints. We know, that for every constraint we have + those subgraph nodes are equal. So whenever we would remove the + lower part of a constraint, remove the higher instead. + """ + while True: + for low, high in constraints: + if low == node and high in nodes: + node = high + break + else: # no break, couldn't find node in constraints + break + return frozenset(nodes - {node}) + + @staticmethod + def _find_permutations(top_partitions, bottom_partitions): + """ + Return the pairs of top/bottom partitions where the partitions are + different. Ensures that all partitions in both top and bottom + partitions have size 1. + """ + # Find permutations + permutations = set() + for top, bot in zip(top_partitions, bottom_partitions): + # top and bot have only one element + if len(top) != 1 or len(bot) != 1: + raise IndexError( + "Not all nodes are coupled. This is" + f" impossible: {top_partitions}, {bottom_partitions}" + ) + if top != bot: + permutations.add(frozenset((next(iter(top)), next(iter(bot))))) + return permutations + + @staticmethod + def _update_orbits(orbits, permutations): + """ + Update orbits based on permutations. Orbits is modified in place. + For every pair of items in permutations their respective orbits are + merged. + """ + for permutation in permutations: + node, node2 = permutation + # Find the orbits that contain node and node2, and replace the + # orbit containing node with the union + first = second = None + for idx, orbit in enumerate(orbits): + if first is not None and second is not None: + break + if node in orbit: + first = idx + if node2 in orbit: + second = idx + if first != second: + orbits[first].update(orbits[second]) + del orbits[second] + + def _couple_nodes( + self, + top_partitions, + bottom_partitions, + pair_idx, + t_node, + b_node, + graph, + edge_colors, + ): + """ + Generate new partitions from top and bottom_partitions where t_node is + coupled to b_node. pair_idx is the index of the partitions where t_ and + b_node can be found. + """ + t_partition = top_partitions[pair_idx] + b_partition = bottom_partitions[pair_idx] + assert t_node in t_partition and b_node in b_partition + # Couple node to node2. This means they get their own partition + new_top_partitions = [top.copy() for top in top_partitions] + new_bottom_partitions = [bot.copy() for bot in bottom_partitions] + new_t_groups = {t_node}, t_partition - {t_node} + new_b_groups = {b_node}, b_partition - {b_node} + # Replace the old partitions with the coupled ones + del new_top_partitions[pair_idx] + del new_bottom_partitions[pair_idx] + new_top_partitions[pair_idx:pair_idx] = new_t_groups + new_bottom_partitions[pair_idx:pair_idx] = new_b_groups + + new_top_partitions = self._refine_node_partitions( + graph, new_top_partitions, edge_colors + ) + new_bottom_partitions = self._refine_node_partitions( + graph, new_bottom_partitions, edge_colors, branch=True + ) + new_top_partitions = list(new_top_partitions) + assert len(new_top_partitions) == 1 + new_top_partitions = new_top_partitions[0] + for bot in new_bottom_partitions: + yield list(new_top_partitions), bot + + def _process_ordered_pair_partitions( + self, + graph, + top_partitions, + bottom_partitions, + edge_colors, + orbits=None, + cosets=None, + ): + """ + Processes ordered pair partitions as per the reference paper. Finds and + returns all permutations and cosets that leave the graph unchanged. + """ + if orbits is None: + orbits = [{node} for node in graph.nodes] + else: + # Note that we don't copy orbits when we are given one. This means + # we leak information between the recursive branches. This is + # intentional! + orbits = orbits + if cosets is None: + cosets = {} + else: + cosets = cosets.copy() + + assert all( + len(t_p) == len(b_p) for t_p, b_p in zip(top_partitions, bottom_partitions) + ) + + # BASECASE + if all(len(top) == 1 for top in top_partitions): + # All nodes are mapped + permutations = self._find_permutations(top_partitions, bottom_partitions) + self._update_orbits(orbits, permutations) + if permutations: + return [permutations], cosets + else: + return [], cosets + + permutations = [] + unmapped_nodes = { + (node, idx) + for idx, t_partition in enumerate(top_partitions) + for node in t_partition + if len(t_partition) > 1 + } + node, pair_idx = min(unmapped_nodes) + b_partition = bottom_partitions[pair_idx] + + for node2 in sorted(b_partition): + if len(b_partition) == 1: + # Can never result in symmetry + continue + if node != node2 and any( + node in orbit and node2 in orbit for orbit in orbits + ): + # Orbit prune branch + continue + # REDUCTION + # Couple node to node2 + partitions = self._couple_nodes( + top_partitions, + bottom_partitions, + pair_idx, + node, + node2, + graph, + edge_colors, + ) + for opp in partitions: + new_top_partitions, new_bottom_partitions = opp + + new_perms, new_cosets = self._process_ordered_pair_partitions( + graph, + new_top_partitions, + new_bottom_partitions, + edge_colors, + orbits, + cosets, + ) + # COMBINATION + permutations += new_perms + cosets.update(new_cosets) + + mapped = { + k + for top, bottom in zip(top_partitions, bottom_partitions) + for k in top + if len(top) == 1 and top == bottom + } + ks = {k for k in graph.nodes if k < node} + # Have all nodes with ID < node been mapped? + find_coset = ks <= mapped and node not in cosets + if find_coset: + # Find the orbit that contains node + for orbit in orbits: + if node in orbit: + cosets[node] = orbit.copy() + return permutations, cosets diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/isomorph.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/isomorph.py new file mode 100644 index 0000000000000000000000000000000000000000..fc3a3fc6a50bf15c49ffc7e4b2b798413cb344b3 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/isomorph.py @@ -0,0 +1,249 @@ +""" +Graph isomorphism functions. +""" + +import networkx as nx +from networkx.exception import NetworkXError + +__all__ = [ + "could_be_isomorphic", + "fast_could_be_isomorphic", + "faster_could_be_isomorphic", + "is_isomorphic", +] + + +@nx._dispatchable(graphs={"G1": 0, "G2": 1}) +def could_be_isomorphic(G1, G2): + """Returns False if graphs are definitely not isomorphic. + True does NOT guarantee isomorphism. + + Parameters + ---------- + G1, G2 : graphs + The two graphs G1 and G2 must be the same type. + + Notes + ----- + Checks for matching degree, triangle, and number of cliques sequences. + The triangle sequence contains the number of triangles each node is part of. + The clique sequence contains for each node the number of maximal cliques + involving that node. + + """ + + # Check global properties + if G1.order() != G2.order(): + return False + + # Check local properties + d1 = G1.degree() + t1 = nx.triangles(G1) + clqs_1 = list(nx.find_cliques(G1)) + c1 = {n: sum(1 for c in clqs_1 if n in c) for n in G1} # number of cliques + props1 = [[d, t1[v], c1[v]] for v, d in d1] + props1.sort() + + d2 = G2.degree() + t2 = nx.triangles(G2) + clqs_2 = list(nx.find_cliques(G2)) + c2 = {n: sum(1 for c in clqs_2 if n in c) for n in G2} # number of cliques + props2 = [[d, t2[v], c2[v]] for v, d in d2] + props2.sort() + + if props1 != props2: + return False + + # OK... + return True + + +graph_could_be_isomorphic = could_be_isomorphic + + +@nx._dispatchable(graphs={"G1": 0, "G2": 1}) +def fast_could_be_isomorphic(G1, G2): + """Returns False if graphs are definitely not isomorphic. + + True does NOT guarantee isomorphism. + + Parameters + ---------- + G1, G2 : graphs + The two graphs G1 and G2 must be the same type. + + Notes + ----- + Checks for matching degree and triangle sequences. The triangle + sequence contains the number of triangles each node is part of. + """ + # Check global properties + if G1.order() != G2.order(): + return False + + # Check local properties + d1 = G1.degree() + t1 = nx.triangles(G1) + props1 = [[d, t1[v]] for v, d in d1] + props1.sort() + + d2 = G2.degree() + t2 = nx.triangles(G2) + props2 = [[d, t2[v]] for v, d in d2] + props2.sort() + + if props1 != props2: + return False + + # OK... + return True + + +fast_graph_could_be_isomorphic = fast_could_be_isomorphic + + +@nx._dispatchable(graphs={"G1": 0, "G2": 1}) +def faster_could_be_isomorphic(G1, G2): + """Returns False if graphs are definitely not isomorphic. + + True does NOT guarantee isomorphism. + + Parameters + ---------- + G1, G2 : graphs + The two graphs G1 and G2 must be the same type. + + Notes + ----- + Checks for matching degree sequences. + """ + # Check global properties + if G1.order() != G2.order(): + return False + + # Check local properties + d1 = sorted(d for n, d in G1.degree()) + d2 = sorted(d for n, d in G2.degree()) + + if d1 != d2: + return False + + # OK... + return True + + +faster_graph_could_be_isomorphic = faster_could_be_isomorphic + + +@nx._dispatchable( + graphs={"G1": 0, "G2": 1}, + preserve_edge_attrs="edge_match", + preserve_node_attrs="node_match", +) +def is_isomorphic(G1, G2, node_match=None, edge_match=None): + """Returns True if the graphs G1 and G2 are isomorphic and False otherwise. + + Parameters + ---------- + G1, G2: graphs + The two graphs G1 and G2 must be the same type. + + node_match : callable + A function that returns True if node n1 in G1 and n2 in G2 should + be considered equal during the isomorphism test. + If node_match is not specified then node attributes are not considered. + + The function will be called like + + node_match(G1.nodes[n1], G2.nodes[n2]). + + That is, the function will receive the node attribute dictionaries + for n1 and n2 as inputs. + + edge_match : callable + A function that returns True if the edge attribute dictionary + for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should + be considered equal during the isomorphism test. If edge_match is + not specified then edge attributes are not considered. + + The function will be called like + + edge_match(G1[u1][v1], G2[u2][v2]). + + That is, the function will receive the edge attribute dictionaries + of the edges under consideration. + + Notes + ----- + Uses the vf2 algorithm [1]_. + + Examples + -------- + >>> import networkx.algorithms.isomorphism as iso + + For digraphs G1 and G2, using 'weight' edge attribute (default: 1) + + >>> G1 = nx.DiGraph() + >>> G2 = nx.DiGraph() + >>> nx.add_path(G1, [1, 2, 3, 4], weight=1) + >>> nx.add_path(G2, [10, 20, 30, 40], weight=2) + >>> em = iso.numerical_edge_match("weight", 1) + >>> nx.is_isomorphic(G1, G2) # no weights considered + True + >>> nx.is_isomorphic(G1, G2, edge_match=em) # match weights + False + + For multidigraphs G1 and G2, using 'fill' node attribute (default: '') + + >>> G1 = nx.MultiDiGraph() + >>> G2 = nx.MultiDiGraph() + >>> G1.add_nodes_from([1, 2, 3], fill="red") + >>> G2.add_nodes_from([10, 20, 30, 40], fill="red") + >>> nx.add_path(G1, [1, 2, 3, 4], weight=3, linewidth=2.5) + >>> nx.add_path(G2, [10, 20, 30, 40], weight=3) + >>> nm = iso.categorical_node_match("fill", "red") + >>> nx.is_isomorphic(G1, G2, node_match=nm) + True + + For multidigraphs G1 and G2, using 'weight' edge attribute (default: 7) + + >>> G1.add_edge(1, 2, weight=7) + 1 + >>> G2.add_edge(10, 20) + 1 + >>> em = iso.numerical_multiedge_match("weight", 7, rtol=1e-6) + >>> nx.is_isomorphic(G1, G2, edge_match=em) + True + + For multigraphs G1 and G2, using 'weight' and 'linewidth' edge attributes + with default values 7 and 2.5. Also using 'fill' node attribute with + default value 'red'. + + >>> em = iso.numerical_multiedge_match(["weight", "linewidth"], [7, 2.5]) + >>> nm = iso.categorical_node_match("fill", "red") + >>> nx.is_isomorphic(G1, G2, edge_match=em, node_match=nm) + True + + See Also + -------- + numerical_node_match, numerical_edge_match, numerical_multiedge_match + categorical_node_match, categorical_edge_match, categorical_multiedge_match + + References + ---------- + .. [1] L. P. Cordella, P. Foggia, C. Sansone, M. Vento, + "An Improved Algorithm for Matching Large Graphs", + 3rd IAPR-TC15 Workshop on Graph-based Representations in + Pattern Recognition, Cuen, pp. 149-159, 2001. + https://www.researchgate.net/publication/200034365_An_Improved_Algorithm_for_Matching_Large_Graphs + """ + if G1.is_directed() and G2.is_directed(): + GM = nx.algorithms.isomorphism.DiGraphMatcher + elif (not G1.is_directed()) and (not G2.is_directed()): + GM = nx.algorithms.isomorphism.GraphMatcher + else: + raise NetworkXError("Graphs G1 and G2 are not of the same type.") + + gm = GM(G1, G2, node_match=node_match, edge_match=edge_match) + + return gm.is_isomorphic() diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/__pycache__/__init__.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/__pycache__/__init__.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..9e683f0ce9302f388e092a5d9be3e624df88e073 Binary files 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0000000000000000000000000000000000000000..0236872094d4c73b0bb132165ce3ec4d1054f5f5 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/si2_b06_m200.B99 differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_ismags.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_ismags.py new file mode 100644 index 0000000000000000000000000000000000000000..bc4070ac5bd5bca33030e537d223373093170040 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_ismags.py @@ -0,0 +1,327 @@ +""" +Tests for ISMAGS isomorphism algorithm. +""" + +import pytest + +import networkx as nx +from networkx.algorithms import isomorphism as iso + + +def _matches_to_sets(matches): + """ + Helper function to facilitate comparing collections of dictionaries in + which order does not matter. + """ + return {frozenset(m.items()) for m in matches} + + +class TestSelfIsomorphism: + data = [ + ( + [ + (0, {"name": "a"}), + (1, {"name": "a"}), + (2, {"name": "b"}), + (3, {"name": "b"}), + (4, {"name": "a"}), + (5, {"name": "a"}), + ], + [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5)], + ), + (range(1, 5), [(1, 2), (2, 4), (4, 3), (3, 1)]), + ( + [], + [ + (0, 1), + (1, 2), + (2, 3), + (3, 4), + (4, 5), + (5, 0), + (0, 6), + (6, 7), + (2, 8), + (8, 9), + (4, 10), + (10, 11), + ], + ), + ([], [(0, 1), (1, 2), (1, 4), (2, 3), (3, 5), (3, 6)]), + ] + + def test_self_isomorphism(self): + """ + For some small, symmetric graphs, make sure that 1) they are isomorphic + to themselves, and 2) that only the identity mapping is found. + """ + for node_data, edge_data in self.data: + graph = nx.Graph() + graph.add_nodes_from(node_data) + graph.add_edges_from(edge_data) + + ismags = iso.ISMAGS( + graph, graph, node_match=iso.categorical_node_match("name", None) + ) + assert ismags.is_isomorphic() + assert ismags.subgraph_is_isomorphic() + assert list(ismags.subgraph_isomorphisms_iter(symmetry=True)) == [ + {n: n for n in graph.nodes} + ] + + def test_edgecase_self_isomorphism(self): + """ + This edgecase is one of the cases in which it is hard to find all + symmetry elements. + """ + graph = nx.Graph() + nx.add_path(graph, range(5)) + graph.add_edges_from([(2, 5), (5, 6)]) + + ismags = iso.ISMAGS(graph, graph) + ismags_answer = list(ismags.find_isomorphisms(True)) + assert ismags_answer == [{n: n for n in graph.nodes}] + + graph = nx.relabel_nodes(graph, {0: 0, 1: 1, 2: 2, 3: 3, 4: 6, 5: 4, 6: 5}) + ismags = iso.ISMAGS(graph, graph) + ismags_answer = list(ismags.find_isomorphisms(True)) + assert ismags_answer == [{n: n for n in graph.nodes}] + + def test_directed_self_isomorphism(self): + """ + For some small, directed, symmetric graphs, make sure that 1) they are + isomorphic to themselves, and 2) that only the identity mapping is + found. + """ + for node_data, edge_data in self.data: + graph = nx.Graph() + graph.add_nodes_from(node_data) + graph.add_edges_from(edge_data) + + ismags = iso.ISMAGS( + graph, graph, node_match=iso.categorical_node_match("name", None) + ) + assert ismags.is_isomorphic() + assert ismags.subgraph_is_isomorphic() + assert list(ismags.subgraph_isomorphisms_iter(symmetry=True)) == [ + {n: n for n in graph.nodes} + ] + + +class TestSubgraphIsomorphism: + def test_isomorphism(self): + g1 = nx.Graph() + nx.add_cycle(g1, range(4)) + + g2 = nx.Graph() + nx.add_cycle(g2, range(4)) + g2.add_edges_from(list(zip(g2, range(4, 8)))) + ismags = iso.ISMAGS(g2, g1) + assert list(ismags.subgraph_isomorphisms_iter(symmetry=True)) == [ + {n: n for n in g1.nodes} + ] + + def test_isomorphism2(self): + g1 = nx.Graph() + nx.add_path(g1, range(3)) + + g2 = g1.copy() + g2.add_edge(1, 3) + + ismags = iso.ISMAGS(g2, g1) + matches = ismags.subgraph_isomorphisms_iter(symmetry=True) + expected_symmetric = [ + {0: 0, 1: 1, 2: 2}, + {0: 0, 1: 1, 3: 2}, + {2: 0, 1: 1, 3: 2}, + ] + assert _matches_to_sets(matches) == _matches_to_sets(expected_symmetric) + + matches = ismags.subgraph_isomorphisms_iter(symmetry=False) + expected_asymmetric = [ + {0: 2, 1: 1, 2: 0}, + {0: 2, 1: 1, 3: 0}, + {2: 2, 1: 1, 3: 0}, + ] + assert _matches_to_sets(matches) == _matches_to_sets( + expected_symmetric + expected_asymmetric + ) + + def test_labeled_nodes(self): + g1 = nx.Graph() + nx.add_cycle(g1, range(3)) + g1.nodes[1]["attr"] = True + + g2 = g1.copy() + g2.add_edge(1, 3) + ismags = iso.ISMAGS(g2, g1, node_match=lambda x, y: x == y) + matches = ismags.subgraph_isomorphisms_iter(symmetry=True) + expected_symmetric = [{0: 0, 1: 1, 2: 2}] + assert _matches_to_sets(matches) == _matches_to_sets(expected_symmetric) + + matches = ismags.subgraph_isomorphisms_iter(symmetry=False) + expected_asymmetric = [{0: 2, 1: 1, 2: 0}] + assert _matches_to_sets(matches) == _matches_to_sets( + expected_symmetric + expected_asymmetric + ) + + def test_labeled_edges(self): + g1 = nx.Graph() + nx.add_cycle(g1, range(3)) + g1.edges[1, 2]["attr"] = True + + g2 = g1.copy() + g2.add_edge(1, 3) + ismags = iso.ISMAGS(g2, g1, edge_match=lambda x, y: x == y) + matches = ismags.subgraph_isomorphisms_iter(symmetry=True) + expected_symmetric = [{0: 0, 1: 1, 2: 2}] + assert _matches_to_sets(matches) == _matches_to_sets(expected_symmetric) + + matches = ismags.subgraph_isomorphisms_iter(symmetry=False) + expected_asymmetric = [{1: 2, 0: 0, 2: 1}] + assert _matches_to_sets(matches) == _matches_to_sets( + expected_symmetric + expected_asymmetric + ) + + +class TestWikipediaExample: + # Nodes 'a', 'b', 'c' and 'd' form a column. + # Nodes 'g', 'h', 'i' and 'j' form a column. + g1edges = [ + ["a", "g"], + ["a", "h"], + ["a", "i"], + ["b", "g"], + ["b", "h"], + ["b", "j"], + ["c", "g"], + ["c", "i"], + ["c", "j"], + ["d", "h"], + ["d", "i"], + ["d", "j"], + ] + + # Nodes 1,2,3,4 form the clockwise corners of a large square. + # Nodes 5,6,7,8 form the clockwise corners of a small square + g2edges = [ + [1, 2], + [2, 3], + [3, 4], + [4, 1], + [5, 6], + [6, 7], + [7, 8], + [8, 5], + [1, 5], + [2, 6], + [3, 7], + [4, 8], + ] + + def test_graph(self): + g1 = nx.Graph() + g2 = nx.Graph() + g1.add_edges_from(self.g1edges) + g2.add_edges_from(self.g2edges) + gm = iso.ISMAGS(g1, g2) + assert gm.is_isomorphic() + + +class TestLargestCommonSubgraph: + def test_mcis(self): + # Example graphs from DOI: 10.1002/spe.588 + graph1 = nx.Graph() + graph1.add_edges_from([(1, 2), (2, 3), (2, 4), (3, 4), (4, 5)]) + graph1.nodes[1]["color"] = 0 + + graph2 = nx.Graph() + graph2.add_edges_from( + [(1, 2), (2, 3), (2, 4), (3, 4), (3, 5), (5, 6), (5, 7), (6, 7)] + ) + graph2.nodes[1]["color"] = 1 + graph2.nodes[6]["color"] = 2 + graph2.nodes[7]["color"] = 2 + + ismags = iso.ISMAGS( + graph1, graph2, node_match=iso.categorical_node_match("color", None) + ) + assert list(ismags.subgraph_isomorphisms_iter(True)) == [] + assert list(ismags.subgraph_isomorphisms_iter(False)) == [] + found_mcis = _matches_to_sets(ismags.largest_common_subgraph()) + expected = _matches_to_sets( + [{2: 2, 3: 4, 4: 3, 5: 5}, {2: 4, 3: 2, 4: 3, 5: 5}] + ) + assert expected == found_mcis + + ismags = iso.ISMAGS( + graph2, graph1, node_match=iso.categorical_node_match("color", None) + ) + assert list(ismags.subgraph_isomorphisms_iter(True)) == [] + assert list(ismags.subgraph_isomorphisms_iter(False)) == [] + found_mcis = _matches_to_sets(ismags.largest_common_subgraph()) + # Same answer, but reversed. + expected = _matches_to_sets( + [{2: 2, 3: 4, 4: 3, 5: 5}, {4: 2, 2: 3, 3: 4, 5: 5}] + ) + assert expected == found_mcis + + def test_symmetry_mcis(self): + graph1 = nx.Graph() + nx.add_path(graph1, range(4)) + + graph2 = nx.Graph() + nx.add_path(graph2, range(3)) + graph2.add_edge(1, 3) + + # Only the symmetry of graph2 is taken into account here. + ismags1 = iso.ISMAGS( + graph1, graph2, node_match=iso.categorical_node_match("color", None) + ) + assert list(ismags1.subgraph_isomorphisms_iter(True)) == [] + found_mcis = _matches_to_sets(ismags1.largest_common_subgraph()) + expected = _matches_to_sets([{0: 0, 1: 1, 2: 2}, {1: 0, 3: 2, 2: 1}]) + assert expected == found_mcis + + # Only the symmetry of graph1 is taken into account here. + ismags2 = iso.ISMAGS( + graph2, graph1, node_match=iso.categorical_node_match("color", None) + ) + assert list(ismags2.subgraph_isomorphisms_iter(True)) == [] + found_mcis = _matches_to_sets(ismags2.largest_common_subgraph()) + expected = _matches_to_sets( + [ + {3: 2, 0: 0, 1: 1}, + {2: 0, 0: 2, 1: 1}, + {3: 0, 0: 2, 1: 1}, + {3: 0, 1: 1, 2: 2}, + {0: 0, 1: 1, 2: 2}, + {2: 0, 3: 2, 1: 1}, + ] + ) + + assert expected == found_mcis + + found_mcis1 = _matches_to_sets(ismags1.largest_common_subgraph(False)) + found_mcis2 = ismags2.largest_common_subgraph(False) + found_mcis2 = [{v: k for k, v in d.items()} for d in found_mcis2] + found_mcis2 = _matches_to_sets(found_mcis2) + + expected = _matches_to_sets( + [ + {3: 2, 1: 3, 2: 1}, + {2: 0, 0: 2, 1: 1}, + {1: 2, 3: 3, 2: 1}, + {3: 0, 1: 3, 2: 1}, + {0: 2, 2: 3, 1: 1}, + {3: 0, 1: 2, 2: 1}, + {2: 0, 0: 3, 1: 1}, + {0: 0, 2: 3, 1: 1}, + {1: 0, 3: 3, 2: 1}, + {1: 0, 3: 2, 2: 1}, + {0: 3, 1: 1, 2: 2}, + {0: 0, 1: 1, 2: 2}, + ] + ) + assert expected == found_mcis1 + assert expected == found_mcis2 diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_isomorphism.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_isomorphism.py new file mode 100644 index 0000000000000000000000000000000000000000..548af808ffd93a32dfe91b7b372b6c3e45a206bf --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_isomorphism.py @@ -0,0 +1,48 @@ +import pytest + +import networkx as nx +from networkx.algorithms import isomorphism as iso + + +class TestIsomorph: + @classmethod + def setup_class(cls): + cls.G1 = nx.Graph() + cls.G2 = nx.Graph() + cls.G3 = nx.Graph() + cls.G4 = nx.Graph() + cls.G5 = nx.Graph() + cls.G6 = nx.Graph() + cls.G1.add_edges_from([[1, 2], [1, 3], [1, 5], [2, 3]]) + cls.G2.add_edges_from([[10, 20], [20, 30], [10, 30], [10, 50]]) + cls.G3.add_edges_from([[1, 2], [1, 3], [1, 5], [2, 5]]) + cls.G4.add_edges_from([[1, 2], [1, 3], [1, 5], [2, 4]]) + cls.G5.add_edges_from([[1, 2], [1, 3]]) + cls.G6.add_edges_from([[10, 20], [20, 30], [10, 30], [10, 50], [20, 50]]) + + def test_could_be_isomorphic(self): + assert iso.could_be_isomorphic(self.G1, self.G2) + assert iso.could_be_isomorphic(self.G1, self.G3) + assert not iso.could_be_isomorphic(self.G1, self.G4) + assert iso.could_be_isomorphic(self.G3, self.G2) + assert not iso.could_be_isomorphic(self.G1, self.G6) + + def test_fast_could_be_isomorphic(self): + assert iso.fast_could_be_isomorphic(self.G3, self.G2) + assert not iso.fast_could_be_isomorphic(self.G3, self.G5) + assert not iso.fast_could_be_isomorphic(self.G1, self.G6) + + def test_faster_could_be_isomorphic(self): + assert iso.faster_could_be_isomorphic(self.G3, self.G2) + assert not iso.faster_could_be_isomorphic(self.G3, self.G5) + assert not iso.faster_could_be_isomorphic(self.G1, self.G6) + + def test_is_isomorphic(self): + assert iso.is_isomorphic(self.G1, self.G2) + assert not iso.is_isomorphic(self.G1, self.G4) + assert iso.is_isomorphic(self.G1.to_directed(), self.G2.to_directed()) + assert not iso.is_isomorphic(self.G1.to_directed(), self.G4.to_directed()) + with pytest.raises( + nx.NetworkXError, match="Graphs G1 and G2 are not of the same type." + ): + iso.is_isomorphic(self.G1.to_directed(), self.G1) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_temporalisomorphvf2.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_temporalisomorphvf2.py new file mode 100644 index 0000000000000000000000000000000000000000..1fe70a42869e4fd1501ae90b849bfb4de50eda2e --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_temporalisomorphvf2.py @@ -0,0 +1,212 @@ +""" +Tests for the temporal aspect of the Temporal VF2 isomorphism algorithm. +""" + +from datetime import date, datetime, timedelta + +import networkx as nx +from networkx.algorithms import isomorphism as iso + + +def provide_g1_edgelist(): + return [(0, 1), (0, 2), (1, 2), (2, 4), (1, 3), (3, 4), (4, 5)] + + +def put_same_time(G, att_name): + for e in G.edges(data=True): + e[2][att_name] = date(2015, 1, 1) + return G + + +def put_same_datetime(G, att_name): + for e in G.edges(data=True): + e[2][att_name] = datetime(2015, 1, 1) + return G + + +def put_sequence_time(G, att_name): + current_date = date(2015, 1, 1) + for e in G.edges(data=True): + current_date += timedelta(days=1) + e[2][att_name] = current_date + return G + + +def put_time_config_0(G, att_name): + G[0][1][att_name] = date(2015, 1, 2) + G[0][2][att_name] = date(2015, 1, 2) + G[1][2][att_name] = date(2015, 1, 3) + G[1][3][att_name] = date(2015, 1, 1) + G[2][4][att_name] = date(2015, 1, 1) + G[3][4][att_name] = date(2015, 1, 3) + G[4][5][att_name] = date(2015, 1, 3) + return G + + +def put_time_config_1(G, att_name): + G[0][1][att_name] = date(2015, 1, 2) + G[0][2][att_name] = date(2015, 1, 1) + G[1][2][att_name] = date(2015, 1, 3) + G[1][3][att_name] = date(2015, 1, 1) + G[2][4][att_name] = date(2015, 1, 2) + G[3][4][att_name] = date(2015, 1, 4) + G[4][5][att_name] = date(2015, 1, 3) + return G + + +def put_time_config_2(G, att_name): + G[0][1][att_name] = date(2015, 1, 1) + G[0][2][att_name] = date(2015, 1, 1) + G[1][2][att_name] = date(2015, 1, 3) + G[1][3][att_name] = date(2015, 1, 2) + G[2][4][att_name] = date(2015, 1, 2) + G[3][4][att_name] = date(2015, 1, 3) + G[4][5][att_name] = date(2015, 1, 2) + return G + + +class TestTimeRespectingGraphMatcher: + """ + A test class for the undirected temporal graph matcher. + """ + + def provide_g1_topology(self): + G1 = nx.Graph() + G1.add_edges_from(provide_g1_edgelist()) + return G1 + + def provide_g2_path_3edges(self): + G2 = nx.Graph() + G2.add_edges_from([(0, 1), (1, 2), (2, 3)]) + return G2 + + def test_timdelta_zero_timeRespecting_returnsTrue(self): + G1 = self.provide_g1_topology() + temporal_name = "date" + G1 = put_same_time(G1, temporal_name) + G2 = self.provide_g2_path_3edges() + d = timedelta() + gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d) + assert gm.subgraph_is_isomorphic() + + def test_timdelta_zero_datetime_timeRespecting_returnsTrue(self): + G1 = self.provide_g1_topology() + temporal_name = "date" + G1 = put_same_datetime(G1, temporal_name) + G2 = self.provide_g2_path_3edges() + d = timedelta() + gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d) + assert gm.subgraph_is_isomorphic() + + def test_attNameStrange_timdelta_zero_timeRespecting_returnsTrue(self): + G1 = self.provide_g1_topology() + temporal_name = "strange_name" + G1 = put_same_time(G1, temporal_name) + G2 = self.provide_g2_path_3edges() + d = timedelta() + gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d) + assert gm.subgraph_is_isomorphic() + + def test_notTimeRespecting_returnsFalse(self): + G1 = self.provide_g1_topology() + temporal_name = "date" + G1 = put_sequence_time(G1, temporal_name) + G2 = self.provide_g2_path_3edges() + d = timedelta() + gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d) + assert not gm.subgraph_is_isomorphic() + + def test_timdelta_one_config0_returns_no_embeddings(self): + G1 = self.provide_g1_topology() + temporal_name = "date" + G1 = put_time_config_0(G1, temporal_name) + G2 = self.provide_g2_path_3edges() + d = timedelta(days=1) + gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d) + count_match = len(list(gm.subgraph_isomorphisms_iter())) + assert count_match == 0 + + def test_timdelta_one_config1_returns_four_embedding(self): + G1 = self.provide_g1_topology() + temporal_name = "date" + G1 = put_time_config_1(G1, temporal_name) + G2 = self.provide_g2_path_3edges() + d = timedelta(days=1) + gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d) + count_match = len(list(gm.subgraph_isomorphisms_iter())) + assert count_match == 4 + + def test_timdelta_one_config2_returns_ten_embeddings(self): + G1 = self.provide_g1_topology() + temporal_name = "date" + G1 = put_time_config_2(G1, temporal_name) + G2 = self.provide_g2_path_3edges() + d = timedelta(days=1) + gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d) + L = list(gm.subgraph_isomorphisms_iter()) + count_match = len(list(gm.subgraph_isomorphisms_iter())) + assert count_match == 10 + + +class TestDiTimeRespectingGraphMatcher: + """ + A test class for the directed time-respecting graph matcher. + """ + + def provide_g1_topology(self): + G1 = nx.DiGraph() + G1.add_edges_from(provide_g1_edgelist()) + return G1 + + def provide_g2_path_3edges(self): + G2 = nx.DiGraph() + G2.add_edges_from([(0, 1), (1, 2), (2, 3)]) + return G2 + + def test_timdelta_zero_same_dates_returns_true(self): + G1 = self.provide_g1_topology() + temporal_name = "date" + G1 = put_same_time(G1, temporal_name) + G2 = self.provide_g2_path_3edges() + d = timedelta() + gm = iso.TimeRespectingDiGraphMatcher(G1, G2, temporal_name, d) + assert gm.subgraph_is_isomorphic() + + def test_attNameStrange_timdelta_zero_same_dates_returns_true(self): + G1 = self.provide_g1_topology() + temporal_name = "strange" + G1 = put_same_time(G1, temporal_name) + G2 = self.provide_g2_path_3edges() + d = timedelta() + gm = iso.TimeRespectingDiGraphMatcher(G1, G2, temporal_name, d) + assert gm.subgraph_is_isomorphic() + + def test_timdelta_one_config0_returns_no_embeddings(self): + G1 = self.provide_g1_topology() + temporal_name = "date" + G1 = put_time_config_0(G1, temporal_name) + G2 = self.provide_g2_path_3edges() + d = timedelta(days=1) + gm = iso.TimeRespectingDiGraphMatcher(G1, G2, temporal_name, d) + count_match = len(list(gm.subgraph_isomorphisms_iter())) + assert count_match == 0 + + def test_timdelta_one_config1_returns_one_embedding(self): + G1 = self.provide_g1_topology() + temporal_name = "date" + G1 = put_time_config_1(G1, temporal_name) + G2 = self.provide_g2_path_3edges() + d = timedelta(days=1) + gm = iso.TimeRespectingDiGraphMatcher(G1, G2, temporal_name, d) + count_match = len(list(gm.subgraph_isomorphisms_iter())) + assert count_match == 1 + + def test_timdelta_one_config2_returns_two_embeddings(self): + G1 = self.provide_g1_topology() + temporal_name = "date" + G1 = put_time_config_2(G1, temporal_name) + G2 = self.provide_g2_path_3edges() + d = timedelta(days=1) + gm = iso.TimeRespectingDiGraphMatcher(G1, G2, temporal_name, d) + count_match = len(list(gm.subgraph_isomorphisms_iter())) + assert count_match == 2 diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_tree_isomorphism.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_tree_isomorphism.py new file mode 100644 index 0000000000000000000000000000000000000000..fa1ab9bbaeff8d27b39e957acbec7a024c10116a --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_tree_isomorphism.py @@ -0,0 +1,292 @@ +import random +import time + +import pytest + +import networkx as nx +from networkx.algorithms.isomorphism.tree_isomorphism import ( + rooted_tree_isomorphism, + tree_isomorphism, +) +from networkx.classes.function import is_directed + + +@pytest.mark.parametrize("graph_constructor", (nx.DiGraph, nx.MultiGraph)) +def test_tree_isomorphism_raises_on_directed_and_multigraphs(graph_constructor): + t1 = graph_constructor([(0, 1)]) + t2 = graph_constructor([(1, 2)]) + with pytest.raises(nx.NetworkXNotImplemented): + nx.isomorphism.tree_isomorphism(t1, t2) + + +# have this work for graph +# given two trees (either the directed or undirected) +# transform t2 according to the isomorphism +# and confirm it is identical to t1 +# randomize the order of the edges when constructing +def check_isomorphism(t1, t2, isomorphism): + # get the name of t1, given the name in t2 + mapping = {v2: v1 for (v1, v2) in isomorphism} + + # these should be the same + d1 = is_directed(t1) + d2 = is_directed(t2) + assert d1 == d2 + + edges_1 = [] + for u, v in t1.edges(): + if d1: + edges_1.append((u, v)) + else: + # if not directed, then need to + # put the edge in a consistent direction + if u < v: + edges_1.append((u, v)) + else: + edges_1.append((v, u)) + + edges_2 = [] + for u, v in t2.edges(): + # translate to names for t1 + u = mapping[u] + v = mapping[v] + if d2: + edges_2.append((u, v)) + else: + if u < v: + edges_2.append((u, v)) + else: + edges_2.append((v, u)) + + return sorted(edges_1) == sorted(edges_2) + + +def test_hardcoded(): + print("hardcoded test") + + # define a test problem + edges_1 = [ + ("a", "b"), + ("a", "c"), + ("a", "d"), + ("b", "e"), + ("b", "f"), + ("e", "j"), + ("e", "k"), + ("c", "g"), + ("c", "h"), + ("g", "m"), + ("d", "i"), + ("f", "l"), + ] + + edges_2 = [ + ("v", "y"), + ("v", "z"), + ("u", "x"), + ("q", "u"), + ("q", "v"), + ("p", "t"), + ("n", "p"), + ("n", "q"), + ("n", "o"), + ("o", "r"), + ("o", "s"), + ("s", "w"), + ] + + # there are two possible correct isomorphisms + # it currently returns isomorphism1 + # but the second is also correct + isomorphism1 = [ + ("a", "n"), + ("b", "q"), + ("c", "o"), + ("d", "p"), + ("e", "v"), + ("f", "u"), + ("g", "s"), + ("h", "r"), + ("i", "t"), + ("j", "y"), + ("k", "z"), + ("l", "x"), + ("m", "w"), + ] + + # could swap y and z + isomorphism2 = [ + ("a", "n"), + ("b", "q"), + ("c", "o"), + ("d", "p"), + ("e", "v"), + ("f", "u"), + ("g", "s"), + ("h", "r"), + ("i", "t"), + ("j", "z"), + ("k", "y"), + ("l", "x"), + ("m", "w"), + ] + + t1 = nx.Graph() + t1.add_edges_from(edges_1) + root1 = "a" + + t2 = nx.Graph() + t2.add_edges_from(edges_2) + root2 = "n" + + isomorphism = sorted(rooted_tree_isomorphism(t1, root1, t2, root2)) + + # is correct by hand + assert isomorphism in (isomorphism1, isomorphism2) + + # check algorithmically + assert check_isomorphism(t1, t2, isomorphism) + + # try again as digraph + t1 = nx.DiGraph() + t1.add_edges_from(edges_1) + root1 = "a" + + t2 = nx.DiGraph() + t2.add_edges_from(edges_2) + root2 = "n" + + isomorphism = sorted(rooted_tree_isomorphism(t1, root1, t2, root2)) + + # is correct by hand + assert isomorphism in (isomorphism1, isomorphism2) + + # check algorithmically + assert check_isomorphism(t1, t2, isomorphism) + + +# randomly swap a tuple (a,b) +def random_swap(t): + (a, b) = t + if random.randint(0, 1) == 1: + return (a, b) + else: + return (b, a) + + +# given a tree t1, create a new tree t2 +# that is isomorphic to t1, with a known isomorphism +# and test that our algorithm found the right one +def positive_single_tree(t1): + assert nx.is_tree(t1) + + nodes1 = list(t1.nodes()) + # get a random permutation of this + nodes2 = nodes1.copy() + random.shuffle(nodes2) + + # this is one isomorphism, however they may be multiple + # so we don't necessarily get this one back + someisomorphism = list(zip(nodes1, nodes2)) + + # map from old to new + map1to2 = dict(someisomorphism) + + # get the edges with the transformed names + edges2 = [random_swap((map1to2[u], map1to2[v])) for (u, v) in t1.edges()] + # randomly permute, to ensure we're not relying on edge order somehow + random.shuffle(edges2) + + # so t2 is isomorphic to t1 + t2 = nx.Graph() + t2.add_edges_from(edges2) + + # lets call our code to see if t1 and t2 are isomorphic + isomorphism = tree_isomorphism(t1, t2) + + # make sure we got a correct solution + # although not necessarily someisomorphism + assert len(isomorphism) > 0 + assert check_isomorphism(t1, t2, isomorphism) + + +# run positive_single_tree over all the +# non-isomorphic trees for k from 4 to maxk +# k = 4 is the first level that has more than 1 non-isomorphic tree +# k = 13 takes about 2.86 seconds to run on my laptop +# larger values run slow down significantly +# as the number of trees grows rapidly +def test_positive(maxk=14): + print("positive test") + + for k in range(2, maxk + 1): + start_time = time.time() + trial = 0 + for t in nx.nonisomorphic_trees(k): + positive_single_tree(t) + trial += 1 + print(k, trial, time.time() - start_time) + + +# test the trivial case of a single node in each tree +# note that nonisomorphic_trees doesn't work for k = 1 +def test_trivial(): + print("trivial test") + + # back to an undirected graph + t1 = nx.Graph() + t1.add_node("a") + root1 = "a" + + t2 = nx.Graph() + t2.add_node("n") + root2 = "n" + + isomorphism = rooted_tree_isomorphism(t1, root1, t2, root2) + + assert isomorphism == [("a", "n")] + + assert check_isomorphism(t1, t2, isomorphism) + + +# test another trivial case where the two graphs have +# different numbers of nodes +def test_trivial_2(): + print("trivial test 2") + + edges_1 = [("a", "b"), ("a", "c")] + + edges_2 = [("v", "y")] + + t1 = nx.Graph() + t1.add_edges_from(edges_1) + + t2 = nx.Graph() + t2.add_edges_from(edges_2) + + isomorphism = tree_isomorphism(t1, t2) + + # they cannot be isomorphic, + # since they have different numbers of nodes + assert isomorphism == [] + + +# the function nonisomorphic_trees generates all the non-isomorphic +# trees of a given size. Take each pair of these and verify that +# they are not isomorphic +# k = 4 is the first level that has more than 1 non-isomorphic tree +# k = 11 takes about 4.76 seconds to run on my laptop +# larger values run slow down significantly +# as the number of trees grows rapidly +def test_negative(maxk=11): + print("negative test") + + for k in range(4, maxk + 1): + test_trees = list(nx.nonisomorphic_trees(k)) + start_time = time.time() + trial = 0 + for i in range(len(test_trees) - 1): + for j in range(i + 1, len(test_trees)): + trial += 1 + assert tree_isomorphism(test_trees[i], test_trees[j]) == [] + print(k, trial, time.time() - start_time) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_vf2pp.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_vf2pp.py new file mode 100644 index 0000000000000000000000000000000000000000..5f3fb901cc8afdc2a73cfb7001538db49371eaf4 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_vf2pp.py @@ -0,0 +1,1608 @@ +import itertools as it + +import pytest + +import networkx as nx +from networkx import vf2pp_is_isomorphic, vf2pp_isomorphism + +labels_same = ["blue"] + +labels_many = [ + "white", + "red", + "blue", + "green", + "orange", + "black", + "purple", + "yellow", + "brown", + "cyan", + "solarized", + "pink", + "none", +] + + +class TestPreCheck: + def test_first_graph_empty(self): + G1 = nx.Graph() + G2 = nx.Graph([(0, 1), (1, 2)]) + assert not vf2pp_is_isomorphic(G1, G2) + + def test_second_graph_empty(self): + G1 = nx.Graph([(0, 1), (1, 2)]) + G2 = nx.Graph() + assert not vf2pp_is_isomorphic(G1, G2) + + def test_different_order1(self): + G1 = nx.path_graph(5) + G2 = nx.path_graph(6) + assert not vf2pp_is_isomorphic(G1, G2) + + def test_different_order2(self): + G1 = nx.barbell_graph(100, 20) + G2 = nx.barbell_graph(101, 20) + assert not vf2pp_is_isomorphic(G1, G2) + + def test_different_order3(self): + G1 = nx.complete_graph(7) + G2 = nx.complete_graph(8) + assert not vf2pp_is_isomorphic(G1, G2) + + def test_different_degree_sequences1(self): + G1 = nx.Graph([(0, 1), (0, 2), (1, 2), (1, 3), (0, 4)]) + G2 = nx.Graph([(0, 1), (0, 2), (1, 2), (1, 3), (0, 4), (2, 5)]) + assert not vf2pp_is_isomorphic(G1, G2) + + G2.remove_node(3) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(["a"]))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle("a"))), "label") + + assert vf2pp_is_isomorphic(G1, G2) + + def test_different_degree_sequences2(self): + G1 = nx.Graph( + [ + (0, 1), + (1, 2), + (0, 2), + (2, 3), + (3, 4), + (4, 5), + (5, 6), + (6, 3), + (4, 7), + (7, 8), + (8, 3), + ] + ) + G2 = G1.copy() + G2.add_edge(8, 0) + assert not vf2pp_is_isomorphic(G1, G2) + + G1.add_edge(6, 1) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(["a"]))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle("a"))), "label") + + assert vf2pp_is_isomorphic(G1, G2) + + def test_different_degree_sequences3(self): + G1 = nx.Graph([(0, 1), (0, 2), (1, 2), (2, 3), (2, 4), (3, 4), (2, 5), (2, 6)]) + G2 = nx.Graph( + [(0, 1), (0, 6), (0, 2), (1, 2), (2, 3), (2, 4), (3, 4), (2, 5), (2, 6)] + ) + assert not vf2pp_is_isomorphic(G1, G2) + + G1.add_edge(3, 5) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(["a"]))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle("a"))), "label") + + assert vf2pp_is_isomorphic(G1, G2) + + def test_label_distribution(self): + G1 = nx.Graph([(0, 1), (0, 2), (1, 2), (2, 3), (2, 4), (3, 4), (2, 5), (2, 6)]) + G2 = nx.Graph([(0, 1), (0, 2), (1, 2), (2, 3), (2, 4), (3, 4), (2, 5), (2, 6)]) + + colors1 = ["blue", "blue", "blue", "yellow", "black", "purple", "purple"] + colors2 = ["blue", "blue", "yellow", "yellow", "black", "purple", "purple"] + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(colors1[::-1]))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(colors2[::-1]))), "label") + + assert not vf2pp_is_isomorphic(G1, G2, node_label="label") + G2.nodes[3]["label"] = "blue" + assert vf2pp_is_isomorphic(G1, G2, node_label="label") + + +class TestAllGraphTypesEdgeCases: + @pytest.mark.parametrize("graph_type", (nx.Graph, nx.MultiGraph, nx.DiGraph)) + def test_both_graphs_empty(self, graph_type): + G = graph_type() + H = graph_type() + assert vf2pp_isomorphism(G, H) is None + + G.add_node(0) + + assert vf2pp_isomorphism(G, H) is None + assert vf2pp_isomorphism(H, G) is None + + H.add_node(0) + assert vf2pp_isomorphism(G, H) == {0: 0} + + @pytest.mark.parametrize("graph_type", (nx.Graph, nx.MultiGraph, nx.DiGraph)) + def test_first_graph_empty(self, graph_type): + G = graph_type() + H = graph_type([(0, 1)]) + assert vf2pp_isomorphism(G, H) is None + + @pytest.mark.parametrize("graph_type", (nx.Graph, nx.MultiGraph, nx.DiGraph)) + def test_second_graph_empty(self, graph_type): + G = graph_type([(0, 1)]) + H = graph_type() + assert vf2pp_isomorphism(G, H) is None + + +class TestGraphISOVF2pp: + def test_custom_graph1_same_labels(self): + G1 = nx.Graph() + + mapped = {1: "A", 2: "B", 3: "C", 4: "D", 5: "Z", 6: "E"} + edges1 = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 6), (3, 4), (5, 1), (5, 2)] + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label") + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Add edge making G1 symmetrical + G1.add_edge(3, 7) + G1.nodes[7]["label"] = "blue" + assert vf2pp_isomorphism(G1, G2, node_label="label") is None + + # Make G2 isomorphic to G1 + G2.add_edges_from([(mapped[3], "X"), (mapped[6], mapped[5])]) + G1.add_edge(4, 7) + G2.nodes["X"]["label"] = "blue" + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Re-structure maintaining isomorphism + G1.remove_edges_from([(1, 4), (1, 3)]) + G2.remove_edges_from([(mapped[1], mapped[5]), (mapped[1], mapped[2])]) + assert vf2pp_isomorphism(G1, G2, node_label="label") + + def test_custom_graph1_different_labels(self): + G1 = nx.Graph() + + mapped = {1: "A", 2: "B", 3: "C", 4: "D", 5: "Z", 6: "E"} + edges1 = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 6), (3, 4), (5, 1), (5, 2)] + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label") + nx.set_node_attributes( + G2, + dict(zip([mapped[n] for n in G1], it.cycle(labels_many))), + "label", + ) + assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped + + def test_custom_graph2_same_labels(self): + G1 = nx.Graph() + + mapped = {1: "A", 2: "C", 3: "D", 4: "E", 5: "G", 7: "B", 6: "F"} + edges1 = [(1, 2), (1, 5), (5, 6), (2, 3), (2, 4), (3, 4), (4, 5), (2, 7)] + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label") + + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Obtain two isomorphic subgraphs from the graph + G2.remove_edge(mapped[1], mapped[2]) + G2.add_edge(mapped[1], mapped[4]) + H1 = nx.Graph(G1.subgraph([2, 3, 4, 7])) + H2 = nx.Graph(G2.subgraph([mapped[1], mapped[4], mapped[5], mapped[6]])) + assert vf2pp_isomorphism(H1, H2, node_label="label") + + # Add edges maintaining isomorphism + H1.add_edges_from([(3, 7), (4, 7)]) + H2.add_edges_from([(mapped[1], mapped[6]), (mapped[4], mapped[6])]) + assert vf2pp_isomorphism(H1, H2, node_label="label") + + def test_custom_graph2_different_labels(self): + G1 = nx.Graph() + + mapped = {1: "A", 2: "C", 3: "D", 4: "E", 5: "G", 7: "B", 6: "F"} + edges1 = [(1, 2), (1, 5), (5, 6), (2, 3), (2, 4), (3, 4), (4, 5), (2, 7)] + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label") + nx.set_node_attributes( + G2, + dict(zip([mapped[n] for n in G1], it.cycle(labels_many))), + "label", + ) + + # Adding new nodes + G1.add_node(0) + G2.add_node("Z") + G1.nodes[0]["label"] = G1.nodes[1]["label"] + G2.nodes["Z"]["label"] = G1.nodes[1]["label"] + mapped.update({0: "Z"}) + + assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped + + # Change the color of one of the nodes + G2.nodes["Z"]["label"] = G1.nodes[2]["label"] + assert vf2pp_isomorphism(G1, G2, node_label="label") is None + + # Add an extra edge + G1.nodes[0]["label"] = "blue" + G2.nodes["Z"]["label"] = "blue" + G1.add_edge(0, 1) + + assert vf2pp_isomorphism(G1, G2, node_label="label") is None + + # Add extra edge to both + G2.add_edge("Z", "A") + assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped + + def test_custom_graph3_same_labels(self): + G1 = nx.Graph() + + mapped = {1: 9, 2: 8, 3: 7, 4: 6, 5: 3, 8: 5, 9: 4, 7: 1, 6: 2} + edges1 = [ + (1, 2), + (1, 3), + (2, 3), + (3, 4), + (4, 5), + (4, 7), + (4, 9), + (5, 8), + (8, 9), + (5, 6), + (6, 7), + (5, 2), + ] + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label") + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Connect nodes maintaining symmetry + G1.add_edges_from([(6, 9), (7, 8)]) + G2.add_edges_from([(mapped[6], mapped[8]), (mapped[7], mapped[9])]) + assert vf2pp_isomorphism(G1, G2, node_label="label") is None + + # Make isomorphic + G1.add_edges_from([(6, 8), (7, 9)]) + G2.add_edges_from([(mapped[6], mapped[9]), (mapped[7], mapped[8])]) + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Connect more nodes + G1.add_edges_from([(2, 7), (3, 6)]) + G2.add_edges_from([(mapped[2], mapped[7]), (mapped[3], mapped[6])]) + G1.add_node(10) + G2.add_node("Z") + G1.nodes[10]["label"] = "blue" + G2.nodes["Z"]["label"] = "blue" + + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Connect the newly added node, to opposite sides of the graph + G1.add_edges_from([(10, 1), (10, 5), (10, 8)]) + G2.add_edges_from([("Z", mapped[1]), ("Z", mapped[4]), ("Z", mapped[9])]) + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Get two subgraphs that are not isomorphic but are easy to make + H1 = nx.Graph(G1.subgraph([2, 3, 4, 5, 6, 7, 10])) + H2 = nx.Graph( + G2.subgraph( + [mapped[4], mapped[5], mapped[6], mapped[7], mapped[8], mapped[9], "Z"] + ) + ) + assert vf2pp_isomorphism(H1, H2, node_label="label") is None + + # Restructure both to make them isomorphic + H1.add_edges_from([(10, 2), (10, 6), (3, 6), (2, 7), (2, 6), (3, 7)]) + H2.add_edges_from( + [("Z", mapped[7]), (mapped[6], mapped[9]), (mapped[7], mapped[8])] + ) + assert vf2pp_isomorphism(H1, H2, node_label="label") + + # Add edges with opposite direction in each Graph + H1.add_edge(3, 5) + H2.add_edge(mapped[5], mapped[7]) + assert vf2pp_isomorphism(H1, H2, node_label="label") is None + + def test_custom_graph3_different_labels(self): + G1 = nx.Graph() + + mapped = {1: 9, 2: 8, 3: 7, 4: 6, 5: 3, 8: 5, 9: 4, 7: 1, 6: 2} + edges1 = [ + (1, 2), + (1, 3), + (2, 3), + (3, 4), + (4, 5), + (4, 7), + (4, 9), + (5, 8), + (8, 9), + (5, 6), + (6, 7), + (5, 2), + ] + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label") + nx.set_node_attributes( + G2, + dict(zip([mapped[n] for n in G1], it.cycle(labels_many))), + "label", + ) + assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped + + # Add extra edge to G1 + G1.add_edge(1, 7) + assert vf2pp_isomorphism(G1, G2, node_label="label") is None + + # Compensate in G2 + G2.add_edge(9, 1) + assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped + + # Add extra node + G1.add_node("A") + G2.add_node("K") + G1.nodes["A"]["label"] = "green" + G2.nodes["K"]["label"] = "green" + mapped.update({"A": "K"}) + + assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped + + # Connect A to one side of G1 and K to the opposite + G1.add_edge("A", 6) + G2.add_edge("K", 5) + assert vf2pp_isomorphism(G1, G2, node_label="label") is None + + # Make the graphs symmetrical + G1.add_edge(1, 5) + G1.add_edge(2, 9) + G2.add_edge(9, 3) + G2.add_edge(8, 4) + assert vf2pp_isomorphism(G1, G2, node_label="label") is None + + # Assign same colors so the two opposite sides are identical + for node in G1.nodes(): + color = "red" + G1.nodes[node]["label"] = color + G2.nodes[mapped[node]]["label"] = color + + assert vf2pp_isomorphism(G1, G2, node_label="label") + + def test_custom_graph4_different_labels(self): + G1 = nx.Graph() + edges1 = [ + (1, 2), + (2, 3), + (3, 8), + (3, 4), + (4, 5), + (4, 6), + (3, 6), + (8, 7), + (8, 9), + (5, 9), + (10, 11), + (11, 12), + (12, 13), + (11, 13), + ] + + mapped = { + 1: "n", + 2: "m", + 3: "l", + 4: "j", + 5: "k", + 6: "i", + 7: "g", + 8: "h", + 9: "f", + 10: "b", + 11: "a", + 12: "d", + 13: "e", + } + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label") + nx.set_node_attributes( + G2, + dict(zip([mapped[n] for n in G1], it.cycle(labels_many))), + "label", + ) + assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped + + def test_custom_graph4_same_labels(self): + G1 = nx.Graph() + edges1 = [ + (1, 2), + (2, 3), + (3, 8), + (3, 4), + (4, 5), + (4, 6), + (3, 6), + (8, 7), + (8, 9), + (5, 9), + (10, 11), + (11, 12), + (12, 13), + (11, 13), + ] + + mapped = { + 1: "n", + 2: "m", + 3: "l", + 4: "j", + 5: "k", + 6: "i", + 7: "g", + 8: "h", + 9: "f", + 10: "b", + 11: "a", + 12: "d", + 13: "e", + } + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label") + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Add nodes of different label + G1.add_node(0) + G2.add_node("z") + G1.nodes[0]["label"] = "green" + G2.nodes["z"]["label"] = "blue" + + assert vf2pp_isomorphism(G1, G2, node_label="label") is None + + # Make the labels identical + G2.nodes["z"]["label"] = "green" + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Change the structure of the graphs, keeping them isomorphic + G1.add_edge(2, 5) + G2.remove_edge("i", "l") + G2.add_edge("g", "l") + G2.add_edge("m", "f") + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Change the structure of the disconnected sub-graph, keeping it isomorphic + G1.remove_node(13) + G2.remove_node("d") + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Connect the newly added node to the disconnected graph, which now is just a path of size 3 + G1.add_edge(0, 10) + G2.add_edge("e", "z") + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Connect the two disconnected sub-graphs, forming a single graph + G1.add_edge(11, 3) + G1.add_edge(0, 8) + G2.add_edge("a", "l") + G2.add_edge("z", "j") + assert vf2pp_isomorphism(G1, G2, node_label="label") + + def test_custom_graph5_same_labels(self): + G1 = nx.Graph() + edges1 = [ + (1, 5), + (1, 2), + (1, 4), + (2, 3), + (2, 6), + (3, 4), + (3, 7), + (4, 8), + (5, 8), + (5, 6), + (6, 7), + (7, 8), + ] + mapped = {1: "a", 2: "h", 3: "d", 4: "i", 5: "g", 6: "b", 7: "j", 8: "c"} + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label") + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Add different edges in each graph, maintaining symmetry + G1.add_edges_from([(3, 6), (2, 7), (2, 5), (1, 3), (4, 7), (6, 8)]) + G2.add_edges_from( + [ + (mapped[6], mapped[3]), + (mapped[2], mapped[7]), + (mapped[1], mapped[6]), + (mapped[5], mapped[7]), + (mapped[3], mapped[8]), + (mapped[2], mapped[4]), + ] + ) + assert vf2pp_isomorphism(G1, G2, node_label="label") + + # Obtain two different but isomorphic subgraphs from G1 and G2 + H1 = nx.Graph(G1.subgraph([1, 5, 8, 6, 7, 3])) + H2 = nx.Graph( + G2.subgraph( + [mapped[1], mapped[4], mapped[8], mapped[7], mapped[3], mapped[5]] + ) + ) + assert vf2pp_isomorphism(H1, H2, node_label="label") + + # Delete corresponding node from the two graphs + H1.remove_node(8) + H2.remove_node(mapped[7]) + assert vf2pp_isomorphism(H1, H2, node_label="label") + + # Re-orient, maintaining isomorphism + H1.add_edge(1, 6) + H1.remove_edge(3, 6) + assert vf2pp_isomorphism(H1, H2, node_label="label") + + def test_custom_graph5_different_labels(self): + G1 = nx.Graph() + edges1 = [ + (1, 5), + (1, 2), + (1, 4), + (2, 3), + (2, 6), + (3, 4), + (3, 7), + (4, 8), + (5, 8), + (5, 6), + (6, 7), + (7, 8), + ] + mapped = {1: "a", 2: "h", 3: "d", 4: "i", 5: "g", 6: "b", 7: "j", 8: "c"} + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + + colors = ["red", "blue", "grey", "none", "brown", "solarized", "yellow", "pink"] + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label") + nx.set_node_attributes( + G2, + dict(zip([mapped[n] for n in G1], it.cycle(labels_many))), + "label", + ) + assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped + + # Assign different colors to matching nodes + c = 0 + for node in G1.nodes(): + color1 = colors[c] + color2 = colors[(c + 3) % len(colors)] + G1.nodes[node]["label"] = color1 + G2.nodes[mapped[node]]["label"] = color2 + c += 1 + + assert vf2pp_isomorphism(G1, G2, node_label="label") is None + + # Get symmetrical sub-graphs of G1,G2 and compare them + H1 = G1.subgraph([1, 5]) + H2 = G2.subgraph(["i", "c"]) + c = 0 + for node1, node2 in zip(H1.nodes(), H2.nodes()): + H1.nodes[node1]["label"] = "red" + H2.nodes[node2]["label"] = "red" + c += 1 + + assert vf2pp_isomorphism(H1, H2, node_label="label") + + def test_disconnected_graph_all_same_labels(self): + G1 = nx.Graph() + G1.add_nodes_from(list(range(10))) + + mapped = {0: 9, 1: 8, 2: 7, 3: 6, 4: 5, 5: 4, 6: 3, 7: 2, 8: 1, 9: 0} + G2 = nx.relabel_nodes(G1, mapped) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label") + assert vf2pp_isomorphism(G1, G2, node_label="label") + + def test_disconnected_graph_all_different_labels(self): + G1 = nx.Graph() + G1.add_nodes_from(list(range(10))) + + mapped = {0: 9, 1: 8, 2: 7, 3: 6, 4: 5, 5: 4, 6: 3, 7: 2, 8: 1, 9: 0} + G2 = nx.relabel_nodes(G1, mapped) + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label") + nx.set_node_attributes( + G2, + dict(zip([mapped[n] for n in G1], it.cycle(labels_many))), + "label", + ) + assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped + + def test_disconnected_graph_some_same_labels(self): + G1 = nx.Graph() + G1.add_nodes_from(list(range(10))) + + mapped = {0: 9, 1: 8, 2: 7, 3: 6, 4: 5, 5: 4, 6: 3, 7: 2, 8: 1, 9: 0} + G2 = nx.relabel_nodes(G1, mapped) + + colors = [ + "white", + "white", + "white", + "purple", + "purple", + "red", + "red", + "pink", + "pink", + "pink", + ] + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(colors))), "label") + nx.set_node_attributes( + G2, dict(zip([mapped[n] for n in G1], it.cycle(colors))), "label" + ) + + assert vf2pp_isomorphism(G1, G2, node_label="label") + + +class TestMultiGraphISOVF2pp: + def test_custom_multigraph1_same_labels(self): + G1 = nx.MultiGraph() + + mapped = {1: "A", 2: "B", 3: "C", 4: "D", 5: "Z", 6: "E"} + edges1 = [ + (1, 2), + (1, 3), + (1, 4), + (1, 4), + (1, 4), + (2, 3), + (2, 6), + (2, 6), + (3, 4), + (3, 4), + (5, 1), + (5, 1), + (5, 2), + (5, 2), + ] + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label") + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Transfer the 2-clique to the right side of G1 + G1.remove_edges_from([(2, 6), (2, 6)]) + G1.add_edges_from([(3, 6), (3, 6)]) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Delete an edges, making them symmetrical, so the position of the 2-clique doesn't matter + G2.remove_edge(mapped[1], mapped[4]) + G1.remove_edge(1, 4) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Add self-loops + G1.add_edges_from([(5, 5), (5, 5), (1, 1)]) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Compensate in G2 + G2.add_edges_from( + [(mapped[1], mapped[1]), (mapped[4], mapped[4]), (mapped[4], mapped[4])] + ) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + def test_custom_multigraph1_different_labels(self): + G1 = nx.MultiGraph() + + mapped = {1: "A", 2: "B", 3: "C", 4: "D", 5: "Z", 6: "E"} + edges1 = [ + (1, 2), + (1, 3), + (1, 4), + (1, 4), + (1, 4), + (2, 3), + (2, 6), + (2, 6), + (3, 4), + (3, 4), + (5, 1), + (5, 1), + (5, 2), + (5, 2), + ] + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label") + nx.set_node_attributes( + G2, + dict(zip([mapped[n] for n in G1], it.cycle(labels_many))), + "label", + ) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + assert m == mapped + + # Re-structure G1, maintaining the degree sequence + G1.remove_edge(1, 4) + G1.add_edge(1, 5) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Restructure G2, making it isomorphic to G1 + G2.remove_edge("A", "D") + G2.add_edge("A", "Z") + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + assert m == mapped + + # Add edge from node to itself + G1.add_edges_from([(6, 6), (6, 6), (6, 6)]) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Same for G2 + G2.add_edges_from([("E", "E"), ("E", "E"), ("E", "E")]) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + assert m == mapped + + def test_custom_multigraph2_same_labels(self): + G1 = nx.MultiGraph() + + mapped = {1: "A", 2: "C", 3: "D", 4: "E", 5: "G", 7: "B", 6: "F"} + edges1 = [ + (1, 2), + (1, 2), + (1, 5), + (1, 5), + (1, 5), + (5, 6), + (2, 3), + (2, 3), + (2, 4), + (3, 4), + (3, 4), + (4, 5), + (4, 5), + (4, 5), + (2, 7), + (2, 7), + (2, 7), + ] + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label") + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Obtain two non-isomorphic subgraphs from the graph + G2.remove_edges_from([(mapped[1], mapped[2]), (mapped[1], mapped[2])]) + G2.add_edge(mapped[1], mapped[4]) + H1 = nx.MultiGraph(G1.subgraph([2, 3, 4, 7])) + H2 = nx.MultiGraph(G2.subgraph([mapped[1], mapped[4], mapped[5], mapped[6]])) + + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert not m + + # Make them isomorphic + H1.remove_edge(3, 4) + H1.add_edges_from([(2, 3), (2, 4), (2, 4)]) + H2.add_edges_from([(mapped[5], mapped[6]), (mapped[5], mapped[6])]) + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + # Remove triangle edge + H1.remove_edges_from([(2, 3), (2, 3), (2, 3)]) + H2.remove_edges_from([(mapped[5], mapped[4])] * 3) + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + # Change the edge orientation such that H1 is rotated H2 + H1.remove_edges_from([(2, 7), (2, 7)]) + H1.add_edges_from([(3, 4), (3, 4)]) + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + # Add extra edges maintaining degree sequence, but in a non-symmetrical manner + H2.add_edge(mapped[5], mapped[1]) + H1.add_edge(3, 4) + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert not m + + def test_custom_multigraph2_different_labels(self): + G1 = nx.MultiGraph() + + mapped = {1: "A", 2: "C", 3: "D", 4: "E", 5: "G", 7: "B", 6: "F"} + edges1 = [ + (1, 2), + (1, 2), + (1, 5), + (1, 5), + (1, 5), + (5, 6), + (2, 3), + (2, 3), + (2, 4), + (3, 4), + (3, 4), + (4, 5), + (4, 5), + (4, 5), + (2, 7), + (2, 7), + (2, 7), + ] + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label") + nx.set_node_attributes( + G2, + dict(zip([mapped[n] for n in G1], it.cycle(labels_many))), + "label", + ) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + assert m == mapped + + # Re-structure G1 + G1.remove_edge(2, 7) + G1.add_edge(5, 6) + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Same for G2 + G2.remove_edge("B", "C") + G2.add_edge("G", "F") + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + assert m == mapped + + # Delete node from G1 and G2, keeping them isomorphic + G1.remove_node(3) + G2.remove_node("D") + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Change G1 edges + G1.remove_edge(1, 2) + G1.remove_edge(2, 7) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Make G2 identical to G1, but with different edge orientation and different labels + G2.add_edges_from([("A", "C"), ("C", "E"), ("C", "E")]) + G2.remove_edges_from( + [("A", "G"), ("A", "G"), ("F", "G"), ("E", "G"), ("E", "G")] + ) + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Make all labels the same, so G1 and G2 are also isomorphic + for n1, n2 in zip(G1.nodes(), G2.nodes()): + G1.nodes[n1]["label"] = "blue" + G2.nodes[n2]["label"] = "blue" + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + def test_custom_multigraph3_same_labels(self): + G1 = nx.MultiGraph() + + mapped = {1: 9, 2: 8, 3: 7, 4: 6, 5: 3, 8: 5, 9: 4, 7: 1, 6: 2} + edges1 = [ + (1, 2), + (1, 3), + (1, 3), + (2, 3), + (2, 3), + (3, 4), + (4, 5), + (4, 7), + (4, 9), + (4, 9), + (4, 9), + (5, 8), + (5, 8), + (8, 9), + (8, 9), + (5, 6), + (6, 7), + (6, 7), + (6, 7), + (5, 2), + ] + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label") + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Connect nodes maintaining symmetry + G1.add_edges_from([(6, 9), (7, 8), (5, 8), (4, 9), (4, 9)]) + G2.add_edges_from( + [ + (mapped[6], mapped[8]), + (mapped[7], mapped[9]), + (mapped[5], mapped[8]), + (mapped[4], mapped[9]), + (mapped[4], mapped[9]), + ] + ) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Make isomorphic + G1.add_edges_from([(6, 8), (6, 8), (7, 9), (7, 9), (7, 9)]) + G2.add_edges_from( + [ + (mapped[6], mapped[8]), + (mapped[6], mapped[9]), + (mapped[7], mapped[8]), + (mapped[7], mapped[9]), + (mapped[7], mapped[9]), + ] + ) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Connect more nodes + G1.add_edges_from([(2, 7), (2, 7), (3, 6), (3, 6)]) + G2.add_edges_from( + [ + (mapped[2], mapped[7]), + (mapped[2], mapped[7]), + (mapped[3], mapped[6]), + (mapped[3], mapped[6]), + ] + ) + G1.add_node(10) + G2.add_node("Z") + G1.nodes[10]["label"] = "blue" + G2.nodes["Z"]["label"] = "blue" + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Connect the newly added node, to opposite sides of the graph + G1.add_edges_from([(10, 1), (10, 5), (10, 8), (10, 10), (10, 10)]) + G2.add_edges_from( + [ + ("Z", mapped[1]), + ("Z", mapped[4]), + ("Z", mapped[9]), + ("Z", "Z"), + ("Z", "Z"), + ] + ) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # We connected the new node to opposite sides, so G1 must be symmetrical to G2. Re-structure them to be so + G1.remove_edges_from([(1, 3), (4, 9), (4, 9), (7, 9)]) + G2.remove_edges_from( + [ + (mapped[1], mapped[3]), + (mapped[4], mapped[9]), + (mapped[4], mapped[9]), + (mapped[7], mapped[9]), + ] + ) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Get two subgraphs that are not isomorphic but are easy to make + H1 = nx.Graph(G1.subgraph([2, 3, 4, 5, 6, 7, 10])) + H2 = nx.Graph( + G2.subgraph( + [mapped[4], mapped[5], mapped[6], mapped[7], mapped[8], mapped[9], "Z"] + ) + ) + + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert not m + + # Restructure both to make them isomorphic + H1.add_edges_from([(10, 2), (10, 6), (3, 6), (2, 7), (2, 6), (3, 7)]) + H2.add_edges_from( + [("Z", mapped[7]), (mapped[6], mapped[9]), (mapped[7], mapped[8])] + ) + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + # Remove one self-loop in H2 + H2.remove_edge("Z", "Z") + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert not m + + # Compensate in H1 + H1.remove_edge(10, 10) + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + def test_custom_multigraph3_different_labels(self): + G1 = nx.MultiGraph() + + mapped = {1: 9, 2: 8, 3: 7, 4: 6, 5: 3, 8: 5, 9: 4, 7: 1, 6: 2} + edges1 = [ + (1, 2), + (1, 3), + (1, 3), + (2, 3), + (2, 3), + (3, 4), + (4, 5), + (4, 7), + (4, 9), + (4, 9), + (4, 9), + (5, 8), + (5, 8), + (8, 9), + (8, 9), + (5, 6), + (6, 7), + (6, 7), + (6, 7), + (5, 2), + ] + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label") + nx.set_node_attributes( + G2, + dict(zip([mapped[n] for n in G1], it.cycle(labels_many))), + "label", + ) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + assert m == mapped + + # Delete edge maintaining isomorphism + G1.remove_edge(4, 9) + G2.remove_edge(4, 6) + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + assert m == mapped + + # Change edge orientation such that G1 mirrors G2 + G1.add_edges_from([(4, 9), (1, 2), (1, 2)]) + G1.remove_edges_from([(1, 3), (1, 3)]) + G2.add_edges_from([(3, 5), (7, 9)]) + G2.remove_edge(8, 9) + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Make all labels the same, so G1 and G2 are also isomorphic + for n1, n2 in zip(G1.nodes(), G2.nodes()): + G1.nodes[n1]["label"] = "blue" + G2.nodes[n2]["label"] = "blue" + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + G1.add_node(10) + G2.add_node("Z") + G1.nodes[10]["label"] = "green" + G2.nodes["Z"]["label"] = "green" + + # Add different number of edges between the new nodes and themselves + G1.add_edges_from([(10, 10), (10, 10)]) + G2.add_edges_from([("Z", "Z")]) + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Make the number of self-edges equal + G1.remove_edge(10, 10) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Connect the new node to the graph + G1.add_edges_from([(10, 3), (10, 4)]) + G2.add_edges_from([("Z", 8), ("Z", 3)]) + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Remove central node + G1.remove_node(4) + G2.remove_node(3) + G1.add_edges_from([(5, 6), (5, 6), (5, 7)]) + G2.add_edges_from([(1, 6), (1, 6), (6, 2)]) + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + def test_custom_multigraph4_same_labels(self): + G1 = nx.MultiGraph() + edges1 = [ + (1, 2), + (1, 2), + (2, 2), + (2, 3), + (3, 8), + (3, 8), + (3, 4), + (4, 5), + (4, 5), + (4, 5), + (4, 6), + (3, 6), + (3, 6), + (6, 6), + (8, 7), + (7, 7), + (8, 9), + (9, 9), + (8, 9), + (8, 9), + (5, 9), + (10, 11), + (11, 12), + (12, 13), + (11, 13), + (10, 10), + (10, 11), + (11, 13), + ] + + mapped = { + 1: "n", + 2: "m", + 3: "l", + 4: "j", + 5: "k", + 6: "i", + 7: "g", + 8: "h", + 9: "f", + 10: "b", + 11: "a", + 12: "d", + 13: "e", + } + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label") + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Add extra but corresponding edges to both graphs + G1.add_edges_from([(2, 2), (2, 3), (2, 8), (3, 4)]) + G2.add_edges_from([("m", "m"), ("m", "l"), ("m", "h"), ("l", "j")]) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Obtain subgraphs + H1 = nx.MultiGraph(G1.subgraph([2, 3, 4, 6, 10, 11, 12, 13])) + H2 = nx.MultiGraph( + G2.subgraph( + [ + mapped[2], + mapped[3], + mapped[8], + mapped[9], + mapped[10], + mapped[11], + mapped[12], + mapped[13], + ] + ) + ) + + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert not m + + # Make them isomorphic + H2.remove_edges_from( + [(mapped[3], mapped[2]), (mapped[9], mapped[8]), (mapped[2], mapped[2])] + ) + H2.add_edges_from([(mapped[9], mapped[9]), (mapped[2], mapped[8])]) + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + # Re-structure the disconnected sub-graph + H1.remove_node(12) + H2.remove_node(mapped[12]) + H1.add_edge(13, 13) + H2.add_edge(mapped[13], mapped[13]) + + # Connect the two disconnected components, forming a single graph + H1.add_edges_from([(3, 13), (6, 11)]) + H2.add_edges_from([(mapped[8], mapped[10]), (mapped[2], mapped[11])]) + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + # Change orientation of self-loops in one graph, maintaining the degree sequence + H1.remove_edges_from([(2, 2), (3, 6)]) + H1.add_edges_from([(6, 6), (2, 3)]) + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert not m + + def test_custom_multigraph4_different_labels(self): + G1 = nx.MultiGraph() + edges1 = [ + (1, 2), + (1, 2), + (2, 2), + (2, 3), + (3, 8), + (3, 8), + (3, 4), + (4, 5), + (4, 5), + (4, 5), + (4, 6), + (3, 6), + (3, 6), + (6, 6), + (8, 7), + (7, 7), + (8, 9), + (9, 9), + (8, 9), + (8, 9), + (5, 9), + (10, 11), + (11, 12), + (12, 13), + (11, 13), + ] + + mapped = { + 1: "n", + 2: "m", + 3: "l", + 4: "j", + 5: "k", + 6: "i", + 7: "g", + 8: "h", + 9: "f", + 10: "b", + 11: "a", + 12: "d", + 13: "e", + } + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label") + nx.set_node_attributes( + G2, + dict(zip([mapped[n] for n in G1], it.cycle(labels_many))), + "label", + ) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m == mapped + + # Add extra but corresponding edges to both graphs + G1.add_edges_from([(2, 2), (2, 3), (2, 8), (3, 4)]) + G2.add_edges_from([("m", "m"), ("m", "l"), ("m", "h"), ("l", "j")]) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m == mapped + + # Obtain isomorphic subgraphs + H1 = nx.MultiGraph(G1.subgraph([2, 3, 4, 6])) + H2 = nx.MultiGraph(G2.subgraph(["m", "l", "j", "i"])) + + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + # Delete the 3-clique, keeping only the path-graph. Also, H1 mirrors H2 + H1.remove_node(4) + H2.remove_node("j") + H1.remove_edges_from([(2, 2), (2, 3), (6, 6)]) + H2.remove_edges_from([("l", "i"), ("m", "m"), ("m", "m")]) + + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert not m + + # Assign the same labels so that mirroring means isomorphic + for n1, n2 in zip(H1.nodes(), H2.nodes()): + H1.nodes[n1]["label"] = "red" + H2.nodes[n2]["label"] = "red" + + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + # Leave only one node with self-loop + H1.remove_nodes_from([3, 6]) + H2.remove_nodes_from(["m", "l"]) + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + # Remove one self-loop from H1 + H1.remove_edge(2, 2) + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert not m + + # Same for H2 + H2.remove_edge("i", "i") + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + # Compose H1 with the disconnected sub-graph of G1. Same for H2 + S1 = nx.compose(H1, nx.MultiGraph(G1.subgraph([10, 11, 12, 13]))) + S2 = nx.compose(H2, nx.MultiGraph(G2.subgraph(["a", "b", "d", "e"]))) + + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + # Connect the two components + S1.add_edges_from([(13, 13), (13, 13), (2, 13)]) + S2.add_edges_from([("a", "a"), ("a", "a"), ("i", "e")]) + m = vf2pp_isomorphism(H1, H2, node_label="label") + assert m + + def test_custom_multigraph5_same_labels(self): + G1 = nx.MultiGraph() + + edges1 = [ + (1, 5), + (1, 2), + (1, 4), + (2, 3), + (2, 6), + (3, 4), + (3, 7), + (4, 8), + (5, 8), + (5, 6), + (6, 7), + (7, 8), + ] + mapped = {1: "a", 2: "h", 3: "d", 4: "i", 5: "g", 6: "b", 7: "j", 8: "c"} + + G1.add_edges_from(edges1) + G2 = nx.relabel_nodes(G1, mapped) + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label") + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Add multiple edges and self-loops, maintaining isomorphism + G1.add_edges_from( + [(1, 2), (1, 2), (3, 7), (8, 8), (8, 8), (7, 8), (2, 3), (5, 6)] + ) + G2.add_edges_from( + [ + ("a", "h"), + ("a", "h"), + ("d", "j"), + ("c", "c"), + ("c", "c"), + ("j", "c"), + ("d", "h"), + ("g", "b"), + ] + ) + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Make G2 to be the rotated G1 + G2.remove_edges_from( + [ + ("a", "h"), + ("a", "h"), + ("d", "j"), + ("c", "c"), + ("c", "c"), + ("j", "c"), + ("d", "h"), + ("g", "b"), + ] + ) + G2.add_edges_from( + [ + ("d", "i"), + ("a", "h"), + ("g", "b"), + ("g", "b"), + ("i", "i"), + ("i", "i"), + ("b", "j"), + ("d", "j"), + ] + ) + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + def test_disconnected_multigraph_all_same_labels(self): + G1 = nx.MultiGraph() + G1.add_nodes_from(list(range(10))) + G1.add_edges_from([(i, i) for i in range(10)]) + + mapped = {0: 9, 1: 8, 2: 7, 3: 6, 4: 5, 5: 4, 6: 3, 7: 2, 8: 1, 9: 0} + G2 = nx.relabel_nodes(G1, mapped) + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label") + nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label") + + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Add self-loops to non-mapped nodes. Should be the same, as the graph is disconnected. + G1.add_edges_from([(i, i) for i in range(5, 8)] * 3) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Compensate in G2 + G2.add_edges_from([(i, i) for i in range(3)] * 3) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + # Add one more self-loop in G2 + G2.add_edges_from([(0, 0), (1, 1), (1, 1)]) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Compensate in G1 + G1.add_edges_from([(5, 5), (7, 7), (7, 7)]) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + def test_disconnected_multigraph_all_different_labels(self): + G1 = nx.MultiGraph() + G1.add_nodes_from(list(range(10))) + G1.add_edges_from([(i, i) for i in range(10)]) + + mapped = {0: 9, 1: 8, 2: 7, 3: 6, 4: 5, 5: 4, 6: 3, 7: 2, 8: 1, 9: 0} + G2 = nx.relabel_nodes(G1, mapped) + + nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label") + nx.set_node_attributes( + G2, + dict(zip([mapped[n] for n in G1], it.cycle(labels_many))), + "label", + ) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + assert m == mapped + + # Add self-loops to non-mapped nodes. Now it is not the same, as there are different labels + G1.add_edges_from([(i, i) for i in range(5, 8)] * 3) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Add self-loops to non mapped nodes in G2 as well + G2.add_edges_from([(mapped[i], mapped[i]) for i in range(3)] * 7) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Add self-loops to mapped nodes in G2 + G2.add_edges_from([(mapped[i], mapped[i]) for i in range(5, 8)] * 3) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert not m + + # Add self-loops to G1 so that they are even in both graphs + G1.add_edges_from([(i, i) for i in range(3)] * 7) + m = vf2pp_isomorphism(G1, G2, node_label="label") + assert m + + +class TestDiGraphISOVF2pp: + def test_wikipedia_graph(self): + edges1 = [ + (1, 5), + (1, 2), + (1, 4), + (3, 2), + (6, 2), + (3, 4), + (7, 3), + (4, 8), + (5, 8), + (6, 5), + (6, 7), + (7, 8), + ] + mapped = {1: "a", 2: "h", 3: "d", 4: "i", 5: "g", 6: "b", 7: "j", 8: "c"} + + G1 = nx.DiGraph(edges1) + G2 = nx.relabel_nodes(G1, mapped) + + assert vf2pp_isomorphism(G1, G2) == mapped + + # Change the direction of an edge + G1.remove_edge(1, 5) + G1.add_edge(5, 1) + assert vf2pp_isomorphism(G1, G2) is None + + def test_non_isomorphic_same_degree_sequence(self): + r""" + G1 G2 + x--------------x x--------------x + | \ | | \ | + | x-------x | | x-------x | + | | | | | | | | + | x-------x | | x-------x | + | / | | \ | + x--------------x x--------------x + """ + edges1 = [ + (1, 5), + (1, 2), + (4, 1), + (3, 2), + (3, 4), + (4, 8), + (5, 8), + (6, 5), + (6, 7), + (7, 8), + ] + edges2 = [ + (1, 5), + (1, 2), + (4, 1), + (3, 2), + (4, 3), + (5, 8), + (6, 5), + (6, 7), + (3, 7), + (8, 7), + ] + + G1 = nx.DiGraph(edges1) + G2 = nx.DiGraph(edges2) + assert vf2pp_isomorphism(G1, G2) is None diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_vf2userfunc.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_vf2userfunc.py new file mode 100644 index 0000000000000000000000000000000000000000..b44f45888519df1fb9d897ae7572fdbce6a8cb9a --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_vf2userfunc.py @@ -0,0 +1,200 @@ +""" +Tests for VF2 isomorphism algorithm for weighted graphs. +""" + +import math +from operator import eq + +import networkx as nx +import networkx.algorithms.isomorphism as iso + + +def test_simple(): + # 16 simple tests + w = "weight" + edges = [(0, 0, 1), (0, 0, 1.5), (0, 1, 2), (1, 0, 3)] + for g1 in [nx.Graph(), nx.DiGraph(), nx.MultiGraph(), nx.MultiDiGraph()]: + g1.add_weighted_edges_from(edges) + g2 = g1.subgraph(g1.nodes()) + if g1.is_multigraph(): + em = iso.numerical_multiedge_match("weight", 1) + else: + em = iso.numerical_edge_match("weight", 1) + assert nx.is_isomorphic(g1, g2, edge_match=em) + + for mod1, mod2 in [(False, True), (True, False), (True, True)]: + # mod1 tests a regular edge + # mod2 tests a selfloop + if g2.is_multigraph(): + if mod1: + data1 = {0: {"weight": 10}} + if mod2: + data2 = {0: {"weight": 1}, 1: {"weight": 2.5}} + else: + if mod1: + data1 = {"weight": 10} + if mod2: + data2 = {"weight": 2.5} + + g2 = g1.subgraph(g1.nodes()).copy() + if mod1: + if not g1.is_directed(): + g2._adj[1][0] = data1 + g2._adj[0][1] = data1 + else: + g2._succ[1][0] = data1 + g2._pred[0][1] = data1 + if mod2: + if not g1.is_directed(): + g2._adj[0][0] = data2 + else: + g2._succ[0][0] = data2 + g2._pred[0][0] = data2 + + assert not nx.is_isomorphic(g1, g2, edge_match=em) + + +def test_weightkey(): + g1 = nx.DiGraph() + g2 = nx.DiGraph() + + g1.add_edge("A", "B", weight=1) + g2.add_edge("C", "D", weight=0) + + assert nx.is_isomorphic(g1, g2) + em = iso.numerical_edge_match("nonexistent attribute", 1) + assert nx.is_isomorphic(g1, g2, edge_match=em) + em = iso.numerical_edge_match("weight", 1) + assert not nx.is_isomorphic(g1, g2, edge_match=em) + + g2 = nx.DiGraph() + g2.add_edge("C", "D") + assert nx.is_isomorphic(g1, g2, edge_match=em) + + +class TestNodeMatch_Graph: + def setup_method(self): + self.g1 = nx.Graph() + self.g2 = nx.Graph() + self.build() + + def build(self): + self.nm = iso.categorical_node_match("color", "") + self.em = iso.numerical_edge_match("weight", 1) + + self.g1.add_node("A", color="red") + self.g2.add_node("C", color="blue") + + self.g1.add_edge("A", "B", weight=1) + self.g2.add_edge("C", "D", weight=1) + + def test_noweight_nocolor(self): + assert nx.is_isomorphic(self.g1, self.g2) + + def test_color1(self): + assert not nx.is_isomorphic(self.g1, self.g2, node_match=self.nm) + + def test_color2(self): + self.g1.nodes["A"]["color"] = "blue" + assert nx.is_isomorphic(self.g1, self.g2, node_match=self.nm) + + def test_weight1(self): + assert nx.is_isomorphic(self.g1, self.g2, edge_match=self.em) + + def test_weight2(self): + self.g1.add_edge("A", "B", weight=2) + assert not nx.is_isomorphic(self.g1, self.g2, edge_match=self.em) + + def test_colorsandweights1(self): + iso = nx.is_isomorphic(self.g1, self.g2, node_match=self.nm, edge_match=self.em) + assert not iso + + def test_colorsandweights2(self): + self.g1.nodes["A"]["color"] = "blue" + iso = nx.is_isomorphic(self.g1, self.g2, node_match=self.nm, edge_match=self.em) + assert iso + + def test_colorsandweights3(self): + # make the weights disagree + self.g1.add_edge("A", "B", weight=2) + assert not nx.is_isomorphic( + self.g1, self.g2, node_match=self.nm, edge_match=self.em + ) + + +class TestEdgeMatch_MultiGraph: + def setup_method(self): + self.g1 = nx.MultiGraph() + self.g2 = nx.MultiGraph() + self.GM = iso.MultiGraphMatcher + self.build() + + def build(self): + g1 = self.g1 + g2 = self.g2 + + # We will assume integer weights only. + g1.add_edge("A", "B", color="green", weight=0, size=0.5) + g1.add_edge("A", "B", color="red", weight=1, size=0.35) + g1.add_edge("A", "B", color="red", weight=2, size=0.65) + + g2.add_edge("C", "D", color="green", weight=1, size=0.5) + g2.add_edge("C", "D", color="red", weight=0, size=0.45) + g2.add_edge("C", "D", color="red", weight=2, size=0.65) + + if g1.is_multigraph(): + self.em = iso.numerical_multiedge_match("weight", 1) + self.emc = iso.categorical_multiedge_match("color", "") + self.emcm = iso.categorical_multiedge_match(["color", "weight"], ["", 1]) + self.emg1 = iso.generic_multiedge_match("color", "red", eq) + self.emg2 = iso.generic_multiedge_match( + ["color", "weight", "size"], + ["red", 1, 0.5], + [eq, eq, math.isclose], + ) + else: + self.em = iso.numerical_edge_match("weight", 1) + self.emc = iso.categorical_edge_match("color", "") + self.emcm = iso.categorical_edge_match(["color", "weight"], ["", 1]) + self.emg1 = iso.generic_multiedge_match("color", "red", eq) + self.emg2 = iso.generic_edge_match( + ["color", "weight", "size"], + ["red", 1, 0.5], + [eq, eq, math.isclose], + ) + + def test_weights_only(self): + assert nx.is_isomorphic(self.g1, self.g2, edge_match=self.em) + + def test_colors_only(self): + gm = self.GM(self.g1, self.g2, edge_match=self.emc) + assert gm.is_isomorphic() + + def test_colorsandweights(self): + gm = self.GM(self.g1, self.g2, edge_match=self.emcm) + assert not gm.is_isomorphic() + + def test_generic1(self): + gm = self.GM(self.g1, self.g2, edge_match=self.emg1) + assert gm.is_isomorphic() + + def test_generic2(self): + gm = self.GM(self.g1, self.g2, edge_match=self.emg2) + assert not gm.is_isomorphic() + + +class TestEdgeMatch_DiGraph(TestNodeMatch_Graph): + def setup_method(self): + TestNodeMatch_Graph.setup_method(self) + self.g1 = nx.DiGraph() + self.g2 = nx.DiGraph() + self.build() + + +class TestEdgeMatch_MultiDiGraph(TestEdgeMatch_MultiGraph): + def setup_method(self): + TestEdgeMatch_MultiGraph.setup_method(self) + self.g1 = nx.MultiDiGraph() + self.g2 = nx.MultiDiGraph() + self.GM = iso.MultiDiGraphMatcher + self.build() diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/vf2pp.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/vf2pp.py new file mode 100644 index 0000000000000000000000000000000000000000..3093d9c977eed4458458783424fad10284176e2f --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/vf2pp.py @@ -0,0 +1,1075 @@ +""" +*************** +VF2++ Algorithm +*************** + +An implementation of the VF2++ algorithm [1]_ for Graph Isomorphism testing. + +The simplest interface to use this module is to call: + +`vf2pp_is_isomorphic`: to check whether two graphs are isomorphic. +`vf2pp_isomorphism`: to obtain the node mapping between two graphs, +in case they are isomorphic. +`vf2pp_all_isomorphisms`: to generate all possible mappings between two graphs, +if isomorphic. + +Introduction +------------ +The VF2++ algorithm, follows a similar logic to that of VF2, while also +introducing new easy-to-check cutting rules and determining the optimal access +order of nodes. It is also implemented in a non-recursive manner, which saves +both time and space, when compared to its previous counterpart. + +The optimal node ordering is obtained after taking into consideration both the +degree but also the label rarity of each node. +This way we place the nodes that are more likely to match, first in the order, +thus examining the most promising branches in the beginning. +The rules also consider node labels, making it easier to prune unfruitful +branches early in the process. + +Examples +-------- + +Suppose G1 and G2 are Isomorphic Graphs. Verification is as follows: + +Without node labels: + +>>> import networkx as nx +>>> G1 = nx.path_graph(4) +>>> G2 = nx.path_graph(4) +>>> nx.vf2pp_is_isomorphic(G1, G2, node_label=None) +True +>>> nx.vf2pp_isomorphism(G1, G2, node_label=None) +{1: 1, 2: 2, 0: 0, 3: 3} + +With node labels: + +>>> G1 = nx.path_graph(4) +>>> G2 = nx.path_graph(4) +>>> mapped = {1: 1, 2: 2, 3: 3, 0: 0} +>>> nx.set_node_attributes( +... G1, dict(zip(G1, ["blue", "red", "green", "yellow"])), "label" +... ) +>>> nx.set_node_attributes( +... G2, +... dict(zip([mapped[u] for u in G1], ["blue", "red", "green", "yellow"])), +... "label", +... ) +>>> nx.vf2pp_is_isomorphic(G1, G2, node_label="label") +True +>>> nx.vf2pp_isomorphism(G1, G2, node_label="label") +{1: 1, 2: 2, 0: 0, 3: 3} + +References +---------- +.. [1] Jüttner, Alpár & Madarasi, Péter. (2018). "VF2++—An improved subgraph + isomorphism algorithm". Discrete Applied Mathematics. 242. + https://doi.org/10.1016/j.dam.2018.02.018 + +""" + +import collections + +import networkx as nx + +__all__ = ["vf2pp_isomorphism", "vf2pp_is_isomorphic", "vf2pp_all_isomorphisms"] + +_GraphParameters = collections.namedtuple( + "_GraphParameters", + [ + "G1", + "G2", + "G1_labels", + "G2_labels", + "nodes_of_G1Labels", + "nodes_of_G2Labels", + "G2_nodes_of_degree", + ], +) + +_StateParameters = collections.namedtuple( + "_StateParameters", + [ + "mapping", + "reverse_mapping", + "T1", + "T1_in", + "T1_tilde", + "T1_tilde_in", + "T2", + "T2_in", + "T2_tilde", + "T2_tilde_in", + ], +) + + +@nx._dispatchable(graphs={"G1": 0, "G2": 1}, node_attrs={"node_label": "default_label"}) +def vf2pp_isomorphism(G1, G2, node_label=None, default_label=None): + """Return an isomorphic mapping between `G1` and `G2` if it exists. + + Parameters + ---------- + G1, G2 : NetworkX Graph or MultiGraph instances. + The two graphs to check for isomorphism. + + node_label : str, optional + The name of the node attribute to be used when comparing nodes. + The default is `None`, meaning node attributes are not considered + in the comparison. Any node that doesn't have the `node_label` + attribute uses `default_label` instead. + + default_label : scalar + Default value to use when a node doesn't have an attribute + named `node_label`. Default is `None`. + + Returns + ------- + dict or None + Node mapping if the two graphs are isomorphic. None otherwise. + """ + try: + mapping = next(vf2pp_all_isomorphisms(G1, G2, node_label, default_label)) + return mapping + except StopIteration: + return None + + +@nx._dispatchable(graphs={"G1": 0, "G2": 1}, node_attrs={"node_label": "default_label"}) +def vf2pp_is_isomorphic(G1, G2, node_label=None, default_label=None): + """Examines whether G1 and G2 are isomorphic. + + Parameters + ---------- + G1, G2 : NetworkX Graph or MultiGraph instances. + The two graphs to check for isomorphism. + + node_label : str, optional + The name of the node attribute to be used when comparing nodes. + The default is `None`, meaning node attributes are not considered + in the comparison. Any node that doesn't have the `node_label` + attribute uses `default_label` instead. + + default_label : scalar + Default value to use when a node doesn't have an attribute + named `node_label`. Default is `None`. + + Returns + ------- + bool + True if the two graphs are isomorphic, False otherwise. + """ + if vf2pp_isomorphism(G1, G2, node_label, default_label) is not None: + return True + return False + + +@nx._dispatchable(graphs={"G1": 0, "G2": 1}, node_attrs={"node_label": "default_label"}) +def vf2pp_all_isomorphisms(G1, G2, node_label=None, default_label=None): + """Yields all the possible mappings between G1 and G2. + + Parameters + ---------- + G1, G2 : NetworkX Graph or MultiGraph instances. + The two graphs to check for isomorphism. + + node_label : str, optional + The name of the node attribute to be used when comparing nodes. + The default is `None`, meaning node attributes are not considered + in the comparison. Any node that doesn't have the `node_label` + attribute uses `default_label` instead. + + default_label : scalar + Default value to use when a node doesn't have an attribute + named `node_label`. Default is `None`. + + Yields + ------ + dict + Isomorphic mapping between the nodes in `G1` and `G2`. + """ + if G1.number_of_nodes() == 0 or G2.number_of_nodes() == 0: + return False + + # Create the degree dicts based on graph type + if G1.is_directed(): + G1_degree = { + n: (in_degree, out_degree) + for (n, in_degree), (_, out_degree) in zip(G1.in_degree, G1.out_degree) + } + G2_degree = { + n: (in_degree, out_degree) + for (n, in_degree), (_, out_degree) in zip(G2.in_degree, G2.out_degree) + } + else: + G1_degree = dict(G1.degree) + G2_degree = dict(G2.degree) + + if not G1.is_directed(): + find_candidates = _find_candidates + restore_Tinout = _restore_Tinout + else: + find_candidates = _find_candidates_Di + restore_Tinout = _restore_Tinout_Di + + # Check that both graphs have the same number of nodes and degree sequence + if G1.order() != G2.order(): + return False + if sorted(G1_degree.values()) != sorted(G2_degree.values()): + return False + + # Initialize parameters and cache necessary information about degree and labels + graph_params, state_params = _initialize_parameters( + G1, G2, G2_degree, node_label, default_label + ) + + # Check if G1 and G2 have the same labels, and that number of nodes per label is equal between the two graphs + if not _precheck_label_properties(graph_params): + return False + + # Calculate the optimal node ordering + node_order = _matching_order(graph_params) + + # Initialize the stack + stack = [] + candidates = iter( + find_candidates(node_order[0], graph_params, state_params, G1_degree) + ) + stack.append((node_order[0], candidates)) + + mapping = state_params.mapping + reverse_mapping = state_params.reverse_mapping + + # Index of the node from the order, currently being examined + matching_node = 1 + + while stack: + current_node, candidate_nodes = stack[-1] + + try: + candidate = next(candidate_nodes) + except StopIteration: + # If no remaining candidates, return to a previous state, and follow another branch + stack.pop() + matching_node -= 1 + if stack: + # Pop the previously added u-v pair, and look for a different candidate _v for u + popped_node1, _ = stack[-1] + popped_node2 = mapping[popped_node1] + mapping.pop(popped_node1) + reverse_mapping.pop(popped_node2) + restore_Tinout(popped_node1, popped_node2, graph_params, state_params) + continue + + if _feasibility(current_node, candidate, graph_params, state_params): + # Terminate if mapping is extended to its full + if len(mapping) == G2.number_of_nodes() - 1: + cp_mapping = mapping.copy() + cp_mapping[current_node] = candidate + yield cp_mapping + continue + + # Feasibility rules pass, so extend the mapping and update the parameters + mapping[current_node] = candidate + reverse_mapping[candidate] = current_node + _update_Tinout(current_node, candidate, graph_params, state_params) + # Append the next node and its candidates to the stack + candidates = iter( + find_candidates( + node_order[matching_node], graph_params, state_params, G1_degree + ) + ) + stack.append((node_order[matching_node], candidates)) + matching_node += 1 + + +def _precheck_label_properties(graph_params): + G1, G2, G1_labels, G2_labels, nodes_of_G1Labels, nodes_of_G2Labels, _ = graph_params + if any( + label not in nodes_of_G1Labels or len(nodes_of_G1Labels[label]) != len(nodes) + for label, nodes in nodes_of_G2Labels.items() + ): + return False + return True + + +def _initialize_parameters(G1, G2, G2_degree, node_label=None, default_label=-1): + """Initializes all the necessary parameters for VF2++ + + Parameters + ---------- + G1,G2: NetworkX Graph or MultiGraph instances. + The two graphs to check for isomorphism or monomorphism + + G1_labels,G2_labels: dict + The label of every node in G1 and G2 respectively + + Returns + ------- + graph_params: namedtuple + Contains all the Graph-related parameters: + + G1,G2 + G1_labels,G2_labels: dict + + state_params: namedtuple + Contains all the State-related parameters: + + mapping: dict + The mapping as extended so far. Maps nodes of G1 to nodes of G2 + + reverse_mapping: dict + The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed + + T1, T2: set + Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are + neighbors of nodes that are. + + T1_out, T2_out: set + Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti + """ + G1_labels = dict(G1.nodes(data=node_label, default=default_label)) + G2_labels = dict(G2.nodes(data=node_label, default=default_label)) + + graph_params = _GraphParameters( + G1, + G2, + G1_labels, + G2_labels, + nx.utils.groups(G1_labels), + nx.utils.groups(G2_labels), + nx.utils.groups(G2_degree), + ) + + T1, T1_in = set(), set() + T2, T2_in = set(), set() + if G1.is_directed(): + T1_tilde, T1_tilde_in = ( + set(G1.nodes()), + set(), + ) # todo: do we need Ti_tilde_in? What nodes does it have? + T2_tilde, T2_tilde_in = set(G2.nodes()), set() + else: + T1_tilde, T1_tilde_in = set(G1.nodes()), set() + T2_tilde, T2_tilde_in = set(G2.nodes()), set() + + state_params = _StateParameters( + {}, + {}, + T1, + T1_in, + T1_tilde, + T1_tilde_in, + T2, + T2_in, + T2_tilde, + T2_tilde_in, + ) + + return graph_params, state_params + + +def _matching_order(graph_params): + """The node ordering as introduced in VF2++. + + Notes + ----- + Taking into account the structure of the Graph and the node labeling, the nodes are placed in an order such that, + most of the unfruitful/infeasible branches of the search space can be pruned on high levels, significantly + decreasing the number of visited states. The premise is that, the algorithm will be able to recognize + inconsistencies early, proceeding to go deep into the search tree only if it's needed. + + Parameters + ---------- + graph_params: namedtuple + Contains: + + G1,G2: NetworkX Graph or MultiGraph instances. + The two graphs to check for isomorphism or monomorphism. + + G1_labels,G2_labels: dict + The label of every node in G1 and G2 respectively. + + Returns + ------- + node_order: list + The ordering of the nodes. + """ + G1, G2, G1_labels, _, _, nodes_of_G2Labels, _ = graph_params + if not G1 and not G2: + return {} + + if G1.is_directed(): + G1 = G1.to_undirected(as_view=True) + + V1_unordered = set(G1.nodes()) + label_rarity = {label: len(nodes) for label, nodes in nodes_of_G2Labels.items()} + used_degrees = {node: 0 for node in G1} + node_order = [] + + while V1_unordered: + max_rarity = min(label_rarity[G1_labels[x]] for x in V1_unordered) + rarest_nodes = [ + n for n in V1_unordered if label_rarity[G1_labels[n]] == max_rarity + ] + max_node = max(rarest_nodes, key=G1.degree) + + for dlevel_nodes in nx.bfs_layers(G1, max_node): + nodes_to_add = dlevel_nodes.copy() + while nodes_to_add: + max_used_degree = max(used_degrees[n] for n in nodes_to_add) + max_used_degree_nodes = [ + n for n in nodes_to_add if used_degrees[n] == max_used_degree + ] + max_degree = max(G1.degree[n] for n in max_used_degree_nodes) + max_degree_nodes = [ + n for n in max_used_degree_nodes if G1.degree[n] == max_degree + ] + next_node = min( + max_degree_nodes, key=lambda x: label_rarity[G1_labels[x]] + ) + + node_order.append(next_node) + for node in G1.neighbors(next_node): + used_degrees[node] += 1 + + nodes_to_add.remove(next_node) + label_rarity[G1_labels[next_node]] -= 1 + V1_unordered.discard(next_node) + + return node_order + + +def _find_candidates( + u, graph_params, state_params, G1_degree +): # todo: make the 4th argument the degree of u + """Given node u of G1, finds the candidates of u from G2. + + Parameters + ---------- + u: Graph node + The node from G1 for which to find the candidates from G2. + + graph_params: namedtuple + Contains all the Graph-related parameters: + + G1,G2: NetworkX Graph or MultiGraph instances. + The two graphs to check for isomorphism or monomorphism + + G1_labels,G2_labels: dict + The label of every node in G1 and G2 respectively + + state_params: namedtuple + Contains all the State-related parameters: + + mapping: dict + The mapping as extended so far. Maps nodes of G1 to nodes of G2 + + reverse_mapping: dict + The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed + + T1, T2: set + Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are + neighbors of nodes that are. + + T1_tilde, T2_tilde: set + Ti_tilde contains all the nodes from Gi, that are neither in the mapping nor in Ti + + Returns + ------- + candidates: set + The nodes from G2 which are candidates for u. + """ + G1, G2, G1_labels, _, _, nodes_of_G2Labels, G2_nodes_of_degree = graph_params + mapping, reverse_mapping, _, _, _, _, _, _, T2_tilde, _ = state_params + + covered_nbrs = [nbr for nbr in G1[u] if nbr in mapping] + if not covered_nbrs: + candidates = set(nodes_of_G2Labels[G1_labels[u]]) + candidates.intersection_update(G2_nodes_of_degree[G1_degree[u]]) + candidates.intersection_update(T2_tilde) + candidates.difference_update(reverse_mapping) + if G1.is_multigraph(): + candidates.difference_update( + { + node + for node in candidates + if G1.number_of_edges(u, u) != G2.number_of_edges(node, node) + } + ) + return candidates + + nbr1 = covered_nbrs[0] + common_nodes = set(G2[mapping[nbr1]]) + + for nbr1 in covered_nbrs[1:]: + common_nodes.intersection_update(G2[mapping[nbr1]]) + + common_nodes.difference_update(reverse_mapping) + common_nodes.intersection_update(G2_nodes_of_degree[G1_degree[u]]) + common_nodes.intersection_update(nodes_of_G2Labels[G1_labels[u]]) + if G1.is_multigraph(): + common_nodes.difference_update( + { + node + for node in common_nodes + if G1.number_of_edges(u, u) != G2.number_of_edges(node, node) + } + ) + return common_nodes + + +def _find_candidates_Di(u, graph_params, state_params, G1_degree): + G1, G2, G1_labels, _, _, nodes_of_G2Labels, G2_nodes_of_degree = graph_params + mapping, reverse_mapping, _, _, _, _, _, _, T2_tilde, _ = state_params + + covered_successors = [succ for succ in G1[u] if succ in mapping] + covered_predecessors = [pred for pred in G1.pred[u] if pred in mapping] + + if not (covered_successors or covered_predecessors): + candidates = set(nodes_of_G2Labels[G1_labels[u]]) + candidates.intersection_update(G2_nodes_of_degree[G1_degree[u]]) + candidates.intersection_update(T2_tilde) + candidates.difference_update(reverse_mapping) + if G1.is_multigraph(): + candidates.difference_update( + { + node + for node in candidates + if G1.number_of_edges(u, u) != G2.number_of_edges(node, node) + } + ) + return candidates + + if covered_successors: + succ1 = covered_successors[0] + common_nodes = set(G2.pred[mapping[succ1]]) + + for succ1 in covered_successors[1:]: + common_nodes.intersection_update(G2.pred[mapping[succ1]]) + else: + pred1 = covered_predecessors.pop() + common_nodes = set(G2[mapping[pred1]]) + + for pred1 in covered_predecessors: + common_nodes.intersection_update(G2[mapping[pred1]]) + + common_nodes.difference_update(reverse_mapping) + common_nodes.intersection_update(G2_nodes_of_degree[G1_degree[u]]) + common_nodes.intersection_update(nodes_of_G2Labels[G1_labels[u]]) + if G1.is_multigraph(): + common_nodes.difference_update( + { + node + for node in common_nodes + if G1.number_of_edges(u, u) != G2.number_of_edges(node, node) + } + ) + return common_nodes + + +def _feasibility(node1, node2, graph_params, state_params): + """Given a candidate pair of nodes u and v from G1 and G2 respectively, checks if it's feasible to extend the + mapping, i.e. if u and v can be matched. + + Notes + ----- + This function performs all the necessary checking by applying both consistency and cutting rules. + + Parameters + ---------- + node1, node2: Graph node + The candidate pair of nodes being checked for matching + + graph_params: namedtuple + Contains all the Graph-related parameters: + + G1,G2: NetworkX Graph or MultiGraph instances. + The two graphs to check for isomorphism or monomorphism + + G1_labels,G2_labels: dict + The label of every node in G1 and G2 respectively + + state_params: namedtuple + Contains all the State-related parameters: + + mapping: dict + The mapping as extended so far. Maps nodes of G1 to nodes of G2 + + reverse_mapping: dict + The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed + + T1, T2: set + Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are + neighbors of nodes that are. + + T1_out, T2_out: set + Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti + + Returns + ------- + True if all checks are successful, False otherwise. + """ + G1 = graph_params.G1 + + if _cut_PT(node1, node2, graph_params, state_params): + return False + + if G1.is_multigraph(): + if not _consistent_PT(node1, node2, graph_params, state_params): + return False + + return True + + +def _cut_PT(u, v, graph_params, state_params): + """Implements the cutting rules for the ISO problem. + + Parameters + ---------- + u, v: Graph node + The two candidate nodes being examined. + + graph_params: namedtuple + Contains all the Graph-related parameters: + + G1,G2: NetworkX Graph or MultiGraph instances. + The two graphs to check for isomorphism or monomorphism + + G1_labels,G2_labels: dict + The label of every node in G1 and G2 respectively + + state_params: namedtuple + Contains all the State-related parameters: + + mapping: dict + The mapping as extended so far. Maps nodes of G1 to nodes of G2 + + reverse_mapping: dict + The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed + + T1, T2: set + Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are + neighbors of nodes that are. + + T1_tilde, T2_tilde: set + Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti + + Returns + ------- + True if we should prune this branch, i.e. the node pair failed the cutting checks. False otherwise. + """ + G1, G2, G1_labels, G2_labels, _, _, _ = graph_params + ( + _, + _, + T1, + T1_in, + T1_tilde, + _, + T2, + T2_in, + T2_tilde, + _, + ) = state_params + + u_labels_predecessors, v_labels_predecessors = {}, {} + if G1.is_directed(): + u_labels_predecessors = nx.utils.groups( + {n1: G1_labels[n1] for n1 in G1.pred[u]} + ) + v_labels_predecessors = nx.utils.groups( + {n2: G2_labels[n2] for n2 in G2.pred[v]} + ) + + if set(u_labels_predecessors.keys()) != set(v_labels_predecessors.keys()): + return True + + u_labels_successors = nx.utils.groups({n1: G1_labels[n1] for n1 in G1[u]}) + v_labels_successors = nx.utils.groups({n2: G2_labels[n2] for n2 in G2[v]}) + + # if the neighbors of u, do not have the same labels as those of v, NOT feasible. + if set(u_labels_successors.keys()) != set(v_labels_successors.keys()): + return True + + for label, G1_nbh in u_labels_successors.items(): + G2_nbh = v_labels_successors[label] + + if G1.is_multigraph(): + # Check for every neighbor in the neighborhood, if u-nbr1 has same edges as v-nbr2 + u_nbrs_edges = sorted(G1.number_of_edges(u, x) for x in G1_nbh) + v_nbrs_edges = sorted(G2.number_of_edges(v, x) for x in G2_nbh) + if any( + u_nbr_edges != v_nbr_edges + for u_nbr_edges, v_nbr_edges in zip(u_nbrs_edges, v_nbrs_edges) + ): + return True + + if len(T1.intersection(G1_nbh)) != len(T2.intersection(G2_nbh)): + return True + if len(T1_tilde.intersection(G1_nbh)) != len(T2_tilde.intersection(G2_nbh)): + return True + if G1.is_directed() and len(T1_in.intersection(G1_nbh)) != len( + T2_in.intersection(G2_nbh) + ): + return True + + if not G1.is_directed(): + return False + + for label, G1_pred in u_labels_predecessors.items(): + G2_pred = v_labels_predecessors[label] + + if G1.is_multigraph(): + # Check for every neighbor in the neighborhood, if u-nbr1 has same edges as v-nbr2 + u_pred_edges = sorted(G1.number_of_edges(u, x) for x in G1_pred) + v_pred_edges = sorted(G2.number_of_edges(v, x) for x in G2_pred) + if any( + u_nbr_edges != v_nbr_edges + for u_nbr_edges, v_nbr_edges in zip(u_pred_edges, v_pred_edges) + ): + return True + + if len(T1.intersection(G1_pred)) != len(T2.intersection(G2_pred)): + return True + if len(T1_tilde.intersection(G1_pred)) != len(T2_tilde.intersection(G2_pred)): + return True + if len(T1_in.intersection(G1_pred)) != len(T2_in.intersection(G2_pred)): + return True + + return False + + +def _consistent_PT(u, v, graph_params, state_params): + """Checks the consistency of extending the mapping using the current node pair. + + Parameters + ---------- + u, v: Graph node + The two candidate nodes being examined. + + graph_params: namedtuple + Contains all the Graph-related parameters: + + G1,G2: NetworkX Graph or MultiGraph instances. + The two graphs to check for isomorphism or monomorphism + + G1_labels,G2_labels: dict + The label of every node in G1 and G2 respectively + + state_params: namedtuple + Contains all the State-related parameters: + + mapping: dict + The mapping as extended so far. Maps nodes of G1 to nodes of G2 + + reverse_mapping: dict + The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed + + T1, T2: set + Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are + neighbors of nodes that are. + + T1_out, T2_out: set + Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti + + Returns + ------- + True if the pair passes all the consistency checks successfully. False otherwise. + """ + G1, G2 = graph_params.G1, graph_params.G2 + mapping, reverse_mapping = state_params.mapping, state_params.reverse_mapping + + for neighbor in G1[u]: + if neighbor in mapping: + if G1.number_of_edges(u, neighbor) != G2.number_of_edges( + v, mapping[neighbor] + ): + return False + + for neighbor in G2[v]: + if neighbor in reverse_mapping: + if G1.number_of_edges(u, reverse_mapping[neighbor]) != G2.number_of_edges( + v, neighbor + ): + return False + + if not G1.is_directed(): + return True + + for predecessor in G1.pred[u]: + if predecessor in mapping: + if G1.number_of_edges(predecessor, u) != G2.number_of_edges( + mapping[predecessor], v + ): + return False + + for predecessor in G2.pred[v]: + if predecessor in reverse_mapping: + if G1.number_of_edges( + reverse_mapping[predecessor], u + ) != G2.number_of_edges(predecessor, v): + return False + + return True + + +def _update_Tinout(new_node1, new_node2, graph_params, state_params): + """Updates the Ti/Ti_out (i=1,2) when a new node pair u-v is added to the mapping. + + Notes + ----- + This function should be called right after the feasibility checks are passed, and node1 is mapped to node2. The + purpose of this function is to avoid brute force computing of Ti/Ti_out by iterating over all nodes of the graph + and checking which nodes satisfy the necessary conditions. Instead, in every step of the algorithm we focus + exclusively on the two nodes that are being added to the mapping, incrementally updating Ti/Ti_out. + + Parameters + ---------- + new_node1, new_node2: Graph node + The two new nodes, added to the mapping. + + graph_params: namedtuple + Contains all the Graph-related parameters: + + G1,G2: NetworkX Graph or MultiGraph instances. + The two graphs to check for isomorphism or monomorphism + + G1_labels,G2_labels: dict + The label of every node in G1 and G2 respectively + + state_params: namedtuple + Contains all the State-related parameters: + + mapping: dict + The mapping as extended so far. Maps nodes of G1 to nodes of G2 + + reverse_mapping: dict + The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed + + T1, T2: set + Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are + neighbors of nodes that are. + + T1_tilde, T2_tilde: set + Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti + """ + G1, G2, _, _, _, _, _ = graph_params + ( + mapping, + reverse_mapping, + T1, + T1_in, + T1_tilde, + T1_tilde_in, + T2, + T2_in, + T2_tilde, + T2_tilde_in, + ) = state_params + + uncovered_successors_G1 = {succ for succ in G1[new_node1] if succ not in mapping} + uncovered_successors_G2 = { + succ for succ in G2[new_node2] if succ not in reverse_mapping + } + + # Add the uncovered neighbors of node1 and node2 in T1 and T2 respectively + T1.update(uncovered_successors_G1) + T2.update(uncovered_successors_G2) + T1.discard(new_node1) + T2.discard(new_node2) + + T1_tilde.difference_update(uncovered_successors_G1) + T2_tilde.difference_update(uncovered_successors_G2) + T1_tilde.discard(new_node1) + T2_tilde.discard(new_node2) + + if not G1.is_directed(): + return + + uncovered_predecessors_G1 = { + pred for pred in G1.pred[new_node1] if pred not in mapping + } + uncovered_predecessors_G2 = { + pred for pred in G2.pred[new_node2] if pred not in reverse_mapping + } + + T1_in.update(uncovered_predecessors_G1) + T2_in.update(uncovered_predecessors_G2) + T1_in.discard(new_node1) + T2_in.discard(new_node2) + + T1_tilde.difference_update(uncovered_predecessors_G1) + T2_tilde.difference_update(uncovered_predecessors_G2) + T1_tilde.discard(new_node1) + T2_tilde.discard(new_node2) + + +def _restore_Tinout(popped_node1, popped_node2, graph_params, state_params): + """Restores the previous version of Ti/Ti_out when a node pair is deleted from the mapping. + + Parameters + ---------- + popped_node1, popped_node2: Graph node + The two nodes deleted from the mapping. + + graph_params: namedtuple + Contains all the Graph-related parameters: + + G1,G2: NetworkX Graph or MultiGraph instances. + The two graphs to check for isomorphism or monomorphism + + G1_labels,G2_labels: dict + The label of every node in G1 and G2 respectively + + state_params: namedtuple + Contains all the State-related parameters: + + mapping: dict + The mapping as extended so far. Maps nodes of G1 to nodes of G2 + + reverse_mapping: dict + The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed + + T1, T2: set + Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are + neighbors of nodes that are. + + T1_tilde, T2_tilde: set + Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti + """ + # If the node we want to remove from the mapping, has at least one covered neighbor, add it to T1. + G1, G2, _, _, _, _, _ = graph_params + ( + mapping, + reverse_mapping, + T1, + T1_in, + T1_tilde, + T1_tilde_in, + T2, + T2_in, + T2_tilde, + T2_tilde_in, + ) = state_params + + is_added = False + for neighbor in G1[popped_node1]: + if neighbor in mapping: + # if a neighbor of the excluded node1 is in the mapping, keep node1 in T1 + is_added = True + T1.add(popped_node1) + else: + # check if its neighbor has another connection with a covered node. If not, only then exclude it from T1 + if any(nbr in mapping for nbr in G1[neighbor]): + continue + T1.discard(neighbor) + T1_tilde.add(neighbor) + + # Case where the node is not present in neither the mapping nor T1. By definition, it should belong to T1_tilde + if not is_added: + T1_tilde.add(popped_node1) + + is_added = False + for neighbor in G2[popped_node2]: + if neighbor in reverse_mapping: + is_added = True + T2.add(popped_node2) + else: + if any(nbr in reverse_mapping for nbr in G2[neighbor]): + continue + T2.discard(neighbor) + T2_tilde.add(neighbor) + + if not is_added: + T2_tilde.add(popped_node2) + + +def _restore_Tinout_Di(popped_node1, popped_node2, graph_params, state_params): + # If the node we want to remove from the mapping, has at least one covered neighbor, add it to T1. + G1, G2, _, _, _, _, _ = graph_params + ( + mapping, + reverse_mapping, + T1, + T1_in, + T1_tilde, + T1_tilde_in, + T2, + T2_in, + T2_tilde, + T2_tilde_in, + ) = state_params + + is_added = False + for successor in G1[popped_node1]: + if successor in mapping: + # if a neighbor of the excluded node1 is in the mapping, keep node1 in T1 + is_added = True + T1_in.add(popped_node1) + else: + # check if its neighbor has another connection with a covered node. If not, only then exclude it from T1 + if not any(pred in mapping for pred in G1.pred[successor]): + T1.discard(successor) + + if not any(succ in mapping for succ in G1[successor]): + T1_in.discard(successor) + + if successor not in T1: + if successor not in T1_in: + T1_tilde.add(successor) + + for predecessor in G1.pred[popped_node1]: + if predecessor in mapping: + # if a neighbor of the excluded node1 is in the mapping, keep node1 in T1 + is_added = True + T1.add(popped_node1) + else: + # check if its neighbor has another connection with a covered node. If not, only then exclude it from T1 + if not any(pred in mapping for pred in G1.pred[predecessor]): + T1.discard(predecessor) + + if not any(succ in mapping for succ in G1[predecessor]): + T1_in.discard(predecessor) + + if not (predecessor in T1 or predecessor in T1_in): + T1_tilde.add(predecessor) + + # Case where the node is not present in neither the mapping nor T1. By definition it should belong to T1_tilde + if not is_added: + T1_tilde.add(popped_node1) + + is_added = False + for successor in G2[popped_node2]: + if successor in reverse_mapping: + is_added = True + T2_in.add(popped_node2) + else: + if not any(pred in reverse_mapping for pred in G2.pred[successor]): + T2.discard(successor) + + if not any(succ in reverse_mapping for succ in G2[successor]): + T2_in.discard(successor) + + if successor not in T2: + if successor not in T2_in: + T2_tilde.add(successor) + + for predecessor in G2.pred[popped_node2]: + if predecessor in reverse_mapping: + # if a neighbor of the excluded node1 is in the mapping, keep node1 in T1 + is_added = True + T2.add(popped_node2) + else: + # check if its neighbor has another connection with a covered node. If not, only then exclude it from T1 + if not any(pred in reverse_mapping for pred in G2.pred[predecessor]): + T2.discard(predecessor) + + if not any(succ in reverse_mapping for succ in G2[predecessor]): + T2_in.discard(predecessor) + + if not (predecessor in T2 or predecessor in T2_in): + T2_tilde.add(predecessor) + + if not is_added: + T2_tilde.add(popped_node2) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/vf2userfunc.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/vf2userfunc.py new file mode 100644 index 0000000000000000000000000000000000000000..6fcf8a15f6ec0ef517d225a9d0095cfe5dc26ab2 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/vf2userfunc.py @@ -0,0 +1,192 @@ +""" +Module to simplify the specification of user-defined equality functions for +node and edge attributes during isomorphism checks. + +During the construction of an isomorphism, the algorithm considers two +candidate nodes n1 in G1 and n2 in G2. The graphs G1 and G2 are then +compared with respect to properties involving n1 and n2, and if the outcome +is good, then the candidate nodes are considered isomorphic. NetworkX +provides a simple mechanism for users to extend the comparisons to include +node and edge attributes. + +Node attributes are handled by the node_match keyword. When considering +n1 and n2, the algorithm passes their node attribute dictionaries to +node_match, and if it returns False, then n1 and n2 cannot be +considered to be isomorphic. + +Edge attributes are handled by the edge_match keyword. When considering +n1 and n2, the algorithm must verify that outgoing edges from n1 are +commensurate with the outgoing edges for n2. If the graph is directed, +then a similar check is also performed for incoming edges. + +Focusing only on outgoing edges, we consider pairs of nodes (n1, v1) from +G1 and (n2, v2) from G2. For graphs and digraphs, there is only one edge +between (n1, v1) and only one edge between (n2, v2). Those edge attribute +dictionaries are passed to edge_match, and if it returns False, then +n1 and n2 cannot be considered isomorphic. For multigraphs and +multidigraphs, there can be multiple edges between (n1, v1) and also +multiple edges between (n2, v2). Now, there must exist an isomorphism +from "all the edges between (n1, v1)" to "all the edges between (n2, v2)". +So, all of the edge attribute dictionaries are passed to edge_match, and +it must determine if there is an isomorphism between the two sets of edges. +""" + +from . import isomorphvf2 as vf2 + +__all__ = ["GraphMatcher", "DiGraphMatcher", "MultiGraphMatcher", "MultiDiGraphMatcher"] + + +def _semantic_feasibility(self, G1_node, G2_node): + """Returns True if mapping G1_node to G2_node is semantically feasible.""" + # Make sure the nodes match + if self.node_match is not None: + nm = self.node_match(self.G1.nodes[G1_node], self.G2.nodes[G2_node]) + if not nm: + return False + + # Make sure the edges match + if self.edge_match is not None: + # Cached lookups + G1nbrs = self.G1_adj[G1_node] + G2nbrs = self.G2_adj[G2_node] + core_1 = self.core_1 + edge_match = self.edge_match + + for neighbor in G1nbrs: + # G1_node is not in core_1, so we must handle R_self separately + if neighbor == G1_node: + if G2_node in G2nbrs and not edge_match( + G1nbrs[G1_node], G2nbrs[G2_node] + ): + return False + elif neighbor in core_1: + G2_nbr = core_1[neighbor] + if G2_nbr in G2nbrs and not edge_match( + G1nbrs[neighbor], G2nbrs[G2_nbr] + ): + return False + # syntactic check has already verified that neighbors are symmetric + + return True + + +class GraphMatcher(vf2.GraphMatcher): + """VF2 isomorphism checker for undirected graphs.""" + + def __init__(self, G1, G2, node_match=None, edge_match=None): + """Initialize graph matcher. + + Parameters + ---------- + G1, G2: graph + The graphs to be tested. + + node_match: callable + A function that returns True iff node n1 in G1 and n2 in G2 + should be considered equal during the isomorphism test. The + function will be called like:: + + node_match(G1.nodes[n1], G2.nodes[n2]) + + That is, the function will receive the node attribute dictionaries + of the nodes under consideration. If None, then no attributes are + considered when testing for an isomorphism. + + edge_match: callable + A function that returns True iff the edge attribute dictionary for + the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be + considered equal during the isomorphism test. The function will be + called like:: + + edge_match(G1[u1][v1], G2[u2][v2]) + + That is, the function will receive the edge attribute dictionaries + of the edges under consideration. If None, then no attributes are + considered when testing for an isomorphism. + + """ + vf2.GraphMatcher.__init__(self, G1, G2) + + self.node_match = node_match + self.edge_match = edge_match + + # These will be modified during checks to minimize code repeat. + self.G1_adj = self.G1.adj + self.G2_adj = self.G2.adj + + semantic_feasibility = _semantic_feasibility + + +class DiGraphMatcher(vf2.DiGraphMatcher): + """VF2 isomorphism checker for directed graphs.""" + + def __init__(self, G1, G2, node_match=None, edge_match=None): + """Initialize graph matcher. + + Parameters + ---------- + G1, G2 : graph + The graphs to be tested. + + node_match : callable + A function that returns True iff node n1 in G1 and n2 in G2 + should be considered equal during the isomorphism test. The + function will be called like:: + + node_match(G1.nodes[n1], G2.nodes[n2]) + + That is, the function will receive the node attribute dictionaries + of the nodes under consideration. If None, then no attributes are + considered when testing for an isomorphism. + + edge_match : callable + A function that returns True iff the edge attribute dictionary for + the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be + considered equal during the isomorphism test. The function will be + called like:: + + edge_match(G1[u1][v1], G2[u2][v2]) + + That is, the function will receive the edge attribute dictionaries + of the edges under consideration. If None, then no attributes are + considered when testing for an isomorphism. + + """ + vf2.DiGraphMatcher.__init__(self, G1, G2) + + self.node_match = node_match + self.edge_match = edge_match + + # These will be modified during checks to minimize code repeat. + self.G1_adj = self.G1.adj + self.G2_adj = self.G2.adj + + def semantic_feasibility(self, G1_node, G2_node): + """Returns True if mapping G1_node to G2_node is semantically feasible.""" + + # Test node_match and also test edge_match on successors + feasible = _semantic_feasibility(self, G1_node, G2_node) + if not feasible: + return False + + # Test edge_match on predecessors + self.G1_adj = self.G1.pred + self.G2_adj = self.G2.pred + feasible = _semantic_feasibility(self, G1_node, G2_node) + self.G1_adj = self.G1.adj + self.G2_adj = self.G2.adj + + return feasible + + +# The "semantics" of edge_match are different for multi(di)graphs, but +# the implementation is the same. So, technically we do not need to +# provide "multi" versions, but we do so to match NetworkX's base classes. + + +class MultiGraphMatcher(GraphMatcher): + """VF2 isomorphism checker for undirected multigraphs.""" + + +class MultiDiGraphMatcher(DiGraphMatcher): + """VF2 isomorphism checker for directed multigraphs.""" diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/matching.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/matching.py new file mode 100644 index 0000000000000000000000000000000000000000..6cfb3c93f6aaa379acb01e5ea3b35b4f20bd40b6 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/matching.py @@ -0,0 +1,1152 @@ +"""Functions for computing and verifying matchings in a graph.""" + +from collections import Counter +from itertools import combinations, repeat + +import networkx as nx +from networkx.utils import not_implemented_for + +__all__ = [ + "is_matching", + "is_maximal_matching", + "is_perfect_matching", + "max_weight_matching", + "min_weight_matching", + "maximal_matching", +] + + +@not_implemented_for("multigraph") +@not_implemented_for("directed") +@nx._dispatchable +def maximal_matching(G): + r"""Find a maximal matching in the graph. + + A matching is a subset of edges in which no node occurs more than once. + A maximal matching cannot add more edges and still be a matching. + + Parameters + ---------- + G : NetworkX graph + Undirected graph + + Returns + ------- + matching : set + A maximal matching of the graph. + + Examples + -------- + >>> G = nx.Graph([(1, 2), (1, 3), (2, 3), (2, 4), (3, 5), (4, 5)]) + >>> sorted(nx.maximal_matching(G)) + [(1, 2), (3, 5)] + + Notes + ----- + The algorithm greedily selects a maximal matching M of the graph G + (i.e. no superset of M exists). It runs in $O(|E|)$ time. + """ + matching = set() + nodes = set() + for edge in G.edges(): + # If the edge isn't covered, add it to the matching + # then remove neighborhood of u and v from consideration. + u, v = edge + if u not in nodes and v not in nodes and u != v: + matching.add(edge) + nodes.update(edge) + return matching + + +def matching_dict_to_set(matching): + """Converts matching dict format to matching set format + + Converts a dictionary representing a matching (as returned by + :func:`max_weight_matching`) to a set representing a matching (as + returned by :func:`maximal_matching`). + + In the definition of maximal matching adopted by NetworkX, + self-loops are not allowed, so the provided dictionary is expected + to never have any mapping from a key to itself. However, the + dictionary is expected to have mirrored key/value pairs, for + example, key ``u`` with value ``v`` and key ``v`` with value ``u``. + + """ + edges = set() + for edge in matching.items(): + u, v = edge + if (v, u) in edges or edge in edges: + continue + if u == v: + raise nx.NetworkXError(f"Selfloops cannot appear in matchings {edge}") + edges.add(edge) + return edges + + +@nx._dispatchable +def is_matching(G, matching): + """Return True if ``matching`` is a valid matching of ``G`` + + A *matching* in a graph is a set of edges in which no two distinct + edges share a common endpoint. Each node is incident to at most one + edge in the matching. The edges are said to be independent. + + Parameters + ---------- + G : NetworkX graph + + matching : dict or set + A dictionary or set representing a matching. If a dictionary, it + must have ``matching[u] == v`` and ``matching[v] == u`` for each + edge ``(u, v)`` in the matching. If a set, it must have elements + of the form ``(u, v)``, where ``(u, v)`` is an edge in the + matching. + + Returns + ------- + bool + Whether the given set or dictionary represents a valid matching + in the graph. + + Raises + ------ + NetworkXError + If the proposed matching has an edge to a node not in G. + Or if the matching is not a collection of 2-tuple edges. + + Examples + -------- + >>> G = nx.Graph([(1, 2), (1, 3), (2, 3), (2, 4), (3, 5), (4, 5)]) + >>> nx.is_maximal_matching(G, {1: 3, 2: 4}) # using dict to represent matching + True + + >>> nx.is_matching(G, {(1, 3), (2, 4)}) # using set to represent matching + True + + """ + if isinstance(matching, dict): + matching = matching_dict_to_set(matching) + + nodes = set() + for edge in matching: + if len(edge) != 2: + raise nx.NetworkXError(f"matching has non-2-tuple edge {edge}") + u, v = edge + if u not in G or v not in G: + raise nx.NetworkXError(f"matching contains edge {edge} with node not in G") + if u == v: + return False + if not G.has_edge(u, v): + return False + if u in nodes or v in nodes: + return False + nodes.update(edge) + return True + + +@nx._dispatchable +def is_maximal_matching(G, matching): + """Return True if ``matching`` is a maximal matching of ``G`` + + A *maximal matching* in a graph is a matching in which adding any + edge would cause the set to no longer be a valid matching. + + Parameters + ---------- + G : NetworkX graph + + matching : dict or set + A dictionary or set representing a matching. If a dictionary, it + must have ``matching[u] == v`` and ``matching[v] == u`` for each + edge ``(u, v)`` in the matching. If a set, it must have elements + of the form ``(u, v)``, where ``(u, v)`` is an edge in the + matching. + + Returns + ------- + bool + Whether the given set or dictionary represents a valid maximal + matching in the graph. + + Examples + -------- + >>> G = nx.Graph([(1, 2), (1, 3), (2, 3), (3, 4), (3, 5)]) + >>> nx.is_maximal_matching(G, {(1, 2), (3, 4)}) + True + + """ + if isinstance(matching, dict): + matching = matching_dict_to_set(matching) + # If the given set is not a matching, then it is not a maximal matching. + edges = set() + nodes = set() + for edge in matching: + if len(edge) != 2: + raise nx.NetworkXError(f"matching has non-2-tuple edge {edge}") + u, v = edge + if u not in G or v not in G: + raise nx.NetworkXError(f"matching contains edge {edge} with node not in G") + if u == v: + return False + if not G.has_edge(u, v): + return False + if u in nodes or v in nodes: + return False + nodes.update(edge) + edges.add(edge) + edges.add((v, u)) + # A matching is maximal if adding any new edge from G to it + # causes the resulting set to match some node twice. + # Be careful to check for adding selfloops + for u, v in G.edges: + if (u, v) not in edges: + # could add edge (u, v) to edges and have a bigger matching + if u not in nodes and v not in nodes and u != v: + return False + return True + + +@nx._dispatchable +def is_perfect_matching(G, matching): + """Return True if ``matching`` is a perfect matching for ``G`` + + A *perfect matching* in a graph is a matching in which exactly one edge + is incident upon each vertex. + + Parameters + ---------- + G : NetworkX graph + + matching : dict or set + A dictionary or set representing a matching. If a dictionary, it + must have ``matching[u] == v`` and ``matching[v] == u`` for each + edge ``(u, v)`` in the matching. If a set, it must have elements + of the form ``(u, v)``, where ``(u, v)`` is an edge in the + matching. + + Returns + ------- + bool + Whether the given set or dictionary represents a valid perfect + matching in the graph. + + Examples + -------- + >>> G = nx.Graph([(1, 2), (1, 3), (2, 3), (2, 4), (3, 5), (4, 5), (4, 6)]) + >>> my_match = {1: 2, 3: 5, 4: 6} + >>> nx.is_perfect_matching(G, my_match) + True + + """ + if isinstance(matching, dict): + matching = matching_dict_to_set(matching) + + nodes = set() + for edge in matching: + if len(edge) != 2: + raise nx.NetworkXError(f"matching has non-2-tuple edge {edge}") + u, v = edge + if u not in G or v not in G: + raise nx.NetworkXError(f"matching contains edge {edge} with node not in G") + if u == v: + return False + if not G.has_edge(u, v): + return False + if u in nodes or v in nodes: + return False + nodes.update(edge) + return len(nodes) == len(G) + + +@not_implemented_for("multigraph") +@not_implemented_for("directed") +@nx._dispatchable(edge_attrs="weight") +def min_weight_matching(G, weight="weight"): + """Computing a minimum-weight maximal matching of G. + + Use the maximum-weight algorithm with edge weights subtracted + from the maximum weight of all edges. + + A matching is a subset of edges in which no node occurs more than once. + The weight of a matching is the sum of the weights of its edges. + A maximal matching cannot add more edges and still be a matching. + The cardinality of a matching is the number of matched edges. + + This method replaces the edge weights with 1 plus the maximum edge weight + minus the original edge weight. + + new_weight = (max_weight + 1) - edge_weight + + then runs :func:`max_weight_matching` with the new weights. + The max weight matching with these new weights corresponds + to the min weight matching using the original weights. + Adding 1 to the max edge weight keeps all edge weights positive + and as integers if they started as integers. + + You might worry that adding 1 to each weight would make the algorithm + favor matchings with more edges. But we use the parameter + `maxcardinality=True` in `max_weight_matching` to ensure that the + number of edges in the competing matchings are the same and thus + the optimum does not change due to changes in the number of edges. + + Read the documentation of `max_weight_matching` for more information. + + Parameters + ---------- + G : NetworkX graph + Undirected graph + + weight: string, optional (default='weight') + Edge data key corresponding to the edge weight. + If key not found, uses 1 as weight. + + Returns + ------- + matching : set + A minimal weight matching of the graph. + + See Also + -------- + max_weight_matching + """ + if len(G.edges) == 0: + return max_weight_matching(G, maxcardinality=True, weight=weight) + G_edges = G.edges(data=weight, default=1) + max_weight = 1 + max(w for _, _, w in G_edges) + InvG = nx.Graph() + edges = ((u, v, max_weight - w) for u, v, w in G_edges) + InvG.add_weighted_edges_from(edges, weight=weight) + return max_weight_matching(InvG, maxcardinality=True, weight=weight) + + +@not_implemented_for("multigraph") +@not_implemented_for("directed") +@nx._dispatchable(edge_attrs="weight") +def max_weight_matching(G, maxcardinality=False, weight="weight"): + """Compute a maximum-weighted matching of G. + + A matching is a subset of edges in which no node occurs more than once. + The weight of a matching is the sum of the weights of its edges. + A maximal matching cannot add more edges and still be a matching. + The cardinality of a matching is the number of matched edges. + + Parameters + ---------- + G : NetworkX graph + Undirected graph + + maxcardinality: bool, optional (default=False) + If maxcardinality is True, compute the maximum-cardinality matching + with maximum weight among all maximum-cardinality matchings. + + weight: string, optional (default='weight') + Edge data key corresponding to the edge weight. + If key not found, uses 1 as weight. + + + Returns + ------- + matching : set + A maximal matching of the graph. + + Examples + -------- + >>> G = nx.Graph() + >>> edges = [(1, 2, 6), (1, 3, 2), (2, 3, 1), (2, 4, 7), (3, 5, 9), (4, 5, 3)] + >>> G.add_weighted_edges_from(edges) + >>> sorted(nx.max_weight_matching(G)) + [(2, 4), (5, 3)] + + Notes + ----- + If G has edges with weight attributes the edge data are used as + weight values else the weights are assumed to be 1. + + This function takes time O(number_of_nodes ** 3). + + If all edge weights are integers, the algorithm uses only integer + computations. If floating point weights are used, the algorithm + could return a slightly suboptimal matching due to numeric + precision errors. + + This method is based on the "blossom" method for finding augmenting + paths and the "primal-dual" method for finding a matching of maximum + weight, both methods invented by Jack Edmonds [1]_. + + Bipartite graphs can also be matched using the functions present in + :mod:`networkx.algorithms.bipartite.matching`. + + References + ---------- + .. [1] "Efficient Algorithms for Finding Maximum Matching in Graphs", + Zvi Galil, ACM Computing Surveys, 1986. + """ + # + # The algorithm is taken from "Efficient Algorithms for Finding Maximum + # Matching in Graphs" by Zvi Galil, ACM Computing Surveys, 1986. + # It is based on the "blossom" method for finding augmenting paths and + # the "primal-dual" method for finding a matching of maximum weight, both + # methods invented by Jack Edmonds. + # + # A C program for maximum weight matching by Ed Rothberg was used + # extensively to validate this new code. + # + # Many terms used in the code comments are explained in the paper + # by Galil. You will probably need the paper to make sense of this code. + # + + class NoNode: + """Dummy value which is different from any node.""" + + class Blossom: + """Representation of a non-trivial blossom or sub-blossom.""" + + __slots__ = ["childs", "edges", "mybestedges"] + + # b.childs is an ordered list of b's sub-blossoms, starting with + # the base and going round the blossom. + + # b.edges is the list of b's connecting edges, such that + # b.edges[i] = (v, w) where v is a vertex in b.childs[i] + # and w is a vertex in b.childs[wrap(i+1)]. + + # If b is a top-level S-blossom, + # b.mybestedges is a list of least-slack edges to neighboring + # S-blossoms, or None if no such list has been computed yet. + # This is used for efficient computation of delta3. + + # Generate the blossom's leaf vertices. + def leaves(self): + stack = [*self.childs] + while stack: + t = stack.pop() + if isinstance(t, Blossom): + stack.extend(t.childs) + else: + yield t + + # Get a list of vertices. + gnodes = list(G) + if not gnodes: + return set() # don't bother with empty graphs + + # Find the maximum edge weight. + maxweight = 0 + allinteger = True + for i, j, d in G.edges(data=True): + wt = d.get(weight, 1) + if i != j and wt > maxweight: + maxweight = wt + allinteger = allinteger and (str(type(wt)).split("'")[1] in ("int", "long")) + + # If v is a matched vertex, mate[v] is its partner vertex. + # If v is a single vertex, v does not occur as a key in mate. + # Initially all vertices are single; updated during augmentation. + mate = {} + + # If b is a top-level blossom, + # label.get(b) is None if b is unlabeled (free), + # 1 if b is an S-blossom, + # 2 if b is a T-blossom. + # The label of a vertex is found by looking at the label of its top-level + # containing blossom. + # If v is a vertex inside a T-blossom, label[v] is 2 iff v is reachable + # from an S-vertex outside the blossom. + # Labels are assigned during a stage and reset after each augmentation. + label = {} + + # If b is a labeled top-level blossom, + # labeledge[b] = (v, w) is the edge through which b obtained its label + # such that w is a vertex in b, or None if b's base vertex is single. + # If w is a vertex inside a T-blossom and label[w] == 2, + # labeledge[w] = (v, w) is an edge through which w is reachable from + # outside the blossom. + labeledge = {} + + # If v is a vertex, inblossom[v] is the top-level blossom to which v + # belongs. + # If v is a top-level vertex, inblossom[v] == v since v is itself + # a (trivial) top-level blossom. + # Initially all vertices are top-level trivial blossoms. + inblossom = dict(zip(gnodes, gnodes)) + + # If b is a sub-blossom, + # blossomparent[b] is its immediate parent (sub-)blossom. + # If b is a top-level blossom, blossomparent[b] is None. + blossomparent = dict(zip(gnodes, repeat(None))) + + # If b is a (sub-)blossom, + # blossombase[b] is its base VERTEX (i.e. recursive sub-blossom). + blossombase = dict(zip(gnodes, gnodes)) + + # If w is a free vertex (or an unreached vertex inside a T-blossom), + # bestedge[w] = (v, w) is the least-slack edge from an S-vertex, + # or None if there is no such edge. + # If b is a (possibly trivial) top-level S-blossom, + # bestedge[b] = (v, w) is the least-slack edge to a different S-blossom + # (v inside b), or None if there is no such edge. + # This is used for efficient computation of delta2 and delta3. + bestedge = {} + + # If v is a vertex, + # dualvar[v] = 2 * u(v) where u(v) is the v's variable in the dual + # optimization problem (if all edge weights are integers, multiplication + # by two ensures that all values remain integers throughout the algorithm). + # Initially, u(v) = maxweight / 2. + dualvar = dict(zip(gnodes, repeat(maxweight))) + + # If b is a non-trivial blossom, + # blossomdual[b] = z(b) where z(b) is b's variable in the dual + # optimization problem. + blossomdual = {} + + # If (v, w) in allowedge or (w, v) in allowedg, then the edge + # (v, w) is known to have zero slack in the optimization problem; + # otherwise the edge may or may not have zero slack. + allowedge = {} + + # Queue of newly discovered S-vertices. + queue = [] + + # Return 2 * slack of edge (v, w) (does not work inside blossoms). + def slack(v, w): + return dualvar[v] + dualvar[w] - 2 * G[v][w].get(weight, 1) + + # Assign label t to the top-level blossom containing vertex w, + # coming through an edge from vertex v. + def assignLabel(w, t, v): + b = inblossom[w] + assert label.get(w) is None and label.get(b) is None + label[w] = label[b] = t + if v is not None: + labeledge[w] = labeledge[b] = (v, w) + else: + labeledge[w] = labeledge[b] = None + bestedge[w] = bestedge[b] = None + if t == 1: + # b became an S-vertex/blossom; add it(s vertices) to the queue. + if isinstance(b, Blossom): + queue.extend(b.leaves()) + else: + queue.append(b) + elif t == 2: + # b became a T-vertex/blossom; assign label S to its mate. + # (If b is a non-trivial blossom, its base is the only vertex + # with an external mate.) + base = blossombase[b] + assignLabel(mate[base], 1, base) + + # Trace back from vertices v and w to discover either a new blossom + # or an augmenting path. Return the base vertex of the new blossom, + # or NoNode if an augmenting path was found. + def scanBlossom(v, w): + # Trace back from v and w, placing breadcrumbs as we go. + path = [] + base = NoNode + while v is not NoNode: + # Look for a breadcrumb in v's blossom or put a new breadcrumb. + b = inblossom[v] + if label[b] & 4: + base = blossombase[b] + break + assert label[b] == 1 + path.append(b) + label[b] = 5 + # Trace one step back. + if labeledge[b] is None: + # The base of blossom b is single; stop tracing this path. + assert blossombase[b] not in mate + v = NoNode + else: + assert labeledge[b][0] == mate[blossombase[b]] + v = labeledge[b][0] + b = inblossom[v] + assert label[b] == 2 + # b is a T-blossom; trace one more step back. + v = labeledge[b][0] + # Swap v and w so that we alternate between both paths. + if w is not NoNode: + v, w = w, v + # Remove breadcrumbs. + for b in path: + label[b] = 1 + # Return base vertex, if we found one. + return base + + # Construct a new blossom with given base, through S-vertices v and w. + # Label the new blossom as S; set its dual variable to zero; + # relabel its T-vertices to S and add them to the queue. + def addBlossom(base, v, w): + bb = inblossom[base] + bv = inblossom[v] + bw = inblossom[w] + # Create blossom. + b = Blossom() + blossombase[b] = base + blossomparent[b] = None + blossomparent[bb] = b + # Make list of sub-blossoms and their interconnecting edge endpoints. + b.childs = path = [] + b.edges = edgs = [(v, w)] + # Trace back from v to base. + while bv != bb: + # Add bv to the new blossom. + blossomparent[bv] = b + path.append(bv) + edgs.append(labeledge[bv]) + assert label[bv] == 2 or ( + label[bv] == 1 and labeledge[bv][0] == mate[blossombase[bv]] + ) + # Trace one step back. + v = labeledge[bv][0] + bv = inblossom[v] + # Add base sub-blossom; reverse lists. + path.append(bb) + path.reverse() + edgs.reverse() + # Trace back from w to base. + while bw != bb: + # Add bw to the new blossom. + blossomparent[bw] = b + path.append(bw) + edgs.append((labeledge[bw][1], labeledge[bw][0])) + assert label[bw] == 2 or ( + label[bw] == 1 and labeledge[bw][0] == mate[blossombase[bw]] + ) + # Trace one step back. + w = labeledge[bw][0] + bw = inblossom[w] + # Set label to S. + assert label[bb] == 1 + label[b] = 1 + labeledge[b] = labeledge[bb] + # Set dual variable to zero. + blossomdual[b] = 0 + # Relabel vertices. + for v in b.leaves(): + if label[inblossom[v]] == 2: + # This T-vertex now turns into an S-vertex because it becomes + # part of an S-blossom; add it to the queue. + queue.append(v) + inblossom[v] = b + # Compute b.mybestedges. + bestedgeto = {} + for bv in path: + if isinstance(bv, Blossom): + if bv.mybestedges is not None: + # Walk this subblossom's least-slack edges. + nblist = bv.mybestedges + # The sub-blossom won't need this data again. + bv.mybestedges = None + else: + # This subblossom does not have a list of least-slack + # edges; get the information from the vertices. + nblist = [ + (v, w) for v in bv.leaves() for w in G.neighbors(v) if v != w + ] + else: + nblist = [(bv, w) for w in G.neighbors(bv) if bv != w] + for k in nblist: + (i, j) = k + if inblossom[j] == b: + i, j = j, i + bj = inblossom[j] + if ( + bj != b + and label.get(bj) == 1 + and ((bj not in bestedgeto) or slack(i, j) < slack(*bestedgeto[bj])) + ): + bestedgeto[bj] = k + # Forget about least-slack edge of the subblossom. + bestedge[bv] = None + b.mybestedges = list(bestedgeto.values()) + # Select bestedge[b]. + mybestedge = None + bestedge[b] = None + for k in b.mybestedges: + kslack = slack(*k) + if mybestedge is None or kslack < mybestslack: + mybestedge = k + mybestslack = kslack + bestedge[b] = mybestedge + + # Expand the given top-level blossom. + def expandBlossom(b, endstage): + # This is an obnoxiously complicated recursive function for the sake of + # a stack-transformation. So, we hack around the complexity by using + # a trampoline pattern. By yielding the arguments to each recursive + # call, we keep the actual callstack flat. + + def _recurse(b, endstage): + # Convert sub-blossoms into top-level blossoms. + for s in b.childs: + blossomparent[s] = None + if isinstance(s, Blossom): + if endstage and blossomdual[s] == 0: + # Recursively expand this sub-blossom. + yield s + else: + for v in s.leaves(): + inblossom[v] = s + else: + inblossom[s] = s + # If we expand a T-blossom during a stage, its sub-blossoms must be + # relabeled. + if (not endstage) and label.get(b) == 2: + # Start at the sub-blossom through which the expanding + # blossom obtained its label, and relabel sub-blossoms untili + # we reach the base. + # Figure out through which sub-blossom the expanding blossom + # obtained its label initially. + entrychild = inblossom[labeledge[b][1]] + # Decide in which direction we will go round the blossom. + j = b.childs.index(entrychild) + if j & 1: + # Start index is odd; go forward and wrap. + j -= len(b.childs) + jstep = 1 + else: + # Start index is even; go backward. + jstep = -1 + # Move along the blossom until we get to the base. + v, w = labeledge[b] + while j != 0: + # Relabel the T-sub-blossom. + if jstep == 1: + p, q = b.edges[j] + else: + q, p = b.edges[j - 1] + label[w] = None + label[q] = None + assignLabel(w, 2, v) + # Step to the next S-sub-blossom and note its forward edge. + allowedge[(p, q)] = allowedge[(q, p)] = True + j += jstep + if jstep == 1: + v, w = b.edges[j] + else: + w, v = b.edges[j - 1] + # Step to the next T-sub-blossom. + allowedge[(v, w)] = allowedge[(w, v)] = True + j += jstep + # Relabel the base T-sub-blossom WITHOUT stepping through to + # its mate (so don't call assignLabel). + bw = b.childs[j] + label[w] = label[bw] = 2 + labeledge[w] = labeledge[bw] = (v, w) + bestedge[bw] = None + # Continue along the blossom until we get back to entrychild. + j += jstep + while b.childs[j] != entrychild: + # Examine the vertices of the sub-blossom to see whether + # it is reachable from a neighboring S-vertex outside the + # expanding blossom. + bv = b.childs[j] + if label.get(bv) == 1: + # This sub-blossom just got label S through one of its + # neighbors; leave it be. + j += jstep + continue + if isinstance(bv, Blossom): + for v in bv.leaves(): + if label.get(v): + break + else: + v = bv + # If the sub-blossom contains a reachable vertex, assign + # label T to the sub-blossom. + if label.get(v): + assert label[v] == 2 + assert inblossom[v] == bv + label[v] = None + label[mate[blossombase[bv]]] = None + assignLabel(v, 2, labeledge[v][0]) + j += jstep + # Remove the expanded blossom entirely. + label.pop(b, None) + labeledge.pop(b, None) + bestedge.pop(b, None) + del blossomparent[b] + del blossombase[b] + del blossomdual[b] + + # Now, we apply the trampoline pattern. We simulate a recursive + # callstack by maintaining a stack of generators, each yielding a + # sequence of function arguments. We grow the stack by appending a call + # to _recurse on each argument tuple, and shrink the stack whenever a + # generator is exhausted. + stack = [_recurse(b, endstage)] + while stack: + top = stack[-1] + for s in top: + stack.append(_recurse(s, endstage)) + break + else: + stack.pop() + + # Swap matched/unmatched edges over an alternating path through blossom b + # between vertex v and the base vertex. Keep blossom bookkeeping + # consistent. + def augmentBlossom(b, v): + # This is an obnoxiously complicated recursive function for the sake of + # a stack-transformation. So, we hack around the complexity by using + # a trampoline pattern. By yielding the arguments to each recursive + # call, we keep the actual callstack flat. + + def _recurse(b, v): + # Bubble up through the blossom tree from vertex v to an immediate + # sub-blossom of b. + t = v + while blossomparent[t] != b: + t = blossomparent[t] + # Recursively deal with the first sub-blossom. + if isinstance(t, Blossom): + yield (t, v) + # Decide in which direction we will go round the blossom. + i = j = b.childs.index(t) + if i & 1: + # Start index is odd; go forward and wrap. + j -= len(b.childs) + jstep = 1 + else: + # Start index is even; go backward. + jstep = -1 + # Move along the blossom until we get to the base. + while j != 0: + # Step to the next sub-blossom and augment it recursively. + j += jstep + t = b.childs[j] + if jstep == 1: + w, x = b.edges[j] + else: + x, w = b.edges[j - 1] + if isinstance(t, Blossom): + yield (t, w) + # Step to the next sub-blossom and augment it recursively. + j += jstep + t = b.childs[j] + if isinstance(t, Blossom): + yield (t, x) + # Match the edge connecting those sub-blossoms. + mate[w] = x + mate[x] = w + # Rotate the list of sub-blossoms to put the new base at the front. + b.childs = b.childs[i:] + b.childs[:i] + b.edges = b.edges[i:] + b.edges[:i] + blossombase[b] = blossombase[b.childs[0]] + assert blossombase[b] == v + + # Now, we apply the trampoline pattern. We simulate a recursive + # callstack by maintaining a stack of generators, each yielding a + # sequence of function arguments. We grow the stack by appending a call + # to _recurse on each argument tuple, and shrink the stack whenever a + # generator is exhausted. + stack = [_recurse(b, v)] + while stack: + top = stack[-1] + for args in top: + stack.append(_recurse(*args)) + break + else: + stack.pop() + + # Swap matched/unmatched edges over an alternating path between two + # single vertices. The augmenting path runs through S-vertices v and w. + def augmentMatching(v, w): + for s, j in ((v, w), (w, v)): + # Match vertex s to vertex j. Then trace back from s + # until we find a single vertex, swapping matched and unmatched + # edges as we go. + while 1: + bs = inblossom[s] + assert label[bs] == 1 + assert (labeledge[bs] is None and blossombase[bs] not in mate) or ( + labeledge[bs][0] == mate[blossombase[bs]] + ) + # Augment through the S-blossom from s to base. + if isinstance(bs, Blossom): + augmentBlossom(bs, s) + # Update mate[s] + mate[s] = j + # Trace one step back. + if labeledge[bs] is None: + # Reached single vertex; stop. + break + t = labeledge[bs][0] + bt = inblossom[t] + assert label[bt] == 2 + # Trace one more step back. + s, j = labeledge[bt] + # Augment through the T-blossom from j to base. + assert blossombase[bt] == t + if isinstance(bt, Blossom): + augmentBlossom(bt, j) + # Update mate[j] + mate[j] = s + + # Verify that the optimum solution has been reached. + def verifyOptimum(): + if maxcardinality: + # Vertices may have negative dual; + # find a constant non-negative number to add to all vertex duals. + vdualoffset = max(0, -min(dualvar.values())) + else: + vdualoffset = 0 + # 0. all dual variables are non-negative + assert min(dualvar.values()) + vdualoffset >= 0 + assert len(blossomdual) == 0 or min(blossomdual.values()) >= 0 + # 0. all edges have non-negative slack and + # 1. all matched edges have zero slack; + for i, j, d in G.edges(data=True): + wt = d.get(weight, 1) + if i == j: + continue # ignore self-loops + s = dualvar[i] + dualvar[j] - 2 * wt + iblossoms = [i] + jblossoms = [j] + while blossomparent[iblossoms[-1]] is not None: + iblossoms.append(blossomparent[iblossoms[-1]]) + while blossomparent[jblossoms[-1]] is not None: + jblossoms.append(blossomparent[jblossoms[-1]]) + iblossoms.reverse() + jblossoms.reverse() + for bi, bj in zip(iblossoms, jblossoms): + if bi != bj: + break + s += 2 * blossomdual[bi] + assert s >= 0 + if mate.get(i) == j or mate.get(j) == i: + assert mate[i] == j and mate[j] == i + assert s == 0 + # 2. all single vertices have zero dual value; + for v in gnodes: + assert (v in mate) or dualvar[v] + vdualoffset == 0 + # 3. all blossoms with positive dual value are full. + for b in blossomdual: + if blossomdual[b] > 0: + assert len(b.edges) % 2 == 1 + for i, j in b.edges[1::2]: + assert mate[i] == j and mate[j] == i + # Ok. + + # Main loop: continue until no further improvement is possible. + while 1: + # Each iteration of this loop is a "stage". + # A stage finds an augmenting path and uses that to improve + # the matching. + + # Remove labels from top-level blossoms/vertices. + label.clear() + labeledge.clear() + + # Forget all about least-slack edges. + bestedge.clear() + for b in blossomdual: + b.mybestedges = None + + # Loss of labeling means that we can not be sure that currently + # allowable edges remain allowable throughout this stage. + allowedge.clear() + + # Make queue empty. + queue[:] = [] + + # Label single blossoms/vertices with S and put them in the queue. + for v in gnodes: + if (v not in mate) and label.get(inblossom[v]) is None: + assignLabel(v, 1, None) + + # Loop until we succeed in augmenting the matching. + augmented = 0 + while 1: + # Each iteration of this loop is a "substage". + # A substage tries to find an augmenting path; + # if found, the path is used to improve the matching and + # the stage ends. If there is no augmenting path, the + # primal-dual method is used to pump some slack out of + # the dual variables. + + # Continue labeling until all vertices which are reachable + # through an alternating path have got a label. + while queue and not augmented: + # Take an S vertex from the queue. + v = queue.pop() + assert label[inblossom[v]] == 1 + + # Scan its neighbors: + for w in G.neighbors(v): + if w == v: + continue # ignore self-loops + # w is a neighbor to v + bv = inblossom[v] + bw = inblossom[w] + if bv == bw: + # this edge is internal to a blossom; ignore it + continue + if (v, w) not in allowedge: + kslack = slack(v, w) + if kslack <= 0: + # edge k has zero slack => it is allowable + allowedge[(v, w)] = allowedge[(w, v)] = True + if (v, w) in allowedge: + if label.get(bw) is None: + # (C1) w is a free vertex; + # label w with T and label its mate with S (R12). + assignLabel(w, 2, v) + elif label.get(bw) == 1: + # (C2) w is an S-vertex (not in the same blossom); + # follow back-links to discover either an + # augmenting path or a new blossom. + base = scanBlossom(v, w) + if base is not NoNode: + # Found a new blossom; add it to the blossom + # bookkeeping and turn it into an S-blossom. + addBlossom(base, v, w) + else: + # Found an augmenting path; augment the + # matching and end this stage. + augmentMatching(v, w) + augmented = 1 + break + elif label.get(w) is None: + # w is inside a T-blossom, but w itself has not + # yet been reached from outside the blossom; + # mark it as reached (we need this to relabel + # during T-blossom expansion). + assert label[bw] == 2 + label[w] = 2 + labeledge[w] = (v, w) + elif label.get(bw) == 1: + # keep track of the least-slack non-allowable edge to + # a different S-blossom. + if bestedge.get(bv) is None or kslack < slack(*bestedge[bv]): + bestedge[bv] = (v, w) + elif label.get(w) is None: + # w is a free vertex (or an unreached vertex inside + # a T-blossom) but we can not reach it yet; + # keep track of the least-slack edge that reaches w. + if bestedge.get(w) is None or kslack < slack(*bestedge[w]): + bestedge[w] = (v, w) + + if augmented: + break + + # There is no augmenting path under these constraints; + # compute delta and reduce slack in the optimization problem. + # (Note that our vertex dual variables, edge slacks and delta's + # are pre-multiplied by two.) + deltatype = -1 + delta = deltaedge = deltablossom = None + + # Compute delta1: the minimum value of any vertex dual. + if not maxcardinality: + deltatype = 1 + delta = min(dualvar.values()) + + # Compute delta2: the minimum slack on any edge between + # an S-vertex and a free vertex. + for v in G.nodes(): + if label.get(inblossom[v]) is None and bestedge.get(v) is not None: + d = slack(*bestedge[v]) + if deltatype == -1 or d < delta: + delta = d + deltatype = 2 + deltaedge = bestedge[v] + + # Compute delta3: half the minimum slack on any edge between + # a pair of S-blossoms. + for b in blossomparent: + if ( + blossomparent[b] is None + and label.get(b) == 1 + and bestedge.get(b) is not None + ): + kslack = slack(*bestedge[b]) + if allinteger: + assert (kslack % 2) == 0 + d = kslack // 2 + else: + d = kslack / 2.0 + if deltatype == -1 or d < delta: + delta = d + deltatype = 3 + deltaedge = bestedge[b] + + # Compute delta4: minimum z variable of any T-blossom. + for b in blossomdual: + if ( + blossomparent[b] is None + and label.get(b) == 2 + and (deltatype == -1 or blossomdual[b] < delta) + ): + delta = blossomdual[b] + deltatype = 4 + deltablossom = b + + if deltatype == -1: + # No further improvement possible; max-cardinality optimum + # reached. Do a final delta update to make the optimum + # verifiable. + assert maxcardinality + deltatype = 1 + delta = max(0, min(dualvar.values())) + + # Update dual variables according to delta. + for v in gnodes: + if label.get(inblossom[v]) == 1: + # S-vertex: 2*u = 2*u - 2*delta + dualvar[v] -= delta + elif label.get(inblossom[v]) == 2: + # T-vertex: 2*u = 2*u + 2*delta + dualvar[v] += delta + for b in blossomdual: + if blossomparent[b] is None: + if label.get(b) == 1: + # top-level S-blossom: z = z + 2*delta + blossomdual[b] += delta + elif label.get(b) == 2: + # top-level T-blossom: z = z - 2*delta + blossomdual[b] -= delta + + # Take action at the point where minimum delta occurred. + if deltatype == 1: + # No further improvement possible; optimum reached. + break + elif deltatype == 2: + # Use the least-slack edge to continue the search. + (v, w) = deltaedge + assert label[inblossom[v]] == 1 + allowedge[(v, w)] = allowedge[(w, v)] = True + queue.append(v) + elif deltatype == 3: + # Use the least-slack edge to continue the search. + (v, w) = deltaedge + allowedge[(v, w)] = allowedge[(w, v)] = True + assert label[inblossom[v]] == 1 + queue.append(v) + elif deltatype == 4: + # Expand the least-z blossom. + expandBlossom(deltablossom, False) + + # End of a this substage. + + # Paranoia check that the matching is symmetric. + for v in mate: + assert mate[mate[v]] == v + + # Stop when no more augmenting path can be found. + if not augmented: + break + + # End of a stage; expand all S-blossoms which have zero dual. + for b in list(blossomdual.keys()): + if b not in blossomdual: + continue # already expanded + if blossomparent[b] is None and label.get(b) == 1 and blossomdual[b] == 0: + expandBlossom(b, True) + + # Verify that we reached the optimum solution (only for integer weights). + if allinteger: + verifyOptimum() + + return matching_dict_to_set(mate) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/__init__.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..cf15ddb592541a959149842a4d581cf9f0a3e5e1 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/__init__.py @@ -0,0 +1,27 @@ +""" +Subpackages related to graph-minor problems. + +In graph theory, an undirected graph H is called a minor of the graph G if H +can be formed from G by deleting edges and vertices and by contracting edges +[1]_. + +References +---------- +.. [1] https://en.wikipedia.org/wiki/Graph_minor +""" + +from networkx.algorithms.minors.contraction import ( + contracted_edge, + contracted_nodes, + equivalence_classes, + identified_nodes, + quotient_graph, +) + +__all__ = [ + "contracted_edge", + "contracted_nodes", + "equivalence_classes", + "identified_nodes", + "quotient_graph", +] diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/__pycache__/contraction.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/__pycache__/contraction.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..7b750b342a7ac8f3c2b5d52520e6efd9cdc1eccd Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/__pycache__/contraction.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/contraction.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/contraction.py new file mode 100644 index 0000000000000000000000000000000000000000..e85b577843650df3f7f02fd1e60c6fc0800409c6 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/contraction.py @@ -0,0 +1,634 @@ +"""Provides functions for computing minors of a graph.""" + +from itertools import chain, combinations, permutations, product + +import networkx as nx +from networkx import density +from networkx.exception import NetworkXException +from networkx.utils import arbitrary_element + +__all__ = [ + "contracted_edge", + "contracted_nodes", + "equivalence_classes", + "identified_nodes", + "quotient_graph", +] + +chaini = chain.from_iterable + + +def equivalence_classes(iterable, relation): + """Returns equivalence classes of `relation` when applied to `iterable`. + + The equivalence classes, or blocks, consist of objects from `iterable` + which are all equivalent. They are defined to be equivalent if the + `relation` function returns `True` when passed any two objects from that + class, and `False` otherwise. To define an equivalence relation the + function must be reflexive, symmetric and transitive. + + Parameters + ---------- + iterable : list, tuple, or set + An iterable of elements/nodes. + + relation : function + A Boolean-valued function that implements an equivalence relation + (reflexive, symmetric, transitive binary relation) on the elements + of `iterable` - it must take two elements and return `True` if + they are related, or `False` if not. + + Returns + ------- + set of frozensets + A set of frozensets representing the partition induced by the equivalence + relation function `relation` on the elements of `iterable`. Each + member set in the return set represents an equivalence class, or + block, of the partition. + + Duplicate elements will be ignored so it makes the most sense for + `iterable` to be a :class:`set`. + + Notes + ----- + This function does not check that `relation` represents an equivalence + relation. You can check that your equivalence classes provide a partition + using `is_partition`. + + Examples + -------- + Let `X` be the set of integers from `0` to `9`, and consider an equivalence + relation `R` on `X` of congruence modulo `3`: this means that two integers + `x` and `y` in `X` are equivalent under `R` if they leave the same + remainder when divided by `3`, i.e. `(x - y) mod 3 = 0`. + + The equivalence classes of this relation are `{0, 3, 6, 9}`, `{1, 4, 7}`, + `{2, 5, 8}`: `0`, `3`, `6`, `9` are all divisible by `3` and leave zero + remainder; `1`, `4`, `7` leave remainder `1`; while `2`, `5` and `8` leave + remainder `2`. We can see this by calling `equivalence_classes` with + `X` and a function implementation of `R`. + + >>> X = set(range(10)) + >>> def mod3(x, y): + ... return (x - y) % 3 == 0 + >>> equivalence_classes(X, mod3) # doctest: +SKIP + {frozenset({1, 4, 7}), frozenset({8, 2, 5}), frozenset({0, 9, 3, 6})} + """ + # For simplicity of implementation, we initialize the return value as a + # list of lists, then convert it to a set of sets at the end of the + # function. + blocks = [] + # Determine the equivalence class for each element of the iterable. + for y in iterable: + # Each element y must be in *exactly one* equivalence class. + # + # Each block is guaranteed to be non-empty + for block in blocks: + x = arbitrary_element(block) + if relation(x, y): + block.append(y) + break + else: + # If the element y is not part of any known equivalence class, it + # must be in its own, so we create a new singleton equivalence + # class for it. + blocks.append([y]) + return {frozenset(block) for block in blocks} + + +@nx._dispatchable(edge_attrs="weight", returns_graph=True) +def quotient_graph( + G, + partition, + edge_relation=None, + node_data=None, + edge_data=None, + weight="weight", + relabel=False, + create_using=None, +): + """Returns the quotient graph of `G` under the specified equivalence + relation on nodes. + + Parameters + ---------- + G : NetworkX graph + The graph for which to return the quotient graph with the + specified node relation. + + partition : function, or dict or list of lists, tuples or sets + If a function, this function must represent an equivalence + relation on the nodes of `G`. It must take two arguments *u* + and *v* and return True exactly when *u* and *v* are in the + same equivalence class. The equivalence classes form the nodes + in the returned graph. + + If a dict of lists/tuples/sets, the keys can be any meaningful + block labels, but the values must be the block lists/tuples/sets + (one list/tuple/set per block), and the blocks must form a valid + partition of the nodes of the graph. That is, each node must be + in exactly one block of the partition. + + If a list of sets, the list must form a valid partition of + the nodes of the graph. That is, each node must be in exactly + one block of the partition. + + edge_relation : Boolean function with two arguments + This function must represent an edge relation on the *blocks* of + the `partition` of `G`. It must take two arguments, *B* and *C*, + each one a set of nodes, and return True exactly when there should be + an edge joining block *B* to block *C* in the returned graph. + + If `edge_relation` is not specified, it is assumed to be the + following relation. Block *B* is related to block *C* if and + only if some node in *B* is adjacent to some node in *C*, + according to the edge set of `G`. + + node_data : function + This function takes one argument, *B*, a set of nodes in `G`, + and must return a dictionary representing the node data + attributes to set on the node representing *B* in the quotient graph. + If None, the following node attributes will be set: + + * 'graph', the subgraph of the graph `G` that this block + represents, + * 'nnodes', the number of nodes in this block, + * 'nedges', the number of edges within this block, + * 'density', the density of the subgraph of `G` that this + block represents. + + edge_data : function + This function takes two arguments, *B* and *C*, each one a set + of nodes, and must return a dictionary representing the edge + data attributes to set on the edge joining *B* and *C*, should + there be an edge joining *B* and *C* in the quotient graph (if + no such edge occurs in the quotient graph as determined by + `edge_relation`, then the output of this function is ignored). + + If the quotient graph would be a multigraph, this function is + not applied, since the edge data from each edge in the graph + `G` appears in the edges of the quotient graph. + + weight : string or None, optional (default="weight") + The name of an edge attribute that holds the numerical value + used as a weight. If None then each edge has weight 1. + + relabel : bool + If True, relabel the nodes of the quotient graph to be + nonnegative integers. Otherwise, the nodes are identified with + :class:`frozenset` instances representing the blocks given in + `partition`. + + create_using : NetworkX graph constructor, optional (default=nx.Graph) + Graph type to create. If graph instance, then cleared before populated. + + Returns + ------- + NetworkX graph + The quotient graph of `G` under the equivalence relation + specified by `partition`. If the partition were given as a + list of :class:`set` instances and `relabel` is False, + each node will be a :class:`frozenset` corresponding to the same + :class:`set`. + + Raises + ------ + NetworkXException + If the given partition is not a valid partition of the nodes of + `G`. + + Examples + -------- + The quotient graph of the complete bipartite graph under the "same + neighbors" equivalence relation is `K_2`. Under this relation, two nodes + are equivalent if they are not adjacent but have the same neighbor set. + + >>> G = nx.complete_bipartite_graph(2, 3) + >>> same_neighbors = lambda u, v: (u not in G[v] and v not in G[u] and G[u] == G[v]) + >>> Q = nx.quotient_graph(G, same_neighbors) + >>> K2 = nx.complete_graph(2) + >>> nx.is_isomorphic(Q, K2) + True + + The quotient graph of a directed graph under the "same strongly connected + component" equivalence relation is the condensation of the graph (see + :func:`condensation`). This example comes from the Wikipedia article + *`Strongly connected component`_*. + + >>> G = nx.DiGraph() + >>> edges = [ + ... "ab", + ... "be", + ... "bf", + ... "bc", + ... "cg", + ... "cd", + ... "dc", + ... "dh", + ... "ea", + ... "ef", + ... "fg", + ... "gf", + ... "hd", + ... "hf", + ... ] + >>> G.add_edges_from(tuple(x) for x in edges) + >>> components = list(nx.strongly_connected_components(G)) + >>> sorted(sorted(component) for component in components) + [['a', 'b', 'e'], ['c', 'd', 'h'], ['f', 'g']] + >>> + >>> C = nx.condensation(G, components) + >>> component_of = C.graph["mapping"] + >>> same_component = lambda u, v: component_of[u] == component_of[v] + >>> Q = nx.quotient_graph(G, same_component) + >>> nx.is_isomorphic(C, Q) + True + + Node identification can be represented as the quotient of a graph under the + equivalence relation that places the two nodes in one block and each other + node in its own singleton block. + + >>> K24 = nx.complete_bipartite_graph(2, 4) + >>> K34 = nx.complete_bipartite_graph(3, 4) + >>> C = nx.contracted_nodes(K34, 1, 2) + >>> nodes = {1, 2} + >>> is_contracted = lambda u, v: u in nodes and v in nodes + >>> Q = nx.quotient_graph(K34, is_contracted) + >>> nx.is_isomorphic(Q, C) + True + >>> nx.is_isomorphic(Q, K24) + True + + The blockmodeling technique described in [1]_ can be implemented as a + quotient graph. + + >>> G = nx.path_graph(6) + >>> partition = [{0, 1}, {2, 3}, {4, 5}] + >>> M = nx.quotient_graph(G, partition, relabel=True) + >>> list(M.edges()) + [(0, 1), (1, 2)] + + Here is the sample example but using partition as a dict of block sets. + + >>> G = nx.path_graph(6) + >>> partition = {0: {0, 1}, 2: {2, 3}, 4: {4, 5}} + >>> M = nx.quotient_graph(G, partition, relabel=True) + >>> list(M.edges()) + [(0, 1), (1, 2)] + + Partitions can be represented in various ways: + + 0. a list/tuple/set of block lists/tuples/sets + 1. a dict with block labels as keys and blocks lists/tuples/sets as values + 2. a dict with block lists/tuples/sets as keys and block labels as values + 3. a function from nodes in the original iterable to block labels + 4. an equivalence relation function on the target iterable + + As `quotient_graph` is designed to accept partitions represented as (0), (1) or + (4) only, the `equivalence_classes` function can be used to get the partitions + in the right form, in order to call `quotient_graph`. + + .. _Strongly connected component: https://en.wikipedia.org/wiki/Strongly_connected_component + + References + ---------- + .. [1] Patrick Doreian, Vladimir Batagelj, and Anuska Ferligoj. + *Generalized Blockmodeling*. + Cambridge University Press, 2004. + + """ + # If the user provided an equivalence relation as a function to compute + # the blocks of the partition on the nodes of G induced by the + # equivalence relation. + if callable(partition): + # equivalence_classes always return partition of whole G. + partition = equivalence_classes(G, partition) + if not nx.community.is_partition(G, partition): + raise nx.NetworkXException( + "Input `partition` is not an equivalence relation for nodes of G" + ) + return _quotient_graph( + G, + partition, + edge_relation, + node_data, + edge_data, + weight, + relabel, + create_using, + ) + + # If the partition is a dict, it is assumed to be one where the keys are + # user-defined block labels, and values are block lists, tuples or sets. + if isinstance(partition, dict): + partition = list(partition.values()) + + # If the user provided partition as a collection of sets. Then we + # need to check if partition covers all of G nodes. If the answer + # is 'No' then we need to prepare suitable subgraph view. + partition_nodes = set().union(*partition) + if len(partition_nodes) != len(G): + G = G.subgraph(partition_nodes) + # Each node in the graph/subgraph must be in exactly one block. + if not nx.community.is_partition(G, partition): + raise NetworkXException("each node must be in exactly one part of `partition`") + return _quotient_graph( + G, + partition, + edge_relation, + node_data, + edge_data, + weight, + relabel, + create_using, + ) + + +def _quotient_graph( + G, partition, edge_relation, node_data, edge_data, weight, relabel, create_using +): + """Construct the quotient graph assuming input has been checked""" + if create_using is None: + H = G.__class__() + else: + H = nx.empty_graph(0, create_using) + # By default set some basic information about the subgraph that each block + # represents on the nodes in the quotient graph. + if node_data is None: + + def node_data(b): + S = G.subgraph(b) + return { + "graph": S, + "nnodes": len(S), + "nedges": S.number_of_edges(), + "density": density(S), + } + + # Each block of the partition becomes a node in the quotient graph. + partition = [frozenset(b) for b in partition] + H.add_nodes_from((b, node_data(b)) for b in partition) + # By default, the edge relation is the relation defined as follows. B is + # adjacent to C if a node in B is adjacent to a node in C, according to the + # edge set of G. + # + # This is not a particularly efficient implementation of this relation: + # there are O(n^2) pairs to check and each check may require O(log n) time + # (to check set membership). This can certainly be parallelized. + if edge_relation is None: + + def edge_relation(b, c): + return any(v in G[u] for u, v in product(b, c)) + + # By default, sum the weights of the edges joining pairs of nodes across + # blocks to get the weight of the edge joining those two blocks. + if edge_data is None: + + def edge_data(b, c): + edgedata = ( + d + for u, v, d in G.edges(b | c, data=True) + if (u in b and v in c) or (u in c and v in b) + ) + return {"weight": sum(d.get(weight, 1) for d in edgedata)} + + block_pairs = permutations(H, 2) if H.is_directed() else combinations(H, 2) + # In a multigraph, add one edge in the quotient graph for each edge + # in the original graph. + if H.is_multigraph(): + edges = chaini( + ( + (b, c, G.get_edge_data(u, v, default={})) + for u, v in product(b, c) + if v in G[u] + ) + for b, c in block_pairs + if edge_relation(b, c) + ) + # In a simple graph, apply the edge data function to each pair of + # blocks to determine the edge data attributes to apply to each edge + # in the quotient graph. + else: + edges = ( + (b, c, edge_data(b, c)) for (b, c) in block_pairs if edge_relation(b, c) + ) + H.add_edges_from(edges) + # If requested by the user, relabel the nodes to be integers, + # numbered in increasing order from zero in the same order as the + # iteration order of `partition`. + if relabel: + # Can't use nx.convert_node_labels_to_integers() here since we + # want the order of iteration to be the same for backward + # compatibility with the nx.blockmodel() function. + labels = {b: i for i, b in enumerate(partition)} + H = nx.relabel_nodes(H, labels) + return H + + +@nx._dispatchable( + preserve_all_attrs=True, mutates_input={"not copy": 4}, returns_graph=True +) +def contracted_nodes(G, u, v, self_loops=True, copy=True): + """Returns the graph that results from contracting `u` and `v`. + + Node contraction identifies the two nodes as a single node incident to any + edge that was incident to the original two nodes. + + Parameters + ---------- + G : NetworkX graph + The graph whose nodes will be contracted. + + u, v : nodes + Must be nodes in `G`. + + self_loops : Boolean + If this is True, any edges joining `u` and `v` in `G` become + self-loops on the new node in the returned graph. + + copy : Boolean + If this is True (default True), make a copy of + `G` and return that instead of directly changing `G`. + + + Returns + ------- + Networkx graph + If Copy is True, + A new graph object of the same type as `G` (leaving `G` unmodified) + with `u` and `v` identified in a single node. The right node `v` + will be merged into the node `u`, so only `u` will appear in the + returned graph. + If copy is False, + Modifies `G` with `u` and `v` identified in a single node. + The right node `v` will be merged into the node `u`, so + only `u` will appear in the returned graph. + + Notes + ----- + For multigraphs, the edge keys for the realigned edges may + not be the same as the edge keys for the old edges. This is + natural because edge keys are unique only within each pair of nodes. + + For non-multigraphs where `u` and `v` are adjacent to a third node + `w`, the edge (`v`, `w`) will be contracted into the edge (`u`, + `w`) with its attributes stored into a "contraction" attribute. + + This function is also available as `identified_nodes`. + + Examples + -------- + Contracting two nonadjacent nodes of the cycle graph on four nodes `C_4` + yields the path graph (ignoring parallel edges): + + >>> G = nx.cycle_graph(4) + >>> M = nx.contracted_nodes(G, 1, 3) + >>> P3 = nx.path_graph(3) + >>> nx.is_isomorphic(M, P3) + True + + >>> G = nx.MultiGraph(P3) + >>> M = nx.contracted_nodes(G, 0, 2) + >>> M.edges + MultiEdgeView([(0, 1, 0), (0, 1, 1)]) + + >>> G = nx.Graph([(1, 2), (2, 2)]) + >>> H = nx.contracted_nodes(G, 1, 2, self_loops=False) + >>> list(H.nodes()) + [1] + >>> list(H.edges()) + [(1, 1)] + + In a ``MultiDiGraph`` with a self loop, the in and out edges will + be treated separately as edges, so while contracting a node which + has a self loop the contraction will add multiple edges: + + >>> G = nx.MultiDiGraph([(1, 2), (2, 2)]) + >>> H = nx.contracted_nodes(G, 1, 2) + >>> list(H.edges()) # edge 1->2, 2->2, 2<-2 from the original Graph G + [(1, 1), (1, 1), (1, 1)] + >>> H = nx.contracted_nodes(G, 1, 2, self_loops=False) + >>> list(H.edges()) # edge 2->2, 2<-2 from the original Graph G + [(1, 1), (1, 1)] + + See Also + -------- + contracted_edge + quotient_graph + + """ + # Copying has significant overhead and can be disabled if needed + if copy: + H = G.copy() + else: + H = G + + # edge code uses G.edges(v) instead of G.adj[v] to handle multiedges + if H.is_directed(): + edges_to_remap = chain(G.in_edges(v, data=True), G.out_edges(v, data=True)) + else: + edges_to_remap = G.edges(v, data=True) + + # If the H=G, the generators change as H changes + # This makes the edges_to_remap independent of H + if not copy: + edges_to_remap = list(edges_to_remap) + + v_data = H.nodes[v] + H.remove_node(v) + + for prev_w, prev_x, d in edges_to_remap: + w = prev_w if prev_w != v else u + x = prev_x if prev_x != v else u + + if ({prev_w, prev_x} == {u, v}) and not self_loops: + continue + + if not H.has_edge(w, x) or G.is_multigraph(): + H.add_edge(w, x, **d) + else: + if "contraction" in H.edges[(w, x)]: + H.edges[(w, x)]["contraction"][(prev_w, prev_x)] = d + else: + H.edges[(w, x)]["contraction"] = {(prev_w, prev_x): d} + + if "contraction" in H.nodes[u]: + H.nodes[u]["contraction"][v] = v_data + else: + H.nodes[u]["contraction"] = {v: v_data} + return H + + +identified_nodes = contracted_nodes + + +@nx._dispatchable( + preserve_edge_attrs=True, mutates_input={"not copy": 3}, returns_graph=True +) +def contracted_edge(G, edge, self_loops=True, copy=True): + """Returns the graph that results from contracting the specified edge. + + Edge contraction identifies the two endpoints of the edge as a single node + incident to any edge that was incident to the original two nodes. A graph + that results from edge contraction is called a *minor* of the original + graph. + + Parameters + ---------- + G : NetworkX graph + The graph whose edge will be contracted. + + edge : tuple + Must be a pair of nodes in `G`. + + self_loops : Boolean + If this is True, any edges (including `edge`) joining the + endpoints of `edge` in `G` become self-loops on the new node in the + returned graph. + + copy : Boolean (default True) + If this is True, a the contraction will be performed on a copy of `G`, + otherwise the contraction will happen in place. + + Returns + ------- + Networkx graph + A new graph object of the same type as `G` (leaving `G` unmodified) + with endpoints of `edge` identified in a single node. The right node + of `edge` will be merged into the left one, so only the left one will + appear in the returned graph. + + Raises + ------ + ValueError + If `edge` is not an edge in `G`. + + Examples + -------- + Attempting to contract two nonadjacent nodes yields an error: + + >>> G = nx.cycle_graph(4) + >>> nx.contracted_edge(G, (1, 3)) + Traceback (most recent call last): + ... + ValueError: Edge (1, 3) does not exist in graph G; cannot contract it + + Contracting two adjacent nodes in the cycle graph on *n* nodes yields the + cycle graph on *n - 1* nodes: + + >>> C5 = nx.cycle_graph(5) + >>> C4 = nx.cycle_graph(4) + >>> M = nx.contracted_edge(C5, (0, 1), self_loops=False) + >>> nx.is_isomorphic(M, C4) + True + + See also + -------- + contracted_nodes + quotient_graph + + """ + u, v = edge[:2] + if not G.has_edge(u, v): + raise ValueError(f"Edge {edge} does not exist in graph G; cannot contract it") + return contracted_nodes(G, u, v, self_loops=self_loops, copy=copy) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/tests/__pycache__/test_contraction.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/tests/__pycache__/test_contraction.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..f73bd1882dc9d2255de1b3a976f257643ca795d0 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/tests/__pycache__/test_contraction.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/tests/test_contraction.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/tests/test_contraction.py new file mode 100644 index 0000000000000000000000000000000000000000..2246886767f80c0a6132d61acc931e51b3034a54 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/minors/tests/test_contraction.py @@ -0,0 +1,446 @@ +"""Unit tests for the :mod:`networkx.algorithms.minors.contraction` module.""" + +import pytest + +import networkx as nx +from networkx.utils import arbitrary_element, edges_equal, nodes_equal + + +def test_quotient_graph_complete_multipartite(): + """Tests that the quotient graph of the complete *n*-partite graph + under the "same neighbors" node relation is the complete graph on *n* + nodes. + + """ + G = nx.complete_multipartite_graph(2, 3, 4) + # Two nodes are equivalent if they are not adjacent but have the same + # neighbor set. + + def same_neighbors(u, v): + return u not in G[v] and v not in G[u] and G[u] == G[v] + + expected = nx.complete_graph(3) + actual = nx.quotient_graph(G, same_neighbors) + # It won't take too long to run a graph isomorphism algorithm on such + # small graphs. + assert nx.is_isomorphic(expected, actual) + + +def test_quotient_graph_complete_bipartite(): + """Tests that the quotient graph of the complete bipartite graph under + the "same neighbors" node relation is `K_2`. + + """ + G = nx.complete_bipartite_graph(2, 3) + # Two nodes are equivalent if they are not adjacent but have the same + # neighbor set. + + def same_neighbors(u, v): + return u not in G[v] and v not in G[u] and G[u] == G[v] + + expected = nx.complete_graph(2) + actual = nx.quotient_graph(G, same_neighbors) + # It won't take too long to run a graph isomorphism algorithm on such + # small graphs. + assert nx.is_isomorphic(expected, actual) + + +def test_quotient_graph_edge_relation(): + """Tests for specifying an alternate edge relation for the quotient + graph. + + """ + G = nx.path_graph(5) + + def identity(u, v): + return u == v + + def same_parity(b, c): + return arbitrary_element(b) % 2 == arbitrary_element(c) % 2 + + actual = nx.quotient_graph(G, identity, same_parity) + expected = nx.Graph() + expected.add_edges_from([(0, 2), (0, 4), (2, 4)]) + expected.add_edge(1, 3) + assert nx.is_isomorphic(actual, expected) + + +def test_condensation_as_quotient(): + """This tests that the condensation of a graph can be viewed as the + quotient graph under the "in the same connected component" equivalence + relation. + + """ + # This example graph comes from the file `test_strongly_connected.py`. + G = nx.DiGraph() + G.add_edges_from( + [ + (1, 2), + (2, 3), + (2, 11), + (2, 12), + (3, 4), + (4, 3), + (4, 5), + (5, 6), + (6, 5), + (6, 7), + (7, 8), + (7, 9), + (7, 10), + (8, 9), + (9, 7), + (10, 6), + (11, 2), + (11, 4), + (11, 6), + (12, 6), + (12, 11), + ] + ) + scc = list(nx.strongly_connected_components(G)) + C = nx.condensation(G, scc) + component_of = C.graph["mapping"] + # Two nodes are equivalent if they are in the same connected component. + + def same_component(u, v): + return component_of[u] == component_of[v] + + Q = nx.quotient_graph(G, same_component) + assert nx.is_isomorphic(C, Q) + + +def test_path(): + G = nx.path_graph(6) + partition = [{0, 1}, {2, 3}, {4, 5}] + M = nx.quotient_graph(G, partition, relabel=True) + assert nodes_equal(M, [0, 1, 2]) + assert edges_equal(M.edges(), [(0, 1), (1, 2)]) + for n in M: + assert M.nodes[n]["nedges"] == 1 + assert M.nodes[n]["nnodes"] == 2 + assert M.nodes[n]["density"] == 1 + + +def test_path__partition_provided_as_dict_of_lists(): + G = nx.path_graph(6) + partition = {0: [0, 1], 2: [2, 3], 4: [4, 5]} + M = nx.quotient_graph(G, partition, relabel=True) + assert nodes_equal(M, [0, 1, 2]) + assert edges_equal(M.edges(), [(0, 1), (1, 2)]) + for n in M: + assert M.nodes[n]["nedges"] == 1 + assert M.nodes[n]["nnodes"] == 2 + assert M.nodes[n]["density"] == 1 + + +def test_path__partition_provided_as_dict_of_tuples(): + G = nx.path_graph(6) + partition = {0: (0, 1), 2: (2, 3), 4: (4, 5)} + M = nx.quotient_graph(G, partition, relabel=True) + assert nodes_equal(M, [0, 1, 2]) + assert edges_equal(M.edges(), [(0, 1), (1, 2)]) + for n in M: + assert M.nodes[n]["nedges"] == 1 + assert M.nodes[n]["nnodes"] == 2 + assert M.nodes[n]["density"] == 1 + + +def test_path__partition_provided_as_dict_of_sets(): + G = nx.path_graph(6) + partition = {0: {0, 1}, 2: {2, 3}, 4: {4, 5}} + M = nx.quotient_graph(G, partition, relabel=True) + assert nodes_equal(M, [0, 1, 2]) + assert edges_equal(M.edges(), [(0, 1), (1, 2)]) + for n in M: + assert M.nodes[n]["nedges"] == 1 + assert M.nodes[n]["nnodes"] == 2 + assert M.nodes[n]["density"] == 1 + + +def test_multigraph_path(): + G = nx.MultiGraph(nx.path_graph(6)) + partition = [{0, 1}, {2, 3}, {4, 5}] + M = nx.quotient_graph(G, partition, relabel=True) + assert nodes_equal(M, [0, 1, 2]) + assert edges_equal(M.edges(), [(0, 1), (1, 2)]) + for n in M: + assert M.nodes[n]["nedges"] == 1 + assert M.nodes[n]["nnodes"] == 2 + assert M.nodes[n]["density"] == 1 + + +def test_directed_path(): + G = nx.DiGraph() + nx.add_path(G, range(6)) + partition = [{0, 1}, {2, 3}, {4, 5}] + M = nx.quotient_graph(G, partition, relabel=True) + assert nodes_equal(M, [0, 1, 2]) + assert edges_equal(M.edges(), [(0, 1), (1, 2)]) + for n in M: + assert M.nodes[n]["nedges"] == 1 + assert M.nodes[n]["nnodes"] == 2 + assert M.nodes[n]["density"] == 0.5 + + +def test_directed_multigraph_path(): + G = nx.MultiDiGraph() + nx.add_path(G, range(6)) + partition = [{0, 1}, {2, 3}, {4, 5}] + M = nx.quotient_graph(G, partition, relabel=True) + assert nodes_equal(M, [0, 1, 2]) + assert edges_equal(M.edges(), [(0, 1), (1, 2)]) + for n in M: + assert M.nodes[n]["nedges"] == 1 + assert M.nodes[n]["nnodes"] == 2 + assert M.nodes[n]["density"] == 0.5 + + +def test_overlapping_blocks(): + with pytest.raises(nx.NetworkXException): + G = nx.path_graph(6) + partition = [{0, 1, 2}, {2, 3}, {4, 5}] + nx.quotient_graph(G, partition) + + +def test_weighted_path(): + G = nx.path_graph(6) + for i in range(5): + G[i][i + 1]["w"] = i + 1 + partition = [{0, 1}, {2, 3}, {4, 5}] + M = nx.quotient_graph(G, partition, weight="w", relabel=True) + assert nodes_equal(M, [0, 1, 2]) + assert edges_equal(M.edges(), [(0, 1), (1, 2)]) + assert M[0][1]["weight"] == 2 + assert M[1][2]["weight"] == 4 + for n in M: + assert M.nodes[n]["nedges"] == 1 + assert M.nodes[n]["nnodes"] == 2 + assert M.nodes[n]["density"] == 1 + + +def test_barbell(): + G = nx.barbell_graph(3, 0) + partition = [{0, 1, 2}, {3, 4, 5}] + M = nx.quotient_graph(G, partition, relabel=True) + assert nodes_equal(M, [0, 1]) + assert edges_equal(M.edges(), [(0, 1)]) + for n in M: + assert M.nodes[n]["nedges"] == 3 + assert M.nodes[n]["nnodes"] == 3 + assert M.nodes[n]["density"] == 1 + + +def test_barbell_plus(): + G = nx.barbell_graph(3, 0) + # Add an extra edge joining the bells. + G.add_edge(0, 5) + partition = [{0, 1, 2}, {3, 4, 5}] + M = nx.quotient_graph(G, partition, relabel=True) + assert nodes_equal(M, [0, 1]) + assert edges_equal(M.edges(), [(0, 1)]) + assert M[0][1]["weight"] == 2 + for n in M: + assert M.nodes[n]["nedges"] == 3 + assert M.nodes[n]["nnodes"] == 3 + assert M.nodes[n]["density"] == 1 + + +def test_blockmodel(): + G = nx.path_graph(6) + partition = [[0, 1], [2, 3], [4, 5]] + M = nx.quotient_graph(G, partition, relabel=True) + assert nodes_equal(M.nodes(), [0, 1, 2]) + assert edges_equal(M.edges(), [(0, 1), (1, 2)]) + for n in M.nodes(): + assert M.nodes[n]["nedges"] == 1 + assert M.nodes[n]["nnodes"] == 2 + assert M.nodes[n]["density"] == 1.0 + + +def test_multigraph_blockmodel(): + G = nx.MultiGraph(nx.path_graph(6)) + partition = [[0, 1], [2, 3], [4, 5]] + M = nx.quotient_graph(G, partition, create_using=nx.MultiGraph(), relabel=True) + assert nodes_equal(M.nodes(), [0, 1, 2]) + assert edges_equal(M.edges(), [(0, 1), (1, 2)]) + for n in M.nodes(): + assert M.nodes[n]["nedges"] == 1 + assert M.nodes[n]["nnodes"] == 2 + assert M.nodes[n]["density"] == 1.0 + + +def test_quotient_graph_incomplete_partition(): + G = nx.path_graph(6) + partition = [] + H = nx.quotient_graph(G, partition, relabel=True) + assert nodes_equal(H.nodes(), []) + assert edges_equal(H.edges(), []) + + partition = [[0, 1], [2, 3], [5]] + H = nx.quotient_graph(G, partition, relabel=True) + assert nodes_equal(H.nodes(), [0, 1, 2]) + assert edges_equal(H.edges(), [(0, 1)]) + + +def test_undirected_node_contraction(): + """Tests for node contraction in an undirected graph.""" + G = nx.cycle_graph(4) + actual = nx.contracted_nodes(G, 0, 1) + expected = nx.cycle_graph(3) + expected.add_edge(0, 0) + assert nx.is_isomorphic(actual, expected) + + +def test_directed_node_contraction(): + """Tests for node contraction in a directed graph.""" + G = nx.DiGraph(nx.cycle_graph(4)) + actual = nx.contracted_nodes(G, 0, 1) + expected = nx.DiGraph(nx.cycle_graph(3)) + expected.add_edge(0, 0) + expected.add_edge(0, 0) + assert nx.is_isomorphic(actual, expected) + + +def test_undirected_node_contraction_no_copy(): + """Tests for node contraction in an undirected graph + by making changes in place.""" + G = nx.cycle_graph(4) + actual = nx.contracted_nodes(G, 0, 1, copy=False) + expected = nx.cycle_graph(3) + expected.add_edge(0, 0) + assert nx.is_isomorphic(actual, G) + assert nx.is_isomorphic(actual, expected) + + +def test_directed_node_contraction_no_copy(): + """Tests for node contraction in a directed graph + by making changes in place.""" + G = nx.DiGraph(nx.cycle_graph(4)) + actual = nx.contracted_nodes(G, 0, 1, copy=False) + expected = nx.DiGraph(nx.cycle_graph(3)) + expected.add_edge(0, 0) + expected.add_edge(0, 0) + assert nx.is_isomorphic(actual, G) + assert nx.is_isomorphic(actual, expected) + + +def test_create_multigraph(): + """Tests that using a MultiGraph creates multiple edges.""" + G = nx.path_graph(3, create_using=nx.MultiGraph()) + G.add_edge(0, 1) + G.add_edge(0, 0) + G.add_edge(0, 2) + actual = nx.contracted_nodes(G, 0, 2) + expected = nx.MultiGraph() + expected.add_edge(0, 1) + expected.add_edge(0, 1) + expected.add_edge(0, 1) + expected.add_edge(0, 0) + expected.add_edge(0, 0) + assert edges_equal(actual.edges, expected.edges) + + +def test_multigraph_keys(): + """Tests that multiedge keys are reset in new graph.""" + G = nx.path_graph(3, create_using=nx.MultiGraph()) + G.add_edge(0, 1, 5) + G.add_edge(0, 0, 0) + G.add_edge(0, 2, 5) + actual = nx.contracted_nodes(G, 0, 2) + expected = nx.MultiGraph() + expected.add_edge(0, 1, 0) + expected.add_edge(0, 1, 5) + expected.add_edge(0, 1, 2) # keyed as 2 b/c 2 edges already in G + expected.add_edge(0, 0, 0) + expected.add_edge(0, 0, 1) # this comes from (0, 2, 5) + assert edges_equal(actual.edges, expected.edges) + + +def test_node_attributes(): + """Tests that node contraction preserves node attributes.""" + G = nx.cycle_graph(4) + # Add some data to the two nodes being contracted. + G.nodes[0]["foo"] = "bar" + G.nodes[1]["baz"] = "xyzzy" + actual = nx.contracted_nodes(G, 0, 1) + # We expect that contracting the nodes 0 and 1 in C_4 yields K_3, but + # with nodes labeled 0, 2, and 3, and with a -loop on 0. + expected = nx.complete_graph(3) + expected = nx.relabel_nodes(expected, {1: 2, 2: 3}) + expected.add_edge(0, 0) + cdict = {1: {"baz": "xyzzy"}} + expected.nodes[0].update({"foo": "bar", "contraction": cdict}) + assert nx.is_isomorphic(actual, expected) + assert actual.nodes == expected.nodes + + +def test_edge_attributes(): + """Tests that node contraction preserves edge attributes.""" + # Shape: src1 --> dest <-- src2 + G = nx.DiGraph([("src1", "dest"), ("src2", "dest")]) + G["src1"]["dest"]["value"] = "src1-->dest" + G["src2"]["dest"]["value"] = "src2-->dest" + H = nx.MultiDiGraph(G) + + G = nx.contracted_nodes(G, "src1", "src2") # New Shape: src1 --> dest + assert G.edges[("src1", "dest")]["value"] == "src1-->dest" + assert ( + G.edges[("src1", "dest")]["contraction"][("src2", "dest")]["value"] + == "src2-->dest" + ) + + H = nx.contracted_nodes(H, "src1", "src2") # New Shape: src1 -(x2)-> dest + assert len(H.edges(("src1", "dest"))) == 2 + + +def test_without_self_loops(): + """Tests for node contraction without preserving -loops.""" + G = nx.cycle_graph(4) + actual = nx.contracted_nodes(G, 0, 1, self_loops=False) + expected = nx.complete_graph(3) + assert nx.is_isomorphic(actual, expected) + + +def test_contract_loop_graph(): + """Tests for node contraction when nodes have loops.""" + G = nx.cycle_graph(4) + G.add_edge(0, 0) + actual = nx.contracted_nodes(G, 0, 1) + expected = nx.complete_graph([0, 2, 3]) + expected.add_edge(0, 0) + expected.add_edge(0, 0) + assert edges_equal(actual.edges, expected.edges) + actual = nx.contracted_nodes(G, 1, 0) + expected = nx.complete_graph([1, 2, 3]) + expected.add_edge(1, 1) + expected.add_edge(1, 1) + assert edges_equal(actual.edges, expected.edges) + + +def test_undirected_edge_contraction(): + """Tests for edge contraction in an undirected graph.""" + G = nx.cycle_graph(4) + actual = nx.contracted_edge(G, (0, 1)) + expected = nx.complete_graph(3) + expected.add_edge(0, 0) + assert nx.is_isomorphic(actual, expected) + + +def test_multigraph_edge_contraction(): + """Tests for edge contraction in a multigraph""" + G = nx.cycle_graph(4) + actual = nx.contracted_edge(G, (0, 1, 0)) + expected = nx.complete_graph(3) + expected.add_edge(0, 0) + assert nx.is_isomorphic(actual, expected) + + +def test_nonexistent_edge(): + """Tests that attempting to contract a nonexistent edge raises an + exception. + + """ + with pytest.raises(ValueError): + G = nx.cycle_graph(4) + nx.contracted_edge(G, (0, 2)) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/moral.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/moral.py new file mode 100644 index 0000000000000000000000000000000000000000..e2acf80f6c3715da57dfc92e4c2d2daf986b3c29 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/moral.py @@ -0,0 +1,59 @@ +r"""Function for computing the moral graph of a directed graph.""" + +import itertools + +import networkx as nx +from networkx.utils import not_implemented_for + +__all__ = ["moral_graph"] + + +@not_implemented_for("undirected") +@nx._dispatchable(returns_graph=True) +def moral_graph(G): + r"""Return the Moral Graph + + Returns the moralized graph of a given directed graph. + + Parameters + ---------- + G : NetworkX graph + Directed graph + + Returns + ------- + H : NetworkX graph + The undirected moralized graph of G + + Raises + ------ + NetworkXNotImplemented + If `G` is undirected. + + Examples + -------- + >>> G = nx.DiGraph([(1, 2), (2, 3), (2, 5), (3, 4), (4, 3)]) + >>> G_moral = nx.moral_graph(G) + >>> G_moral.edges() + EdgeView([(1, 2), (2, 3), (2, 5), (2, 4), (3, 4)]) + + Notes + ----- + A moral graph is an undirected graph H = (V, E) generated from a + directed Graph, where if a node has more than one parent node, edges + between these parent nodes are inserted and all directed edges become + undirected. + + https://en.wikipedia.org/wiki/Moral_graph + + References + ---------- + .. [1] Wray L. Buntine. 1995. Chain graphs for learning. + In Proceedings of the Eleventh conference on Uncertainty + in artificial intelligence (UAI'95) + """ + H = G.to_undirected() + for preds in G.pred.values(): + predecessors_combinations = itertools.combinations(preds, r=2) + H.add_edges_from(predecessors_combinations) + return H diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/polynomials.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/polynomials.py new file mode 100644 index 0000000000000000000000000000000000000000..7ebc7554a7654c8961c9d8a8024d17210ccf44ca --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/polynomials.py @@ -0,0 +1,306 @@ +"""Provides algorithms supporting the computation of graph polynomials. + +Graph polynomials are polynomial-valued graph invariants that encode a wide +variety of structural information. Examples include the Tutte polynomial, +chromatic polynomial, characteristic polynomial, and matching polynomial. An +extensive treatment is provided in [1]_. + +For a simple example, the `~sympy.matrices.matrices.MatrixDeterminant.charpoly` +method can be used to compute the characteristic polynomial from the adjacency +matrix of a graph. Consider the complete graph ``K_4``: + +>>> import sympy +>>> x = sympy.Symbol("x") +>>> G = nx.complete_graph(4) +>>> A = nx.to_numpy_array(G, dtype=int) +>>> M = sympy.SparseMatrix(A) +>>> M.charpoly(x).as_expr() +x**4 - 6*x**2 - 8*x - 3 + + +.. [1] Y. Shi, M. Dehmer, X. Li, I. Gutman, + "Graph Polynomials" +""" + +from collections import deque + +import networkx as nx +from networkx.utils import not_implemented_for + +__all__ = ["tutte_polynomial", "chromatic_polynomial"] + + +@not_implemented_for("directed") +@nx._dispatchable +def tutte_polynomial(G): + r"""Returns the Tutte polynomial of `G` + + This function computes the Tutte polynomial via an iterative version of + the deletion-contraction algorithm. + + The Tutte polynomial `T_G(x, y)` is a fundamental graph polynomial invariant in + two variables. It encodes a wide array of information related to the + edge-connectivity of a graph; "Many problems about graphs can be reduced to + problems of finding and evaluating the Tutte polynomial at certain values" [1]_. + In fact, every deletion-contraction-expressible feature of a graph is a + specialization of the Tutte polynomial [2]_ (see Notes for examples). + + There are several equivalent definitions; here are three: + + Def 1 (rank-nullity expansion): For `G` an undirected graph, `n(G)` the + number of vertices of `G`, `E` the edge set of `G`, `V` the vertex set of + `G`, and `c(A)` the number of connected components of the graph with vertex + set `V` and edge set `A` [3]_: + + .. math:: + + T_G(x, y) = \sum_{A \in E} (x-1)^{c(A) - c(E)} (y-1)^{c(A) + |A| - n(G)} + + Def 2 (spanning tree expansion): Let `G` be an undirected graph, `T` a spanning + tree of `G`, and `E` the edge set of `G`. Let `E` have an arbitrary strict + linear order `L`. Let `B_e` be the unique minimal nonempty edge cut of + $E \setminus T \cup {e}$. An edge `e` is internally active with respect to + `T` and `L` if `e` is the least edge in `B_e` according to the linear order + `L`. The internal activity of `T` (denoted `i(T)`) is the number of edges + in $E \setminus T$ that are internally active with respect to `T` and `L`. + Let `P_e` be the unique path in $T \cup {e}$ whose source and target vertex + are the same. An edge `e` is externally active with respect to `T` and `L` + if `e` is the least edge in `P_e` according to the linear order `L`. The + external activity of `T` (denoted `e(T)`) is the number of edges in + $E \setminus T$ that are externally active with respect to `T` and `L`. + Then [4]_ [5]_: + + .. math:: + + T_G(x, y) = \sum_{T \text{ a spanning tree of } G} x^{i(T)} y^{e(T)} + + Def 3 (deletion-contraction recurrence): For `G` an undirected graph, `G-e` + the graph obtained from `G` by deleting edge `e`, `G/e` the graph obtained + from `G` by contracting edge `e`, `k(G)` the number of cut-edges of `G`, + and `l(G)` the number of self-loops of `G`: + + .. math:: + T_G(x, y) = \begin{cases} + x^{k(G)} y^{l(G)}, & \text{if all edges are cut-edges or self-loops} \\ + T_{G-e}(x, y) + T_{G/e}(x, y), & \text{otherwise, for an arbitrary edge $e$ not a cut-edge or loop} + \end{cases} + + Parameters + ---------- + G : NetworkX graph + + Returns + ------- + instance of `sympy.core.add.Add` + A Sympy expression representing the Tutte polynomial for `G`. + + Examples + -------- + >>> C = nx.cycle_graph(5) + >>> nx.tutte_polynomial(C) + x**4 + x**3 + x**2 + x + y + + >>> D = nx.diamond_graph() + >>> nx.tutte_polynomial(D) + x**3 + 2*x**2 + 2*x*y + x + y**2 + y + + Notes + ----- + Some specializations of the Tutte polynomial: + + - `T_G(1, 1)` counts the number of spanning trees of `G` + - `T_G(1, 2)` counts the number of connected spanning subgraphs of `G` + - `T_G(2, 1)` counts the number of spanning forests in `G` + - `T_G(0, 2)` counts the number of strong orientations of `G` + - `T_G(2, 0)` counts the number of acyclic orientations of `G` + + Edge contraction is defined and deletion-contraction is introduced in [6]_. + Combinatorial meaning of the coefficients is introduced in [7]_. + Universality, properties, and applications are discussed in [8]_. + + Practically, up-front computation of the Tutte polynomial may be useful when + users wish to repeatedly calculate edge-connectivity-related information + about one or more graphs. + + References + ---------- + .. [1] M. Brandt, + "The Tutte Polynomial." + Talking About Combinatorial Objects Seminar, 2015 + https://math.berkeley.edu/~brandtm/talks/tutte.pdf + .. [2] A. Björklund, T. Husfeldt, P. Kaski, M. Koivisto, + "Computing the Tutte polynomial in vertex-exponential time" + 49th Annual IEEE Symposium on Foundations of Computer Science, 2008 + https://ieeexplore.ieee.org/abstract/document/4691000 + .. [3] Y. Shi, M. Dehmer, X. Li, I. Gutman, + "Graph Polynomials," p. 14 + .. [4] Y. Shi, M. Dehmer, X. Li, I. Gutman, + "Graph Polynomials," p. 46 + .. [5] A. Nešetril, J. Goodall, + "Graph invariants, homomorphisms, and the Tutte polynomial" + https://iuuk.mff.cuni.cz/~andrew/Tutte.pdf + .. [6] D. B. West, + "Introduction to Graph Theory," p. 84 + .. [7] G. Coutinho, + "A brief introduction to the Tutte polynomial" + Structural Analysis of Complex Networks, 2011 + https://homepages.dcc.ufmg.br/~gabriel/seminars/coutinho_tuttepolynomial_seminar.pdf + .. [8] J. A. Ellis-Monaghan, C. Merino, + "Graph polynomials and their applications I: The Tutte polynomial" + Structural Analysis of Complex Networks, 2011 + https://arxiv.org/pdf/0803.3079.pdf + """ + import sympy + + x = sympy.Symbol("x") + y = sympy.Symbol("y") + stack = deque() + stack.append(nx.MultiGraph(G)) + + polynomial = 0 + while stack: + G = stack.pop() + bridges = set(nx.bridges(G)) + + e = None + for i in G.edges: + if (i[0], i[1]) not in bridges and i[0] != i[1]: + e = i + break + if not e: + loops = list(nx.selfloop_edges(G, keys=True)) + polynomial += x ** len(bridges) * y ** len(loops) + else: + # deletion-contraction + C = nx.contracted_edge(G, e, self_loops=True) + C.remove_edge(e[0], e[0]) + G.remove_edge(*e) + stack.append(G) + stack.append(C) + return sympy.simplify(polynomial) + + +@not_implemented_for("directed") +@nx._dispatchable +def chromatic_polynomial(G): + r"""Returns the chromatic polynomial of `G` + + This function computes the chromatic polynomial via an iterative version of + the deletion-contraction algorithm. + + The chromatic polynomial `X_G(x)` is a fundamental graph polynomial + invariant in one variable. Evaluating `X_G(k)` for an natural number `k` + enumerates the proper k-colorings of `G`. + + There are several equivalent definitions; here are three: + + Def 1 (explicit formula): + For `G` an undirected graph, `c(G)` the number of connected components of + `G`, `E` the edge set of `G`, and `G(S)` the spanning subgraph of `G` with + edge set `S` [1]_: + + .. math:: + + X_G(x) = \sum_{S \subseteq E} (-1)^{|S|} x^{c(G(S))} + + + Def 2 (interpolating polynomial): + For `G` an undirected graph, `n(G)` the number of vertices of `G`, `k_0 = 0`, + and `k_i` the number of distinct ways to color the vertices of `G` with `i` + unique colors (for `i` a natural number at most `n(G)`), `X_G(x)` is the + unique Lagrange interpolating polynomial of degree `n(G)` through the points + `(0, k_0), (1, k_1), \dots, (n(G), k_{n(G)})` [2]_. + + + Def 3 (chromatic recurrence): + For `G` an undirected graph, `G-e` the graph obtained from `G` by deleting + edge `e`, `G/e` the graph obtained from `G` by contracting edge `e`, `n(G)` + the number of vertices of `G`, and `e(G)` the number of edges of `G` [3]_: + + .. math:: + X_G(x) = \begin{cases} + x^{n(G)}, & \text{if $e(G)=0$} \\ + X_{G-e}(x) - X_{G/e}(x), & \text{otherwise, for an arbitrary edge $e$} + \end{cases} + + This formulation is also known as the Fundamental Reduction Theorem [4]_. + + + Parameters + ---------- + G : NetworkX graph + + Returns + ------- + instance of `sympy.core.add.Add` + A Sympy expression representing the chromatic polynomial for `G`. + + Examples + -------- + >>> C = nx.cycle_graph(5) + >>> nx.chromatic_polynomial(C) + x**5 - 5*x**4 + 10*x**3 - 10*x**2 + 4*x + + >>> G = nx.complete_graph(4) + >>> nx.chromatic_polynomial(G) + x**4 - 6*x**3 + 11*x**2 - 6*x + + Notes + ----- + Interpretation of the coefficients is discussed in [5]_. Several special + cases are listed in [2]_. + + The chromatic polynomial is a specialization of the Tutte polynomial; in + particular, ``X_G(x) = T_G(x, 0)`` [6]_. + + The chromatic polynomial may take negative arguments, though evaluations + may not have chromatic interpretations. For instance, ``X_G(-1)`` enumerates + the acyclic orientations of `G` [7]_. + + References + ---------- + .. [1] D. B. West, + "Introduction to Graph Theory," p. 222 + .. [2] E. W. Weisstein + "Chromatic Polynomial" + MathWorld--A Wolfram Web Resource + https://mathworld.wolfram.com/ChromaticPolynomial.html + .. [3] D. B. West, + "Introduction to Graph Theory," p. 221 + .. [4] J. Zhang, J. Goodall, + "An Introduction to Chromatic Polynomials" + https://math.mit.edu/~apost/courses/18.204_2018/Julie_Zhang_paper.pdf + .. [5] R. C. Read, + "An Introduction to Chromatic Polynomials" + Journal of Combinatorial Theory, 1968 + https://math.berkeley.edu/~mrklug/ReadChromatic.pdf + .. [6] W. T. Tutte, + "Graph-polynomials" + Advances in Applied Mathematics, 2004 + https://www.sciencedirect.com/science/article/pii/S0196885803000411 + .. [7] R. P. Stanley, + "Acyclic orientations of graphs" + Discrete Mathematics, 2006 + https://math.mit.edu/~rstan/pubs/pubfiles/18.pdf + """ + import sympy + + x = sympy.Symbol("x") + stack = deque() + stack.append(nx.MultiGraph(G, contraction_idx=0)) + + polynomial = 0 + while stack: + G = stack.pop() + edges = list(G.edges) + if not edges: + polynomial += (-1) ** G.graph["contraction_idx"] * x ** len(G) + else: + e = edges[0] + C = nx.contracted_edge(G, e, self_loops=True) + C.graph["contraction_idx"] = G.graph["contraction_idx"] + 1 + C.remove_edge(e[0], e[0]) + G.remove_edge(*e) + stack.append(G) + stack.append(C) + return polynomial diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/__init__.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..eb0d91cecc902f6390cb8309c017cb1558f7753f --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/__init__.py @@ -0,0 +1,5 @@ +from networkx.algorithms.shortest_paths.generic import * +from networkx.algorithms.shortest_paths.unweighted import * +from networkx.algorithms.shortest_paths.weighted import * +from networkx.algorithms.shortest_paths.astar import * +from networkx.algorithms.shortest_paths.dense import * diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/__pycache__/astar.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/__pycache__/astar.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..0c2cdc1e33c12b61bbcf97480e8bb57402c1d254 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/__pycache__/astar.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/__pycache__/generic.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/__pycache__/generic.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..260f18b794d806c777edd410e6cc8d1cb5648abc Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/__pycache__/generic.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/__pycache__/weighted.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/__pycache__/weighted.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..a189d90023495624c313eb8b3ed0b8a4ea36876c Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/__pycache__/weighted.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/astar.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/astar.py new file mode 100644 index 0000000000000000000000000000000000000000..8d988477b2c1034cacd99cec70d932055ba96a8e --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/astar.py @@ -0,0 +1,241 @@ +"""Shortest paths and path lengths using the A* ("A star") algorithm.""" + +from heapq import heappop, heappush +from itertools import count + +import networkx as nx +from networkx.algorithms.shortest_paths.weighted import _weight_function + +__all__ = ["astar_path", "astar_path_length"] + + +@nx._dispatchable(edge_attrs="weight", preserve_node_attrs="heuristic") +def astar_path(G, source, target, heuristic=None, weight="weight", *, cutoff=None): + """Returns a list of nodes in a shortest path between source and target + using the A* ("A-star") algorithm. + + There may be more than one shortest path. This returns only one. + + Parameters + ---------- + G : NetworkX graph + + source : node + Starting node for path + + target : node + Ending node for path + + heuristic : function + A function to evaluate the estimate of the distance + from the a node to the target. The function takes + two nodes arguments and must return a number. + If the heuristic is inadmissible (if it might + overestimate the cost of reaching the goal from a node), + the result may not be a shortest path. + The algorithm does not support updating heuristic + values for the same node due to caching the first + heuristic calculation per node. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + cutoff : float, optional + If this is provided, the search will be bounded to this value. I.e. if + the evaluation function surpasses this value for a node n, the node will not + be expanded further and will be ignored. More formally, let h'(n) be the + heuristic function, and g(n) be the cost of reaching n from the source node. Then, + if g(n) + h'(n) > cutoff, the node will not be explored further. + Note that if the heuristic is inadmissible, it is possible that paths + are ignored even though they satisfy the cutoff. + + Raises + ------ + NetworkXNoPath + If no path exists between source and target. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> print(nx.astar_path(G, 0, 4)) + [0, 1, 2, 3, 4] + >>> G = nx.grid_graph(dim=[3, 3]) # nodes are two-tuples (x,y) + >>> nx.set_edge_attributes(G, {e: e[1][0] * 2 for e in G.edges()}, "cost") + >>> def dist(a, b): + ... (x1, y1) = a + ... (x2, y2) = b + ... return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5 + >>> print(nx.astar_path(G, (0, 0), (2, 2), heuristic=dist, weight="cost")) + [(0, 0), (0, 1), (0, 2), (1, 2), (2, 2)] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The weight function can be used to hide edges by returning None. + So ``weight = lambda u, v, d: 1 if d['color']=="red" else None`` + will find the shortest red path. + + See Also + -------- + shortest_path, dijkstra_path + + """ + if source not in G: + raise nx.NodeNotFound(f"Source {source} is not in G") + + if target not in G: + raise nx.NodeNotFound(f"Target {target} is not in G") + + if heuristic is None: + # The default heuristic is h=0 - same as Dijkstra's algorithm + def heuristic(u, v): + return 0 + + push = heappush + pop = heappop + weight = _weight_function(G, weight) + + G_succ = G._adj # For speed-up (and works for both directed and undirected graphs) + + # The queue stores priority, node, cost to reach, and parent. + # Uses Python heapq to keep in priority order. + # Add a counter to the queue to prevent the underlying heap from + # attempting to compare the nodes themselves. The hash breaks ties in the + # priority and is guaranteed unique for all nodes in the graph. + c = count() + queue = [(0, next(c), source, 0, None)] + + # Maps enqueued nodes to distance of discovered paths and the + # computed heuristics to target. We avoid computing the heuristics + # more than once and inserting the node into the queue too many times. + enqueued = {} + # Maps explored nodes to parent closest to the source. + explored = {} + + while queue: + # Pop the smallest item from queue. + _, __, curnode, dist, parent = pop(queue) + + if curnode == target: + path = [curnode] + node = parent + while node is not None: + path.append(node) + node = explored[node] + path.reverse() + return path + + if curnode in explored: + # Do not override the parent of starting node + if explored[curnode] is None: + continue + + # Skip bad paths that were enqueued before finding a better one + qcost, h = enqueued[curnode] + if qcost < dist: + continue + + explored[curnode] = parent + + for neighbor, w in G_succ[curnode].items(): + cost = weight(curnode, neighbor, w) + if cost is None: + continue + ncost = dist + cost + if neighbor in enqueued: + qcost, h = enqueued[neighbor] + # if qcost <= ncost, a less costly path from the + # neighbor to the source was already determined. + # Therefore, we won't attempt to push this neighbor + # to the queue + if qcost <= ncost: + continue + else: + h = heuristic(neighbor, target) + + if cutoff and ncost + h > cutoff: + continue + + enqueued[neighbor] = ncost, h + push(queue, (ncost + h, next(c), neighbor, ncost, curnode)) + + raise nx.NetworkXNoPath(f"Node {target} not reachable from {source}") + + +@nx._dispatchable(edge_attrs="weight", preserve_node_attrs="heuristic") +def astar_path_length( + G, source, target, heuristic=None, weight="weight", *, cutoff=None +): + """Returns the length of the shortest path between source and target using + the A* ("A-star") algorithm. + + Parameters + ---------- + G : NetworkX graph + + source : node + Starting node for path + + target : node + Ending node for path + + heuristic : function + A function to evaluate the estimate of the distance + from the a node to the target. The function takes + two nodes arguments and must return a number. + If the heuristic is inadmissible (if it might + overestimate the cost of reaching the goal from a node), + the result may not be a shortest path. + The algorithm does not support updating heuristic + values for the same node due to caching the first + heuristic calculation per node. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + cutoff : float, optional + If this is provided, the search will be bounded to this value. I.e. if + the evaluation function surpasses this value for a node n, the node will not + be expanded further and will be ignored. More formally, let h'(n) be the + heuristic function, and g(n) be the cost of reaching n from the source node. Then, + if g(n) + h'(n) > cutoff, the node will not be explored further. + Note that if the heuristic is inadmissible, it is possible that paths + are ignored even though they satisfy the cutoff. + + Raises + ------ + NetworkXNoPath + If no path exists between source and target. + + See Also + -------- + astar_path + + """ + if source not in G or target not in G: + msg = f"Either source {source} or target {target} is not in G" + raise nx.NodeNotFound(msg) + + weight = _weight_function(G, weight) + path = astar_path(G, source, target, heuristic, weight, cutoff=cutoff) + return sum(weight(u, v, G[u][v]) for u, v in zip(path[:-1], path[1:])) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/dense.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/dense.py new file mode 100644 index 0000000000000000000000000000000000000000..107b920884a0cde29b77257e941cd2e172f140e6 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/dense.py @@ -0,0 +1,260 @@ +"""Floyd-Warshall algorithm for shortest paths.""" + +import networkx as nx + +__all__ = [ + "floyd_warshall", + "floyd_warshall_predecessor_and_distance", + "reconstruct_path", + "floyd_warshall_numpy", +] + + +@nx._dispatchable(edge_attrs="weight") +def floyd_warshall_numpy(G, nodelist=None, weight="weight"): + """Find all-pairs shortest path lengths using Floyd's algorithm. + + This algorithm for finding shortest paths takes advantage of + matrix representations of a graph and works well for dense + graphs where all-pairs shortest path lengths are desired. + The results are returned as a NumPy array, distance[i, j], + where i and j are the indexes of two nodes in nodelist. + The entry distance[i, j] is the distance along a shortest + path from i to j. If no path exists the distance is Inf. + + Parameters + ---------- + G : NetworkX graph + + nodelist : list, optional (default=G.nodes) + The rows and columns are ordered by the nodes in nodelist. + If nodelist is None then the ordering is produced by G.nodes. + Nodelist should include all nodes in G. + + weight: string, optional (default='weight') + Edge data key corresponding to the edge weight. + + Returns + ------- + distance : 2D numpy.ndarray + A numpy array of shortest path distances between nodes. + If there is no path between two nodes the value is Inf. + + Examples + -------- + >>> G = nx.DiGraph() + >>> G.add_weighted_edges_from( + ... [(0, 1, 5), (1, 2, 2), (2, 3, -3), (1, 3, 10), (3, 2, 8)] + ... ) + >>> nx.floyd_warshall_numpy(G) + array([[ 0., 5., 7., 4.], + [inf, 0., 2., -1.], + [inf, inf, 0., -3.], + [inf, inf, 8., 0.]]) + + Notes + ----- + Floyd's algorithm is appropriate for finding shortest paths in + dense graphs or graphs with negative weights when Dijkstra's + algorithm fails. This algorithm can still fail if there are negative + cycles. It has running time $O(n^3)$ with running space of $O(n^2)$. + + Raises + ------ + NetworkXError + If nodelist is not a list of the nodes in G. + """ + import numpy as np + + if nodelist is not None: + if not (len(nodelist) == len(G) == len(set(nodelist))): + raise nx.NetworkXError( + "nodelist must contain every node in G with no repeats." + "If you wanted a subgraph of G use G.subgraph(nodelist)" + ) + + # To handle cases when an edge has weight=0, we must make sure that + # nonedges are not given the value 0 as well. + A = nx.to_numpy_array( + G, nodelist, multigraph_weight=min, weight=weight, nonedge=np.inf + ) + n, m = A.shape + np.fill_diagonal(A, 0) # diagonal elements should be zero + for i in range(n): + # The second term has the same shape as A due to broadcasting + A = np.minimum(A, A[i, :][np.newaxis, :] + A[:, i][:, np.newaxis]) + return A + + +@nx._dispatchable(edge_attrs="weight") +def floyd_warshall_predecessor_and_distance(G, weight="weight"): + """Find all-pairs shortest path lengths using Floyd's algorithm. + + Parameters + ---------- + G : NetworkX graph + + weight: string, optional (default= 'weight') + Edge data key corresponding to the edge weight. + + Returns + ------- + predecessor,distance : dictionaries + Dictionaries, keyed by source and target, of predecessors and distances + in the shortest path. + + Examples + -------- + >>> G = nx.DiGraph() + >>> G.add_weighted_edges_from( + ... [ + ... ("s", "u", 10), + ... ("s", "x", 5), + ... ("u", "v", 1), + ... ("u", "x", 2), + ... ("v", "y", 1), + ... ("x", "u", 3), + ... ("x", "v", 5), + ... ("x", "y", 2), + ... ("y", "s", 7), + ... ("y", "v", 6), + ... ] + ... ) + >>> predecessors, _ = nx.floyd_warshall_predecessor_and_distance(G) + >>> print(nx.reconstruct_path("s", "v", predecessors)) + ['s', 'x', 'u', 'v'] + + Notes + ----- + Floyd's algorithm is appropriate for finding shortest paths + in dense graphs or graphs with negative weights when Dijkstra's algorithm + fails. This algorithm can still fail if there are negative cycles. + It has running time $O(n^3)$ with running space of $O(n^2)$. + + See Also + -------- + floyd_warshall + floyd_warshall_numpy + all_pairs_shortest_path + all_pairs_shortest_path_length + """ + from collections import defaultdict + + # dictionary-of-dictionaries representation for dist and pred + # use some defaultdict magick here + # for dist the default is the floating point inf value + dist = defaultdict(lambda: defaultdict(lambda: float("inf"))) + for u in G: + dist[u][u] = 0 + pred = defaultdict(dict) + # initialize path distance dictionary to be the adjacency matrix + # also set the distance to self to 0 (zero diagonal) + undirected = not G.is_directed() + for u, v, d in G.edges(data=True): + e_weight = d.get(weight, 1.0) + dist[u][v] = min(e_weight, dist[u][v]) + pred[u][v] = u + if undirected: + dist[v][u] = min(e_weight, dist[v][u]) + pred[v][u] = v + for w in G: + dist_w = dist[w] # save recomputation + for u in G: + dist_u = dist[u] # save recomputation + for v in G: + d = dist_u[w] + dist_w[v] + if dist_u[v] > d: + dist_u[v] = d + pred[u][v] = pred[w][v] + return dict(pred), dict(dist) + + +@nx._dispatchable(graphs=None) +def reconstruct_path(source, target, predecessors): + """Reconstruct a path from source to target using the predecessors + dict as returned by floyd_warshall_predecessor_and_distance + + Parameters + ---------- + source : node + Starting node for path + + target : node + Ending node for path + + predecessors: dictionary + Dictionary, keyed by source and target, of predecessors in the + shortest path, as returned by floyd_warshall_predecessor_and_distance + + Returns + ------- + path : list + A list of nodes containing the shortest path from source to target + + If source and target are the same, an empty list is returned + + Notes + ----- + This function is meant to give more applicability to the + floyd_warshall_predecessor_and_distance function + + See Also + -------- + floyd_warshall_predecessor_and_distance + """ + if source == target: + return [] + prev = predecessors[source] + curr = prev[target] + path = [target, curr] + while curr != source: + curr = prev[curr] + path.append(curr) + return list(reversed(path)) + + +@nx._dispatchable(edge_attrs="weight") +def floyd_warshall(G, weight="weight"): + """Find all-pairs shortest path lengths using Floyd's algorithm. + + Parameters + ---------- + G : NetworkX graph + + weight: string, optional (default= 'weight') + Edge data key corresponding to the edge weight. + + + Returns + ------- + distance : dict + A dictionary, keyed by source and target, of shortest paths distances + between nodes. + + Examples + -------- + >>> G = nx.DiGraph() + >>> G.add_weighted_edges_from( + ... [(0, 1, 5), (1, 2, 2), (2, 3, -3), (1, 3, 10), (3, 2, 8)] + ... ) + >>> fw = nx.floyd_warshall(G, weight="weight") + >>> results = {a: dict(b) for a, b in fw.items()} + >>> print(results) + {0: {0: 0, 1: 5, 2: 7, 3: 4}, 1: {1: 0, 2: 2, 3: -1, 0: inf}, 2: {2: 0, 3: -3, 0: inf, 1: inf}, 3: {3: 0, 2: 8, 0: inf, 1: inf}} + + Notes + ----- + Floyd's algorithm is appropriate for finding shortest paths + in dense graphs or graphs with negative weights when Dijkstra's algorithm + fails. This algorithm can still fail if there are negative cycles. + It has running time $O(n^3)$ with running space of $O(n^2)$. + + See Also + -------- + floyd_warshall_predecessor_and_distance + floyd_warshall_numpy + all_pairs_shortest_path + all_pairs_shortest_path_length + """ + # could make this its own function to reduce memory costs + return floyd_warshall_predecessor_and_distance(G, weight=weight)[1] diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__init__.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_astar.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_astar.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..87f506c5682ac19e8ae7fd441f4ca8acbe2aa08c Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_astar.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_dense.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_dense.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..dd3254f45cf2a2094f651a28bd18a50e51ffe639 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_dense.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_dense_numpy.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_dense_numpy.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..0ed4f25e368d3d894cb4db286ee4c4a0090de47d Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_dense_numpy.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_generic.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_generic.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..1b85ede95ef41b13fcbbc4b1142e1173b7db697f Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_generic.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_weighted.cpython-310.pyc b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_weighted.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..420beeb0425168c7361873449ec06fb6379a0505 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/__pycache__/test_weighted.cpython-310.pyc differ diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/test_dense.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/test_dense.py new file mode 100644 index 0000000000000000000000000000000000000000..6923bfef856c83bd3e65573b97fe96ff16cdbc71 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/test_dense.py @@ -0,0 +1,212 @@ +import pytest + +import networkx as nx + + +class TestFloyd: + @classmethod + def setup_class(cls): + pass + + def test_floyd_warshall_predecessor_and_distance(self): + XG = nx.DiGraph() + XG.add_weighted_edges_from( + [ + ("s", "u", 10), + ("s", "x", 5), + ("u", "v", 1), + ("u", "x", 2), + ("v", "y", 1), + ("x", "u", 3), + ("x", "v", 5), + ("x", "y", 2), + ("y", "s", 7), + ("y", "v", 6), + ] + ) + path, dist = nx.floyd_warshall_predecessor_and_distance(XG) + assert dist["s"]["v"] == 9 + assert path["s"]["v"] == "u" + assert dist == { + "y": {"y": 0, "x": 12, "s": 7, "u": 15, "v": 6}, + "x": {"y": 2, "x": 0, "s": 9, "u": 3, "v": 4}, + "s": {"y": 7, "x": 5, "s": 0, "u": 8, "v": 9}, + "u": {"y": 2, "x": 2, "s": 9, "u": 0, "v": 1}, + "v": {"y": 1, "x": 13, "s": 8, "u": 16, "v": 0}, + } + + GG = XG.to_undirected() + # make sure we get lower weight + # to_undirected might choose either edge with weight 2 or weight 3 + GG["u"]["x"]["weight"] = 2 + path, dist = nx.floyd_warshall_predecessor_and_distance(GG) + assert dist["s"]["v"] == 8 + # skip this test, could be alternate path s-u-v + # assert_equal(path['s']['v'],'y') + + G = nx.DiGraph() # no weights + G.add_edges_from( + [ + ("s", "u"), + ("s", "x"), + ("u", "v"), + ("u", "x"), + ("v", "y"), + ("x", "u"), + ("x", "v"), + ("x", "y"), + ("y", "s"), + ("y", "v"), + ] + ) + path, dist = nx.floyd_warshall_predecessor_and_distance(G) + assert dist["s"]["v"] == 2 + # skip this test, could be alternate path s-u-v + # assert_equal(path['s']['v'],'x') + + # alternate interface + dist = nx.floyd_warshall(G) + assert dist["s"]["v"] == 2 + + # floyd_warshall_predecessor_and_distance returns + # dicts-of-defautdicts + # make sure we don't get empty dictionary + XG = nx.DiGraph() + XG.add_weighted_edges_from( + [("v", "x", 5.0), ("y", "x", 5.0), ("v", "y", 6.0), ("x", "u", 2.0)] + ) + path, dist = nx.floyd_warshall_predecessor_and_distance(XG) + inf = float("inf") + assert dist == { + "v": {"v": 0, "x": 5.0, "y": 6.0, "u": 7.0}, + "x": {"x": 0, "u": 2.0, "v": inf, "y": inf}, + "y": {"y": 0, "x": 5.0, "v": inf, "u": 7.0}, + "u": {"u": 0, "v": inf, "x": inf, "y": inf}, + } + assert path == { + "v": {"x": "v", "y": "v", "u": "x"}, + "x": {"u": "x"}, + "y": {"x": "y", "u": "x"}, + } + + def test_reconstruct_path(self): + with pytest.raises(KeyError): + XG = nx.DiGraph() + XG.add_weighted_edges_from( + [ + ("s", "u", 10), + ("s", "x", 5), + ("u", "v", 1), + ("u", "x", 2), + ("v", "y", 1), + ("x", "u", 3), + ("x", "v", 5), + ("x", "y", 2), + ("y", "s", 7), + ("y", "v", 6), + ] + ) + predecessors, _ = nx.floyd_warshall_predecessor_and_distance(XG) + + path = nx.reconstruct_path("s", "v", predecessors) + assert path == ["s", "x", "u", "v"] + + path = nx.reconstruct_path("s", "s", predecessors) + assert path == [] + + # this part raises the keyError + nx.reconstruct_path("1", "2", predecessors) + + def test_cycle(self): + path, dist = nx.floyd_warshall_predecessor_and_distance(nx.cycle_graph(7)) + assert dist[0][3] == 3 + assert path[0][3] == 2 + assert dist[0][4] == 3 + + def test_weighted(self): + XG3 = nx.Graph() + XG3.add_weighted_edges_from( + [[0, 1, 2], [1, 2, 12], [2, 3, 1], [3, 4, 5], [4, 5, 1], [5, 0, 10]] + ) + path, dist = nx.floyd_warshall_predecessor_and_distance(XG3) + assert dist[0][3] == 15 + assert path[0][3] == 2 + + def test_weighted2(self): + XG4 = nx.Graph() + XG4.add_weighted_edges_from( + [ + [0, 1, 2], + [1, 2, 2], + [2, 3, 1], + [3, 4, 1], + [4, 5, 1], + [5, 6, 1], + [6, 7, 1], + [7, 0, 1], + ] + ) + path, dist = nx.floyd_warshall_predecessor_and_distance(XG4) + assert dist[0][2] == 4 + assert path[0][2] == 1 + + def test_weight_parameter(self): + XG4 = nx.Graph() + XG4.add_edges_from( + [ + (0, 1, {"heavy": 2}), + (1, 2, {"heavy": 2}), + (2, 3, {"heavy": 1}), + (3, 4, {"heavy": 1}), + (4, 5, {"heavy": 1}), + (5, 6, {"heavy": 1}), + (6, 7, {"heavy": 1}), + (7, 0, {"heavy": 1}), + ] + ) + path, dist = nx.floyd_warshall_predecessor_and_distance(XG4, weight="heavy") + assert dist[0][2] == 4 + assert path[0][2] == 1 + + def test_zero_distance(self): + XG = nx.DiGraph() + XG.add_weighted_edges_from( + [ + ("s", "u", 10), + ("s", "x", 5), + ("u", "v", 1), + ("u", "x", 2), + ("v", "y", 1), + ("x", "u", 3), + ("x", "v", 5), + ("x", "y", 2), + ("y", "s", 7), + ("y", "v", 6), + ] + ) + path, dist = nx.floyd_warshall_predecessor_and_distance(XG) + + for u in XG: + assert dist[u][u] == 0 + + GG = XG.to_undirected() + # make sure we get lower weight + # to_undirected might choose either edge with weight 2 or weight 3 + GG["u"]["x"]["weight"] = 2 + path, dist = nx.floyd_warshall_predecessor_and_distance(GG) + + for u in GG: + dist[u][u] = 0 + + def test_zero_weight(self): + G = nx.DiGraph() + edges = [(1, 2, -2), (2, 3, -4), (1, 5, 1), (5, 4, 0), (4, 3, -5), (2, 5, -7)] + G.add_weighted_edges_from(edges) + dist = nx.floyd_warshall(G) + assert dist[1][3] == -14 + + G = nx.MultiDiGraph() + edges.append((2, 5, -7)) + G.add_weighted_edges_from(edges) + dist = nx.floyd_warshall(G) + assert dist[1][3] == -14 diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/test_generic.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/test_generic.py new file mode 100644 index 0000000000000000000000000000000000000000..e30de51771eb8654b9f31c283306b207d80e8bce --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/tests/test_generic.py @@ -0,0 +1,450 @@ +import pytest + +import networkx as nx + + +def validate_grid_path(r, c, s, t, p): + assert isinstance(p, list) + assert p[0] == s + assert p[-1] == t + s = ((s - 1) // c, (s - 1) % c) + t = ((t - 1) // c, (t - 1) % c) + assert len(p) == abs(t[0] - s[0]) + abs(t[1] - s[1]) + 1 + p = [((u - 1) // c, (u - 1) % c) for u in p] + for u in p: + assert 0 <= u[0] < r + assert 0 <= u[1] < c + for u, v in zip(p[:-1], p[1:]): + assert (abs(v[0] - u[0]), abs(v[1] - u[1])) in [(0, 1), (1, 0)] + + +class TestGenericPath: + @classmethod + def setup_class(cls): + from networkx import convert_node_labels_to_integers as cnlti + + cls.grid = cnlti(nx.grid_2d_graph(4, 4), first_label=1, ordering="sorted") + cls.cycle = nx.cycle_graph(7) + cls.directed_cycle = nx.cycle_graph(7, create_using=nx.DiGraph()) + cls.neg_weights = nx.DiGraph() + cls.neg_weights.add_edge(0, 1, weight=1) + cls.neg_weights.add_edge(0, 2, weight=3) + cls.neg_weights.add_edge(1, 3, weight=1) + cls.neg_weights.add_edge(2, 3, weight=-2) + + def test_shortest_path(self): + assert nx.shortest_path(self.cycle, 0, 3) == [0, 1, 2, 3] + assert nx.shortest_path(self.cycle, 0, 4) == [0, 6, 5, 4] + validate_grid_path(4, 4, 1, 12, nx.shortest_path(self.grid, 1, 12)) + assert nx.shortest_path(self.directed_cycle, 0, 3) == [0, 1, 2, 3] + # now with weights + assert nx.shortest_path(self.cycle, 0, 3, weight="weight") == [0, 1, 2, 3] + assert nx.shortest_path(self.cycle, 0, 4, weight="weight") == [0, 6, 5, 4] + validate_grid_path( + 4, 4, 1, 12, nx.shortest_path(self.grid, 1, 12, weight="weight") + ) + assert nx.shortest_path(self.directed_cycle, 0, 3, weight="weight") == [ + 0, + 1, + 2, + 3, + ] + # weights and method specified + assert nx.shortest_path( + self.directed_cycle, 0, 3, weight="weight", method="dijkstra" + ) == [0, 1, 2, 3] + assert nx.shortest_path( + self.directed_cycle, 0, 3, weight="weight", method="bellman-ford" + ) == [0, 1, 2, 3] + # when Dijkstra's will probably (depending on precise implementation) + # incorrectly return [0, 1, 3] instead + assert nx.shortest_path( + self.neg_weights, 0, 3, weight="weight", method="bellman-ford" + ) == [0, 2, 3] + # confirm bad method rejection + pytest.raises(ValueError, nx.shortest_path, self.cycle, method="SPAM") + # confirm absent source rejection + pytest.raises(nx.NodeNotFound, nx.shortest_path, self.cycle, 8) + + def test_shortest_path_target(self): + answer = {0: [0, 1], 1: [1], 2: [2, 1]} + sp = nx.shortest_path(nx.path_graph(3), target=1) + assert sp == answer + # with weights + sp = nx.shortest_path(nx.path_graph(3), target=1, weight="weight") + assert sp == answer + # weights and method specified + sp = nx.shortest_path( + nx.path_graph(3), target=1, weight="weight", method="dijkstra" + ) + assert sp == answer + sp = nx.shortest_path( + nx.path_graph(3), target=1, weight="weight", method="bellman-ford" + ) + assert sp == answer + + def test_shortest_path_length(self): + assert nx.shortest_path_length(self.cycle, 0, 3) == 3 + assert nx.shortest_path_length(self.grid, 1, 12) == 5 + assert nx.shortest_path_length(self.directed_cycle, 0, 4) == 4 + # now with weights + assert nx.shortest_path_length(self.cycle, 0, 3, weight="weight") == 3 + assert nx.shortest_path_length(self.grid, 1, 12, weight="weight") == 5 + assert nx.shortest_path_length(self.directed_cycle, 0, 4, weight="weight") == 4 + # weights and method specified + assert ( + nx.shortest_path_length( + self.cycle, 0, 3, weight="weight", method="dijkstra" + ) + == 3 + ) + assert ( + nx.shortest_path_length( + self.cycle, 0, 3, weight="weight", method="bellman-ford" + ) + == 3 + ) + # confirm bad method rejection + pytest.raises(ValueError, nx.shortest_path_length, self.cycle, method="SPAM") + # confirm absent source rejection + pytest.raises(nx.NodeNotFound, nx.shortest_path_length, self.cycle, 8) + + def test_shortest_path_length_target(self): + answer = {0: 1, 1: 0, 2: 1} + sp = dict(nx.shortest_path_length(nx.path_graph(3), target=1)) + assert sp == answer + # with weights + sp = nx.shortest_path_length(nx.path_graph(3), target=1, weight="weight") + assert sp == answer + # weights and method specified + sp = nx.shortest_path_length( + nx.path_graph(3), target=1, weight="weight", method="dijkstra" + ) + assert sp == answer + sp = nx.shortest_path_length( + nx.path_graph(3), target=1, weight="weight", method="bellman-ford" + ) + assert sp == answer + + def test_single_source_shortest_path(self): + p = nx.shortest_path(self.cycle, 0) + assert p[3] == [0, 1, 2, 3] + assert p == nx.single_source_shortest_path(self.cycle, 0) + p = nx.shortest_path(self.grid, 1) + validate_grid_path(4, 4, 1, 12, p[12]) + # now with weights + p = nx.shortest_path(self.cycle, 0, weight="weight") + assert p[3] == [0, 1, 2, 3] + assert p == nx.single_source_dijkstra_path(self.cycle, 0) + p = nx.shortest_path(self.grid, 1, weight="weight") + validate_grid_path(4, 4, 1, 12, p[12]) + # weights and method specified + p = nx.shortest_path(self.cycle, 0, method="dijkstra", weight="weight") + assert p[3] == [0, 1, 2, 3] + assert p == nx.single_source_shortest_path(self.cycle, 0) + p = nx.shortest_path(self.cycle, 0, method="bellman-ford", weight="weight") + assert p[3] == [0, 1, 2, 3] + assert p == nx.single_source_shortest_path(self.cycle, 0) + + def test_single_source_shortest_path_length(self): + ans = dict(nx.shortest_path_length(self.cycle, 0)) + assert ans == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1} + assert ans == dict(nx.single_source_shortest_path_length(self.cycle, 0)) + ans = dict(nx.shortest_path_length(self.grid, 1)) + assert ans[16] == 6 + # now with weights + ans = dict(nx.shortest_path_length(self.cycle, 0, weight="weight")) + assert ans == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1} + assert ans == dict(nx.single_source_dijkstra_path_length(self.cycle, 0)) + ans = dict(nx.shortest_path_length(self.grid, 1, weight="weight")) + assert ans[16] == 6 + # weights and method specified + ans = dict( + nx.shortest_path_length(self.cycle, 0, weight="weight", method="dijkstra") + ) + assert ans == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1} + assert ans == dict(nx.single_source_dijkstra_path_length(self.cycle, 0)) + ans = dict( + nx.shortest_path_length( + self.cycle, 0, weight="weight", method="bellman-ford" + ) + ) + assert ans == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1} + assert ans == dict(nx.single_source_bellman_ford_path_length(self.cycle, 0)) + + def test_single_source_all_shortest_paths(self): + cycle_ans = {0: [[0]], 1: [[0, 1]], 2: [[0, 1, 2], [0, 3, 2]], 3: [[0, 3]]} + ans = dict(nx.single_source_all_shortest_paths(nx.cycle_graph(4), 0)) + assert sorted(ans[2]) == cycle_ans[2] + ans = dict(nx.single_source_all_shortest_paths(self.grid, 1)) + grid_ans = [ + [1, 2, 3, 7, 11], + [1, 2, 6, 7, 11], + [1, 2, 6, 10, 11], + [1, 5, 6, 7, 11], + [1, 5, 6, 10, 11], + [1, 5, 9, 10, 11], + ] + assert sorted(ans[11]) == grid_ans + ans = dict( + nx.single_source_all_shortest_paths(nx.cycle_graph(4), 0, weight="weight") + ) + assert sorted(ans[2]) == cycle_ans[2] + ans = dict( + nx.single_source_all_shortest_paths( + nx.cycle_graph(4), 0, method="bellman-ford", weight="weight" + ) + ) + assert sorted(ans[2]) == cycle_ans[2] + ans = dict(nx.single_source_all_shortest_paths(self.grid, 1, weight="weight")) + assert sorted(ans[11]) == grid_ans + ans = dict( + nx.single_source_all_shortest_paths( + self.grid, 1, method="bellman-ford", weight="weight" + ) + ) + assert sorted(ans[11]) == grid_ans + G = nx.cycle_graph(4) + G.add_node(4) + ans = dict(nx.single_source_all_shortest_paths(G, 0)) + assert sorted(ans[2]) == [[0, 1, 2], [0, 3, 2]] + ans = dict(nx.single_source_all_shortest_paths(G, 4)) + assert sorted(ans[4]) == [[4]] + + def test_all_pairs_shortest_path(self): + # shortest_path w/o source and target will return a generator instead of + # a dict beginning in version 3.5. Only the first call needs changed here. + p = nx.shortest_path(self.cycle) + assert p[0][3] == [0, 1, 2, 3] + assert p == dict(nx.all_pairs_shortest_path(self.cycle)) + p = dict(nx.shortest_path(self.grid)) + validate_grid_path(4, 4, 1, 12, p[1][12]) + # now with weights + p = dict(nx.shortest_path(self.cycle, weight="weight")) + assert p[0][3] == [0, 1, 2, 3] + assert p == dict(nx.all_pairs_dijkstra_path(self.cycle)) + p = dict(nx.shortest_path(self.grid, weight="weight")) + validate_grid_path(4, 4, 1, 12, p[1][12]) + # weights and method specified + p = dict(nx.shortest_path(self.cycle, weight="weight", method="dijkstra")) + assert p[0][3] == [0, 1, 2, 3] + assert p == dict(nx.all_pairs_dijkstra_path(self.cycle)) + p = dict(nx.shortest_path(self.cycle, weight="weight", method="bellman-ford")) + assert p[0][3] == [0, 1, 2, 3] + assert p == dict(nx.all_pairs_bellman_ford_path(self.cycle)) + + def test_all_pairs_shortest_path_length(self): + ans = dict(nx.shortest_path_length(self.cycle)) + assert ans[0] == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1} + assert ans == dict(nx.all_pairs_shortest_path_length(self.cycle)) + ans = dict(nx.shortest_path_length(self.grid)) + assert ans[1][16] == 6 + # now with weights + ans = dict(nx.shortest_path_length(self.cycle, weight="weight")) + assert ans[0] == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1} + assert ans == dict(nx.all_pairs_dijkstra_path_length(self.cycle)) + ans = dict(nx.shortest_path_length(self.grid, weight="weight")) + assert ans[1][16] == 6 + # weights and method specified + ans = dict( + nx.shortest_path_length(self.cycle, weight="weight", method="dijkstra") + ) + assert ans[0] == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1} + assert ans == dict(nx.all_pairs_dijkstra_path_length(self.cycle)) + ans = dict( + nx.shortest_path_length(self.cycle, weight="weight", method="bellman-ford") + ) + assert ans[0] == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1} + assert ans == dict(nx.all_pairs_bellman_ford_path_length(self.cycle)) + + def test_all_pairs_all_shortest_paths(self): + ans = dict(nx.all_pairs_all_shortest_paths(nx.cycle_graph(4))) + assert sorted(ans[1][3]) == [[1, 0, 3], [1, 2, 3]] + ans = dict(nx.all_pairs_all_shortest_paths(nx.cycle_graph(4)), weight="weight") + assert sorted(ans[1][3]) == [[1, 0, 3], [1, 2, 3]] + ans = dict( + nx.all_pairs_all_shortest_paths(nx.cycle_graph(4)), + method="bellman-ford", + weight="weight", + ) + assert sorted(ans[1][3]) == [[1, 0, 3], [1, 2, 3]] + G = nx.cycle_graph(4) + G.add_node(4) + ans = dict(nx.all_pairs_all_shortest_paths(G)) + assert sorted(ans[4][4]) == [[4]] + + def test_has_path(self): + G = nx.Graph() + nx.add_path(G, range(3)) + nx.add_path(G, range(3, 5)) + assert nx.has_path(G, 0, 2) + assert not nx.has_path(G, 0, 4) + + def test_has_path_singleton(self): + G = nx.empty_graph(1) + assert nx.has_path(G, 0, 0) + + def test_all_shortest_paths(self): + G = nx.Graph() + nx.add_path(G, [0, 1, 2, 3]) + nx.add_path(G, [0, 10, 20, 3]) + assert [[0, 1, 2, 3], [0, 10, 20, 3]] == sorted(nx.all_shortest_paths(G, 0, 3)) + # with weights + G = nx.Graph() + nx.add_path(G, [0, 1, 2, 3]) + nx.add_path(G, [0, 10, 20, 3]) + assert [[0, 1, 2, 3], [0, 10, 20, 3]] == sorted( + nx.all_shortest_paths(G, 0, 3, weight="weight") + ) + # weights and method specified + G = nx.Graph() + nx.add_path(G, [0, 1, 2, 3]) + nx.add_path(G, [0, 10, 20, 3]) + assert [[0, 1, 2, 3], [0, 10, 20, 3]] == sorted( + nx.all_shortest_paths(G, 0, 3, weight="weight", method="dijkstra") + ) + G = nx.Graph() + nx.add_path(G, [0, 1, 2, 3]) + nx.add_path(G, [0, 10, 20, 3]) + assert [[0, 1, 2, 3], [0, 10, 20, 3]] == sorted( + nx.all_shortest_paths(G, 0, 3, weight="weight", method="bellman-ford") + ) + + def test_all_shortest_paths_raise(self): + with pytest.raises(nx.NetworkXNoPath): + G = nx.path_graph(4) + G.add_node(4) + list(nx.all_shortest_paths(G, 0, 4)) + + def test_bad_method(self): + with pytest.raises(ValueError): + G = nx.path_graph(2) + list(nx.all_shortest_paths(G, 0, 1, weight="weight", method="SPAM")) + + def test_single_source_all_shortest_paths_bad_method(self): + with pytest.raises(ValueError): + G = nx.path_graph(2) + dict( + nx.single_source_all_shortest_paths( + G, 0, weight="weight", method="SPAM" + ) + ) + + def test_all_shortest_paths_zero_weight_edge(self): + g = nx.Graph() + nx.add_path(g, [0, 1, 3]) + nx.add_path(g, [0, 1, 2, 3]) + g.edges[1, 2]["weight"] = 0 + paths30d = list( + nx.all_shortest_paths(g, 3, 0, weight="weight", method="dijkstra") + ) + paths03d = list( + nx.all_shortest_paths(g, 0, 3, weight="weight", method="dijkstra") + ) + paths30b = list( + nx.all_shortest_paths(g, 3, 0, weight="weight", method="bellman-ford") + ) + paths03b = list( + nx.all_shortest_paths(g, 0, 3, weight="weight", method="bellman-ford") + ) + assert sorted(paths03d) == sorted(p[::-1] for p in paths30d) + assert sorted(paths03d) == sorted(p[::-1] for p in paths30b) + assert sorted(paths03b) == sorted(p[::-1] for p in paths30b) + + +class TestAverageShortestPathLength: + def test_cycle_graph(self): + ans = nx.average_shortest_path_length(nx.cycle_graph(7)) + assert ans == pytest.approx(2, abs=1e-7) + + def test_path_graph(self): + ans = nx.average_shortest_path_length(nx.path_graph(5)) + assert ans == pytest.approx(2, abs=1e-7) + + def test_weighted(self): + G = nx.Graph() + nx.add_cycle(G, range(7), weight=2) + ans = nx.average_shortest_path_length(G, weight="weight") + assert ans == pytest.approx(4, abs=1e-7) + G = nx.Graph() + nx.add_path(G, range(5), weight=2) + ans = nx.average_shortest_path_length(G, weight="weight") + assert ans == pytest.approx(4, abs=1e-7) + + def test_specified_methods(self): + G = nx.Graph() + nx.add_cycle(G, range(7), weight=2) + ans = nx.average_shortest_path_length(G, weight="weight", method="dijkstra") + assert ans == pytest.approx(4, abs=1e-7) + ans = nx.average_shortest_path_length(G, weight="weight", method="bellman-ford") + assert ans == pytest.approx(4, abs=1e-7) + ans = nx.average_shortest_path_length( + G, weight="weight", method="floyd-warshall" + ) + assert ans == pytest.approx(4, abs=1e-7) + + G = nx.Graph() + nx.add_path(G, range(5), weight=2) + ans = nx.average_shortest_path_length(G, weight="weight", method="dijkstra") + assert ans == pytest.approx(4, abs=1e-7) + ans = nx.average_shortest_path_length(G, weight="weight", method="bellman-ford") + assert ans == pytest.approx(4, abs=1e-7) + ans = nx.average_shortest_path_length( + G, weight="weight", method="floyd-warshall" + ) + assert ans == pytest.approx(4, abs=1e-7) + + def test_directed_not_strongly_connected(self): + G = nx.DiGraph([(0, 1)]) + with pytest.raises(nx.NetworkXError, match="Graph is not strongly connected"): + nx.average_shortest_path_length(G) + + def test_undirected_not_connected(self): + g = nx.Graph() + g.add_nodes_from(range(3)) + g.add_edge(0, 1) + pytest.raises(nx.NetworkXError, nx.average_shortest_path_length, g) + + def test_trivial_graph(self): + """Tests that the trivial graph has average path length zero, + since there is exactly one path of length zero in the trivial + graph. + + For more information, see issue #1960. + + """ + G = nx.trivial_graph() + assert nx.average_shortest_path_length(G) == 0 + + def test_null_graph(self): + with pytest.raises(nx.NetworkXPointlessConcept): + nx.average_shortest_path_length(nx.null_graph()) + + def test_bad_method(self): + with pytest.raises(ValueError): + G = nx.path_graph(2) + nx.average_shortest_path_length(G, weight="weight", method="SPAM") + + +class TestAverageShortestPathLengthNumpy: + @classmethod + def setup_class(cls): + global np + import pytest + + np = pytest.importorskip("numpy") + + def test_specified_methods_numpy(self): + G = nx.Graph() + nx.add_cycle(G, range(7), weight=2) + ans = nx.average_shortest_path_length( + G, weight="weight", method="floyd-warshall-numpy" + ) + np.testing.assert_almost_equal(ans, 4) + + G = nx.Graph() + nx.add_path(G, range(5), weight=2) + ans = nx.average_shortest_path_length( + G, weight="weight", method="floyd-warshall-numpy" + ) + np.testing.assert_almost_equal(ans, 4) diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/unweighted.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/unweighted.py new file mode 100644 index 0000000000000000000000000000000000000000..3aeef85478f94d5cfff34f9b7aa2bb4595adef9d --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/unweighted.py @@ -0,0 +1,579 @@ +""" +Shortest path algorithms for unweighted graphs. +""" + +import warnings + +import networkx as nx + +__all__ = [ + "bidirectional_shortest_path", + "single_source_shortest_path", + "single_source_shortest_path_length", + "single_target_shortest_path", + "single_target_shortest_path_length", + "all_pairs_shortest_path", + "all_pairs_shortest_path_length", + "predecessor", +] + + +@nx._dispatchable +def single_source_shortest_path_length(G, source, cutoff=None): + """Compute the shortest path lengths from source to all reachable nodes. + + Parameters + ---------- + G : NetworkX graph + + source : node + Starting node for path + + cutoff : integer, optional + Depth to stop the search. Only paths of length <= cutoff are returned. + + Returns + ------- + lengths : dict + Dict keyed by node to shortest path length to source. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> length = nx.single_source_shortest_path_length(G, 0) + >>> length[4] + 4 + >>> for node in length: + ... print(f"{node}: {length[node]}") + 0: 0 + 1: 1 + 2: 2 + 3: 3 + 4: 4 + + See Also + -------- + shortest_path_length + """ + if source not in G: + raise nx.NodeNotFound(f"Source {source} is not in G") + if cutoff is None: + cutoff = float("inf") + nextlevel = [source] + return dict(_single_shortest_path_length(G._adj, nextlevel, cutoff)) + + +def _single_shortest_path_length(adj, firstlevel, cutoff): + """Yields (node, level) in a breadth first search + + Shortest Path Length helper function + Parameters + ---------- + adj : dict + Adjacency dict or view + firstlevel : list + starting nodes, e.g. [source] or [target] + cutoff : int or float + level at which we stop the process + """ + seen = set(firstlevel) + nextlevel = firstlevel + level = 0 + n = len(adj) + for v in nextlevel: + yield (v, level) + while nextlevel and cutoff > level: + level += 1 + thislevel = nextlevel + nextlevel = [] + for v in thislevel: + for w in adj[v]: + if w not in seen: + seen.add(w) + nextlevel.append(w) + yield (w, level) + if len(seen) == n: + return + + +@nx._dispatchable +def single_target_shortest_path_length(G, target, cutoff=None): + """Compute the shortest path lengths to target from all reachable nodes. + + Parameters + ---------- + G : NetworkX graph + + target : node + Target node for path + + cutoff : integer, optional + Depth to stop the search. Only paths of length <= cutoff are returned. + + Returns + ------- + lengths : iterator + (source, shortest path length) iterator + + Examples + -------- + >>> G = nx.path_graph(5, create_using=nx.DiGraph()) + >>> length = dict(nx.single_target_shortest_path_length(G, 4)) + >>> length[0] + 4 + >>> for node in range(5): + ... print(f"{node}: {length[node]}") + 0: 4 + 1: 3 + 2: 2 + 3: 1 + 4: 0 + + See Also + -------- + single_source_shortest_path_length, shortest_path_length + """ + if target not in G: + raise nx.NodeNotFound(f"Target {target} is not in G") + + warnings.warn( + ( + "\n\nsingle_target_shortest_path_length will return a dict instead of" + "\nan iterator in version 3.5" + ), + FutureWarning, + stacklevel=3, + ) + + if cutoff is None: + cutoff = float("inf") + # handle either directed or undirected + adj = G._pred if G.is_directed() else G._adj + nextlevel = [target] + # for version 3.3 we will return a dict like this: + # return dict(_single_shortest_path_length(adj, nextlevel, cutoff)) + return _single_shortest_path_length(adj, nextlevel, cutoff) + + +@nx._dispatchable +def all_pairs_shortest_path_length(G, cutoff=None): + """Computes the shortest path lengths between all nodes in `G`. + + Parameters + ---------- + G : NetworkX graph + + cutoff : integer, optional + Depth at which to stop the search. Only paths of length at most + `cutoff` are returned. + + Returns + ------- + lengths : iterator + (source, dictionary) iterator with dictionary keyed by target and + shortest path length as the key value. + + Notes + ----- + The iterator returned only has reachable node pairs. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> length = dict(nx.all_pairs_shortest_path_length(G)) + >>> for node in [0, 1, 2, 3, 4]: + ... print(f"1 - {node}: {length[1][node]}") + 1 - 0: 1 + 1 - 1: 0 + 1 - 2: 1 + 1 - 3: 2 + 1 - 4: 3 + >>> length[3][2] + 1 + >>> length[2][2] + 0 + + """ + length = single_source_shortest_path_length + # TODO This can be trivially parallelized. + for n in G: + yield (n, length(G, n, cutoff=cutoff)) + + +@nx._dispatchable +def bidirectional_shortest_path(G, source, target): + """Returns a list of nodes in a shortest path between source and target. + + Parameters + ---------- + G : NetworkX graph + + source : node label + starting node for path + + target : node label + ending node for path + + Returns + ------- + path: list + List of nodes in a path from source to target. + + Raises + ------ + NetworkXNoPath + If no path exists between source and target. + + Examples + -------- + >>> G = nx.Graph() + >>> nx.add_path(G, [0, 1, 2, 3, 0, 4, 5, 6, 7, 4]) + >>> nx.bidirectional_shortest_path(G, 2, 6) + [2, 1, 0, 4, 5, 6] + + See Also + -------- + shortest_path + + Notes + ----- + This algorithm is used by shortest_path(G, source, target). + """ + + if source not in G: + raise nx.NodeNotFound(f"Source {source} is not in G") + + if target not in G: + raise nx.NodeNotFound(f"Target {target} is not in G") + + # call helper to do the real work + results = _bidirectional_pred_succ(G, source, target) + pred, succ, w = results + + # build path from pred+w+succ + path = [] + # from source to w + while w is not None: + path.append(w) + w = pred[w] + path.reverse() + # from w to target + w = succ[path[-1]] + while w is not None: + path.append(w) + w = succ[w] + + return path + + +def _bidirectional_pred_succ(G, source, target): + """Bidirectional shortest path helper. + + Returns (pred, succ, w) where + pred is a dictionary of predecessors from w to the source, and + succ is a dictionary of successors from w to the target. + """ + # does BFS from both source and target and meets in the middle + if target == source: + return ({target: None}, {source: None}, source) + + # handle either directed or undirected + if G.is_directed(): + Gpred = G.pred + Gsucc = G.succ + else: + Gpred = G.adj + Gsucc = G.adj + + # predecessor and successors in search + pred = {source: None} + succ = {target: None} + + # initialize fringes, start with forward + forward_fringe = [source] + reverse_fringe = [target] + + while forward_fringe and reverse_fringe: + if len(forward_fringe) <= len(reverse_fringe): + this_level = forward_fringe + forward_fringe = [] + for v in this_level: + for w in Gsucc[v]: + if w not in pred: + forward_fringe.append(w) + pred[w] = v + if w in succ: # path found + return pred, succ, w + else: + this_level = reverse_fringe + reverse_fringe = [] + for v in this_level: + for w in Gpred[v]: + if w not in succ: + succ[w] = v + reverse_fringe.append(w) + if w in pred: # found path + return pred, succ, w + + raise nx.NetworkXNoPath(f"No path between {source} and {target}.") + + +@nx._dispatchable +def single_source_shortest_path(G, source, cutoff=None): + """Compute shortest path between source + and all other nodes reachable from source. + + Parameters + ---------- + G : NetworkX graph + + source : node label + Starting node for path + + cutoff : integer, optional + Depth to stop the search. Only paths of length <= cutoff are returned. + + Returns + ------- + paths : dictionary + Dictionary, keyed by target, of shortest paths. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> path = nx.single_source_shortest_path(G, 0) + >>> path[4] + [0, 1, 2, 3, 4] + + Notes + ----- + The shortest path is not necessarily unique. So there can be multiple + paths between the source and each target node, all of which have the + same 'shortest' length. For each target node, this function returns + only one of those paths. + + See Also + -------- + shortest_path + """ + if source not in G: + raise nx.NodeNotFound(f"Source {source} not in G") + + def join(p1, p2): + return p1 + p2 + + if cutoff is None: + cutoff = float("inf") + nextlevel = {source: 1} # list of nodes to check at next level + paths = {source: [source]} # paths dictionary (paths to key from source) + return dict(_single_shortest_path(G.adj, nextlevel, paths, cutoff, join)) + + +def _single_shortest_path(adj, firstlevel, paths, cutoff, join): + """Returns shortest paths + + Shortest Path helper function + Parameters + ---------- + adj : dict + Adjacency dict or view + firstlevel : dict + starting nodes, e.g. {source: 1} or {target: 1} + paths : dict + paths for starting nodes, e.g. {source: [source]} + cutoff : int or float + level at which we stop the process + join : function + function to construct a path from two partial paths. Requires two + list inputs `p1` and `p2`, and returns a list. Usually returns + `p1 + p2` (forward from source) or `p2 + p1` (backward from target) + """ + level = 0 # the current level + nextlevel = firstlevel + while nextlevel and cutoff > level: + thislevel = nextlevel + nextlevel = {} + for v in thislevel: + for w in adj[v]: + if w not in paths: + paths[w] = join(paths[v], [w]) + nextlevel[w] = 1 + level += 1 + return paths + + +@nx._dispatchable +def single_target_shortest_path(G, target, cutoff=None): + """Compute shortest path to target from all nodes that reach target. + + Parameters + ---------- + G : NetworkX graph + + target : node label + Target node for path + + cutoff : integer, optional + Depth to stop the search. Only paths of length <= cutoff are returned. + + Returns + ------- + paths : dictionary + Dictionary, keyed by target, of shortest paths. + + Examples + -------- + >>> G = nx.path_graph(5, create_using=nx.DiGraph()) + >>> path = nx.single_target_shortest_path(G, 4) + >>> path[0] + [0, 1, 2, 3, 4] + + Notes + ----- + The shortest path is not necessarily unique. So there can be multiple + paths between the source and each target node, all of which have the + same 'shortest' length. For each target node, this function returns + only one of those paths. + + See Also + -------- + shortest_path, single_source_shortest_path + """ + if target not in G: + raise nx.NodeNotFound(f"Target {target} not in G") + + def join(p1, p2): + return p2 + p1 + + # handle undirected graphs + adj = G.pred if G.is_directed() else G.adj + if cutoff is None: + cutoff = float("inf") + nextlevel = {target: 1} # list of nodes to check at next level + paths = {target: [target]} # paths dictionary (paths to key from source) + return dict(_single_shortest_path(adj, nextlevel, paths, cutoff, join)) + + +@nx._dispatchable +def all_pairs_shortest_path(G, cutoff=None): + """Compute shortest paths between all nodes. + + Parameters + ---------- + G : NetworkX graph + + cutoff : integer, optional + Depth at which to stop the search. Only paths of length at most + `cutoff` are returned. + + Returns + ------- + paths : iterator + Dictionary, keyed by source and target, of shortest paths. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> path = dict(nx.all_pairs_shortest_path(G)) + >>> print(path[0][4]) + [0, 1, 2, 3, 4] + + Notes + ----- + There may be multiple shortest paths with the same length between + two nodes. For each pair, this function returns only one of those paths. + + See Also + -------- + floyd_warshall + all_pairs_all_shortest_paths + + """ + # TODO This can be trivially parallelized. + for n in G: + yield (n, single_source_shortest_path(G, n, cutoff=cutoff)) + + +@nx._dispatchable +def predecessor(G, source, target=None, cutoff=None, return_seen=None): + """Returns dict of predecessors for the path from source to all nodes in G. + + Parameters + ---------- + G : NetworkX graph + + source : node label + Starting node for path + + target : node label, optional + Ending node for path. If provided only predecessors between + source and target are returned + + cutoff : integer, optional + Depth to stop the search. Only paths of length <= cutoff are returned. + + return_seen : bool, optional (default=None) + Whether to return a dictionary, keyed by node, of the level (number of + hops) to reach the node (as seen during breadth-first-search). + + Returns + ------- + pred : dictionary + Dictionary, keyed by node, of predecessors in the shortest path. + + + (pred, seen): tuple of dictionaries + If `return_seen` argument is set to `True`, then a tuple of dictionaries + is returned. The first element is the dictionary, keyed by node, of + predecessors in the shortest path. The second element is the dictionary, + keyed by node, of the level (number of hops) to reach the node (as seen + during breadth-first-search). + + Examples + -------- + >>> G = nx.path_graph(4) + >>> list(G) + [0, 1, 2, 3] + >>> nx.predecessor(G, 0) + {0: [], 1: [0], 2: [1], 3: [2]} + >>> nx.predecessor(G, 0, return_seen=True) + ({0: [], 1: [0], 2: [1], 3: [2]}, {0: 0, 1: 1, 2: 2, 3: 3}) + + + """ + if source not in G: + raise nx.NodeNotFound(f"Source {source} not in G") + + level = 0 # the current level + nextlevel = [source] # list of nodes to check at next level + seen = {source: level} # level (number of hops) when seen in BFS + pred = {source: []} # predecessor dictionary + while nextlevel: + level = level + 1 + thislevel = nextlevel + nextlevel = [] + for v in thislevel: + for w in G[v]: + if w not in seen: + pred[w] = [v] + seen[w] = level + nextlevel.append(w) + elif seen[w] == level: # add v to predecessor list if it + pred[w].append(v) # is at the correct level + if cutoff and cutoff <= level: + break + + if target is not None: + if return_seen: + if target not in pred: + return ([], -1) # No predecessor + return (pred[target], seen[target]) + else: + if target not in pred: + return [] # No predecessor + return pred[target] + else: + if return_seen: + return (pred, seen) + else: + return pred diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/weighted.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/weighted.py new file mode 100644 index 0000000000000000000000000000000000000000..f8421d42b5d65b23dea79bb16cc8280940f83127 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/shortest_paths/weighted.py @@ -0,0 +1,2520 @@ +""" +Shortest path algorithms for weighted graphs. +""" + +from collections import deque +from heapq import heappop, heappush +from itertools import count + +import networkx as nx +from networkx.algorithms.shortest_paths.generic import _build_paths_from_predecessors + +__all__ = [ + "dijkstra_path", + "dijkstra_path_length", + "bidirectional_dijkstra", + "single_source_dijkstra", + "single_source_dijkstra_path", + "single_source_dijkstra_path_length", + "multi_source_dijkstra", + "multi_source_dijkstra_path", + "multi_source_dijkstra_path_length", + "all_pairs_dijkstra", + "all_pairs_dijkstra_path", + "all_pairs_dijkstra_path_length", + "dijkstra_predecessor_and_distance", + "bellman_ford_path", + "bellman_ford_path_length", + "single_source_bellman_ford", + "single_source_bellman_ford_path", + "single_source_bellman_ford_path_length", + "all_pairs_bellman_ford_path", + "all_pairs_bellman_ford_path_length", + "bellman_ford_predecessor_and_distance", + "negative_edge_cycle", + "find_negative_cycle", + "goldberg_radzik", + "johnson", +] + + +def _weight_function(G, weight): + """Returns a function that returns the weight of an edge. + + The returned function is specifically suitable for input to + functions :func:`_dijkstra` and :func:`_bellman_ford_relaxation`. + + Parameters + ---------- + G : NetworkX graph. + + weight : string or function + If it is callable, `weight` itself is returned. If it is a string, + it is assumed to be the name of the edge attribute that represents + the weight of an edge. In that case, a function is returned that + gets the edge weight according to the specified edge attribute. + + Returns + ------- + function + This function returns a callable that accepts exactly three inputs: + a node, an node adjacent to the first one, and the edge attribute + dictionary for the eedge joining those nodes. That function returns + a number representing the weight of an edge. + + If `G` is a multigraph, and `weight` is not callable, the + minimum edge weight over all parallel edges is returned. If any edge + does not have an attribute with key `weight`, it is assumed to + have weight one. + + """ + if callable(weight): + return weight + # If the weight keyword argument is not callable, we assume it is a + # string representing the edge attribute containing the weight of + # the edge. + if G.is_multigraph(): + return lambda u, v, d: min(attr.get(weight, 1) for attr in d.values()) + return lambda u, v, data: data.get(weight, 1) + + +@nx._dispatchable(edge_attrs="weight") +def dijkstra_path(G, source, target, weight="weight"): + """Returns the shortest weighted path from source to target in G. + + Uses Dijkstra's Method to compute the shortest weighted path + between two nodes in a graph. + + Parameters + ---------- + G : NetworkX graph + + source : node + Starting node + + target : node + Ending node + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Returns + ------- + path : list + List of nodes in a shortest path. + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + NetworkXNoPath + If no path exists between source and target. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> print(nx.dijkstra_path(G, 0, 4)) + [0, 1, 2, 3, 4] + + Find edges of shortest path in Multigraph + + >>> G = nx.MultiDiGraph() + >>> G.add_weighted_edges_from([(1, 2, 0.75), (1, 2, 0.5), (2, 3, 0.5), (1, 3, 1.5)]) + >>> nodes = nx.dijkstra_path(G, 1, 3) + >>> edges = nx.utils.pairwise(nodes) + >>> list( + ... (u, v, min(G[u][v], key=lambda k: G[u][v][k].get("weight", 1))) + ... for u, v in edges + ... ) + [(1, 2, 1), (2, 3, 0)] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The weight function can be used to hide edges by returning None. + So ``weight = lambda u, v, d: 1 if d['color']=="red" else None`` + will find the shortest red path. + + The weight function can be used to include node weights. + + >>> def func(u, v, d): + ... node_u_wt = G.nodes[u].get("node_weight", 1) + ... node_v_wt = G.nodes[v].get("node_weight", 1) + ... edge_wt = d.get("weight", 1) + ... return node_u_wt / 2 + node_v_wt / 2 + edge_wt + + In this example we take the average of start and end node + weights of an edge and add it to the weight of the edge. + + The function :func:`single_source_dijkstra` computes both + path and length-of-path if you need both, use that. + + See Also + -------- + bidirectional_dijkstra + bellman_ford_path + single_source_dijkstra + """ + (length, path) = single_source_dijkstra(G, source, target=target, weight=weight) + return path + + +@nx._dispatchable(edge_attrs="weight") +def dijkstra_path_length(G, source, target, weight="weight"): + """Returns the shortest weighted path length in G from source to target. + + Uses Dijkstra's Method to compute the shortest weighted path length + between two nodes in a graph. + + Parameters + ---------- + G : NetworkX graph + + source : node label + starting node for path + + target : node label + ending node for path + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Returns + ------- + length : number + Shortest path length. + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + NetworkXNoPath + If no path exists between source and target. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> nx.dijkstra_path_length(G, 0, 4) + 4 + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The weight function can be used to hide edges by returning None. + So ``weight = lambda u, v, d: 1 if d['color']=="red" else None`` + will find the shortest red path. + + The function :func:`single_source_dijkstra` computes both + path and length-of-path if you need both, use that. + + See Also + -------- + bidirectional_dijkstra + bellman_ford_path_length + single_source_dijkstra + + """ + if source not in G: + raise nx.NodeNotFound(f"Node {source} not found in graph") + if source == target: + return 0 + weight = _weight_function(G, weight) + length = _dijkstra(G, source, weight, target=target) + try: + return length[target] + except KeyError as err: + raise nx.NetworkXNoPath(f"Node {target} not reachable from {source}") from err + + +@nx._dispatchable(edge_attrs="weight") +def single_source_dijkstra_path(G, source, cutoff=None, weight="weight"): + """Find shortest weighted paths in G from a source node. + + Compute shortest path between source and all other reachable + nodes for a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + source : node + Starting node for path. + + cutoff : integer or float, optional + Length (sum of edge weights) at which the search is stopped. + If cutoff is provided, only return paths with summed weight <= cutoff. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Returns + ------- + paths : dictionary + Dictionary of shortest path lengths keyed by target. + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> path = nx.single_source_dijkstra_path(G, 0) + >>> path[4] + [0, 1, 2, 3, 4] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The weight function can be used to hide edges by returning None. + So ``weight = lambda u, v, d: 1 if d['color']=="red" else None`` + will find the shortest red path. + + See Also + -------- + single_source_dijkstra, single_source_bellman_ford + + """ + return multi_source_dijkstra_path(G, {source}, cutoff=cutoff, weight=weight) + + +@nx._dispatchable(edge_attrs="weight") +def single_source_dijkstra_path_length(G, source, cutoff=None, weight="weight"): + """Find shortest weighted path lengths in G from a source node. + + Compute the shortest path length between source and all other + reachable nodes for a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + source : node label + Starting node for path + + cutoff : integer or float, optional + Length (sum of edge weights) at which the search is stopped. + If cutoff is provided, only return paths with summed weight <= cutoff. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Returns + ------- + length : dict + Dict keyed by node to shortest path length from source. + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> length = nx.single_source_dijkstra_path_length(G, 0) + >>> length[4] + 4 + >>> for node in [0, 1, 2, 3, 4]: + ... print(f"{node}: {length[node]}") + 0: 0 + 1: 1 + 2: 2 + 3: 3 + 4: 4 + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The weight function can be used to hide edges by returning None. + So ``weight = lambda u, v, d: 1 if d['color']=="red" else None`` + will find the shortest red path. + + See Also + -------- + single_source_dijkstra, single_source_bellman_ford_path_length + + """ + return multi_source_dijkstra_path_length(G, {source}, cutoff=cutoff, weight=weight) + + +@nx._dispatchable(edge_attrs="weight") +def single_source_dijkstra(G, source, target=None, cutoff=None, weight="weight"): + """Find shortest weighted paths and lengths from a source node. + + Compute the shortest path length between source and all other + reachable nodes for a weighted graph. + + Uses Dijkstra's algorithm to compute shortest paths and lengths + between a source and all other reachable nodes in a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + source : node label + Starting node for path + + target : node label, optional + Ending node for path + + cutoff : integer or float, optional + Length (sum of edge weights) at which the search is stopped. + If cutoff is provided, only return paths with summed weight <= cutoff. + + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Returns + ------- + distance, path : pair of dictionaries, or numeric and list. + If target is None, paths and lengths to all nodes are computed. + The return value is a tuple of two dictionaries keyed by target nodes. + The first dictionary stores distance to each target node. + The second stores the path to each target node. + If target is not None, returns a tuple (distance, path), where + distance is the distance from source to target and path is a list + representing the path from source to target. + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> length, path = nx.single_source_dijkstra(G, 0) + >>> length[4] + 4 + >>> for node in [0, 1, 2, 3, 4]: + ... print(f"{node}: {length[node]}") + 0: 0 + 1: 1 + 2: 2 + 3: 3 + 4: 4 + >>> path[4] + [0, 1, 2, 3, 4] + >>> length, path = nx.single_source_dijkstra(G, 0, 1) + >>> length + 1 + >>> path + [0, 1] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The weight function can be used to hide edges by returning None. + So ``weight = lambda u, v, d: 1 if d['color']=="red" else None`` + will find the shortest red path. + + Based on the Python cookbook recipe (119466) at + https://code.activestate.com/recipes/119466/ + + This algorithm is not guaranteed to work if edge weights + are negative or are floating point numbers + (overflows and roundoff errors can cause problems). + + See Also + -------- + single_source_dijkstra_path + single_source_dijkstra_path_length + single_source_bellman_ford + """ + return multi_source_dijkstra( + G, {source}, cutoff=cutoff, target=target, weight=weight + ) + + +@nx._dispatchable(edge_attrs="weight") +def multi_source_dijkstra_path(G, sources, cutoff=None, weight="weight"): + """Find shortest weighted paths in G from a given set of source + nodes. + + Compute shortest path between any of the source nodes and all other + reachable nodes for a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + sources : non-empty set of nodes + Starting nodes for paths. If this is just a set containing a + single node, then all paths computed by this function will start + from that node. If there are two or more nodes in the set, the + computed paths may begin from any one of the start nodes. + + cutoff : integer or float, optional + Length (sum of edge weights) at which the search is stopped. + If cutoff is provided, only return paths with summed weight <= cutoff. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Returns + ------- + paths : dictionary + Dictionary of shortest paths keyed by target. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> path = nx.multi_source_dijkstra_path(G, {0, 4}) + >>> path[1] + [0, 1] + >>> path[3] + [4, 3] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The weight function can be used to hide edges by returning None. + So ``weight = lambda u, v, d: 1 if d['color']=="red" else None`` + will find the shortest red path. + + Raises + ------ + ValueError + If `sources` is empty. + NodeNotFound + If any of `sources` is not in `G`. + + See Also + -------- + multi_source_dijkstra, multi_source_bellman_ford + + """ + length, path = multi_source_dijkstra(G, sources, cutoff=cutoff, weight=weight) + return path + + +@nx._dispatchable(edge_attrs="weight") +def multi_source_dijkstra_path_length(G, sources, cutoff=None, weight="weight"): + """Find shortest weighted path lengths in G from a given set of + source nodes. + + Compute the shortest path length between any of the source nodes and + all other reachable nodes for a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + sources : non-empty set of nodes + Starting nodes for paths. If this is just a set containing a + single node, then all paths computed by this function will start + from that node. If there are two or more nodes in the set, the + computed paths may begin from any one of the start nodes. + + cutoff : integer or float, optional + Length (sum of edge weights) at which the search is stopped. + If cutoff is provided, only return paths with summed weight <= cutoff. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Returns + ------- + length : dict + Dict keyed by node to shortest path length to nearest source. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> length = nx.multi_source_dijkstra_path_length(G, {0, 4}) + >>> for node in [0, 1, 2, 3, 4]: + ... print(f"{node}: {length[node]}") + 0: 0 + 1: 1 + 2: 2 + 3: 1 + 4: 0 + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The weight function can be used to hide edges by returning None. + So ``weight = lambda u, v, d: 1 if d['color']=="red" else None`` + will find the shortest red path. + + Raises + ------ + ValueError + If `sources` is empty. + NodeNotFound + If any of `sources` is not in `G`. + + See Also + -------- + multi_source_dijkstra + + """ + if not sources: + raise ValueError("sources must not be empty") + for s in sources: + if s not in G: + raise nx.NodeNotFound(f"Node {s} not found in graph") + weight = _weight_function(G, weight) + return _dijkstra_multisource(G, sources, weight, cutoff=cutoff) + + +@nx._dispatchable(edge_attrs="weight") +def multi_source_dijkstra(G, sources, target=None, cutoff=None, weight="weight"): + """Find shortest weighted paths and lengths from a given set of + source nodes. + + Uses Dijkstra's algorithm to compute the shortest paths and lengths + between one of the source nodes and the given `target`, or all other + reachable nodes if not specified, for a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + sources : non-empty set of nodes + Starting nodes for paths. If this is just a set containing a + single node, then all paths computed by this function will start + from that node. If there are two or more nodes in the set, the + computed paths may begin from any one of the start nodes. + + target : node label, optional + Ending node for path + + cutoff : integer or float, optional + Length (sum of edge weights) at which the search is stopped. + If cutoff is provided, only return paths with summed weight <= cutoff. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Returns + ------- + distance, path : pair of dictionaries, or numeric and list + If target is None, returns a tuple of two dictionaries keyed by node. + The first dictionary stores distance from one of the source nodes. + The second stores the path from one of the sources to that node. + If target is not None, returns a tuple of (distance, path) where + distance is the distance from source to target and path is a list + representing the path from source to target. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> length, path = nx.multi_source_dijkstra(G, {0, 4}) + >>> for node in [0, 1, 2, 3, 4]: + ... print(f"{node}: {length[node]}") + 0: 0 + 1: 1 + 2: 2 + 3: 1 + 4: 0 + >>> path[1] + [0, 1] + >>> path[3] + [4, 3] + + >>> length, path = nx.multi_source_dijkstra(G, {0, 4}, 1) + >>> length + 1 + >>> path + [0, 1] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The weight function can be used to hide edges by returning None. + So ``weight = lambda u, v, d: 1 if d['color']=="red" else None`` + will find the shortest red path. + + Based on the Python cookbook recipe (119466) at + https://code.activestate.com/recipes/119466/ + + This algorithm is not guaranteed to work if edge weights + are negative or are floating point numbers + (overflows and roundoff errors can cause problems). + + Raises + ------ + ValueError + If `sources` is empty. + NodeNotFound + If any of `sources` is not in `G`. + + See Also + -------- + multi_source_dijkstra_path + multi_source_dijkstra_path_length + + """ + if not sources: + raise ValueError("sources must not be empty") + for s in sources: + if s not in G: + raise nx.NodeNotFound(f"Node {s} not found in graph") + if target in sources: + return (0, [target]) + weight = _weight_function(G, weight) + paths = {source: [source] for source in sources} # dictionary of paths + dist = _dijkstra_multisource( + G, sources, weight, paths=paths, cutoff=cutoff, target=target + ) + if target is None: + return (dist, paths) + try: + return (dist[target], paths[target]) + except KeyError as err: + raise nx.NetworkXNoPath(f"No path to {target}.") from err + + +def _dijkstra(G, source, weight, pred=None, paths=None, cutoff=None, target=None): + """Uses Dijkstra's algorithm to find shortest weighted paths from a + single source. + + This is a convenience function for :func:`_dijkstra_multisource` + with all the arguments the same, except the keyword argument + `sources` set to ``[source]``. + + """ + return _dijkstra_multisource( + G, [source], weight, pred=pred, paths=paths, cutoff=cutoff, target=target + ) + + +def _dijkstra_multisource( + G, sources, weight, pred=None, paths=None, cutoff=None, target=None +): + """Uses Dijkstra's algorithm to find shortest weighted paths + + Parameters + ---------- + G : NetworkX graph + + sources : non-empty iterable of nodes + Starting nodes for paths. If this is just an iterable containing + a single node, then all paths computed by this function will + start from that node. If there are two or more nodes in this + iterable, the computed paths may begin from any one of the start + nodes. + + weight: function + Function with (u, v, data) input that returns that edge's weight + or None to indicate a hidden edge + + pred: dict of lists, optional(default=None) + dict to store a list of predecessors keyed by that node + If None, predecessors are not stored. + + paths: dict, optional (default=None) + dict to store the path list from source to each node, keyed by node. + If None, paths are not stored. + + target : node label, optional + Ending node for path. Search is halted when target is found. + + cutoff : integer or float, optional + Length (sum of edge weights) at which the search is stopped. + If cutoff is provided, only return paths with summed weight <= cutoff. + + Returns + ------- + distance : dictionary + A mapping from node to shortest distance to that node from one + of the source nodes. + + Raises + ------ + NodeNotFound + If any of `sources` is not in `G`. + + Notes + ----- + The optional predecessor and path dictionaries can be accessed by + the caller through the original pred and paths objects passed + as arguments. No need to explicitly return pred or paths. + + """ + G_succ = G._adj # For speed-up (and works for both directed and undirected graphs) + + push = heappush + pop = heappop + dist = {} # dictionary of final distances + seen = {} + # fringe is heapq with 3-tuples (distance,c,node) + # use the count c to avoid comparing nodes (may not be able to) + c = count() + fringe = [] + for source in sources: + seen[source] = 0 + push(fringe, (0, next(c), source)) + while fringe: + (d, _, v) = pop(fringe) + if v in dist: + continue # already searched this node. + dist[v] = d + if v == target: + break + for u, e in G_succ[v].items(): + cost = weight(v, u, e) + if cost is None: + continue + vu_dist = dist[v] + cost + if cutoff is not None: + if vu_dist > cutoff: + continue + if u in dist: + u_dist = dist[u] + if vu_dist < u_dist: + raise ValueError("Contradictory paths found:", "negative weights?") + elif pred is not None and vu_dist == u_dist: + pred[u].append(v) + elif u not in seen or vu_dist < seen[u]: + seen[u] = vu_dist + push(fringe, (vu_dist, next(c), u)) + if paths is not None: + paths[u] = paths[v] + [u] + if pred is not None: + pred[u] = [v] + elif vu_dist == seen[u]: + if pred is not None: + pred[u].append(v) + + # The optional predecessor and path dictionaries can be accessed + # by the caller via the pred and paths objects passed as arguments. + return dist + + +@nx._dispatchable(edge_attrs="weight") +def dijkstra_predecessor_and_distance(G, source, cutoff=None, weight="weight"): + """Compute weighted shortest path length and predecessors. + + Uses Dijkstra's Method to obtain the shortest weighted paths + and return dictionaries of predecessors for each node and + distance for each node from the `source`. + + Parameters + ---------- + G : NetworkX graph + + source : node label + Starting node for path + + cutoff : integer or float, optional + Length (sum of edge weights) at which the search is stopped. + If cutoff is provided, only return paths with summed weight <= cutoff. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Returns + ------- + pred, distance : dictionaries + Returns two dictionaries representing a list of predecessors + of a node and the distance to each node. + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The list of predecessors contains more than one element only when + there are more than one shortest paths to the key node. + + Examples + -------- + >>> G = nx.path_graph(5, create_using=nx.DiGraph()) + >>> pred, dist = nx.dijkstra_predecessor_and_distance(G, 0) + >>> sorted(pred.items()) + [(0, []), (1, [0]), (2, [1]), (3, [2]), (4, [3])] + >>> sorted(dist.items()) + [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)] + + >>> pred, dist = nx.dijkstra_predecessor_and_distance(G, 0, 1) + >>> sorted(pred.items()) + [(0, []), (1, [0])] + >>> sorted(dist.items()) + [(0, 0), (1, 1)] + """ + if source not in G: + raise nx.NodeNotFound(f"Node {source} is not found in the graph") + weight = _weight_function(G, weight) + pred = {source: []} # dictionary of predecessors + return (pred, _dijkstra(G, source, weight, pred=pred, cutoff=cutoff)) + + +@nx._dispatchable(edge_attrs="weight") +def all_pairs_dijkstra(G, cutoff=None, weight="weight"): + """Find shortest weighted paths and lengths between all nodes. + + Parameters + ---------- + G : NetworkX graph + + cutoff : integer or float, optional + Length (sum of edge weights) at which the search is stopped. + If cutoff is provided, only return paths with summed weight <= cutoff. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edge[u][v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Yields + ------ + (node, (distance, path)) : (node obj, (dict, dict)) + Each source node has two associated dicts. The first holds distance + keyed by target and the second holds paths keyed by target. + (See single_source_dijkstra for the source/target node terminology.) + If desired you can apply `dict()` to this function to create a dict + keyed by source node to the two dicts. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> len_path = dict(nx.all_pairs_dijkstra(G)) + >>> len_path[3][0][1] + 2 + >>> for node in [0, 1, 2, 3, 4]: + ... print(f"3 - {node}: {len_path[3][0][node]}") + 3 - 0: 3 + 3 - 1: 2 + 3 - 2: 1 + 3 - 3: 0 + 3 - 4: 1 + >>> len_path[3][1][1] + [3, 2, 1] + >>> for n, (dist, path) in nx.all_pairs_dijkstra(G): + ... print(path[1]) + [0, 1] + [1] + [2, 1] + [3, 2, 1] + [4, 3, 2, 1] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The yielded dicts only have keys for reachable nodes. + """ + for n in G: + dist, path = single_source_dijkstra(G, n, cutoff=cutoff, weight=weight) + yield (n, (dist, path)) + + +@nx._dispatchable(edge_attrs="weight") +def all_pairs_dijkstra_path_length(G, cutoff=None, weight="weight"): + """Compute shortest path lengths between all nodes in a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + cutoff : integer or float, optional + Length (sum of edge weights) at which the search is stopped. + If cutoff is provided, only return paths with summed weight <= cutoff. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Returns + ------- + distance : iterator + (source, dictionary) iterator with dictionary keyed by target and + shortest path length as the key value. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> length = dict(nx.all_pairs_dijkstra_path_length(G)) + >>> for node in [0, 1, 2, 3, 4]: + ... print(f"1 - {node}: {length[1][node]}") + 1 - 0: 1 + 1 - 1: 0 + 1 - 2: 1 + 1 - 3: 2 + 1 - 4: 3 + >>> length[3][2] + 1 + >>> length[2][2] + 0 + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The dictionary returned only has keys for reachable node pairs. + """ + length = single_source_dijkstra_path_length + for n in G: + yield (n, length(G, n, cutoff=cutoff, weight=weight)) + + +@nx._dispatchable(edge_attrs="weight") +def all_pairs_dijkstra_path(G, cutoff=None, weight="weight"): + """Compute shortest paths between all nodes in a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + cutoff : integer or float, optional + Length (sum of edge weights) at which the search is stopped. + If cutoff is provided, only return paths with summed weight <= cutoff. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Returns + ------- + paths : iterator + (source, dictionary) iterator with dictionary keyed by target and + shortest path as the key value. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> path = dict(nx.all_pairs_dijkstra_path(G)) + >>> path[0][4] + [0, 1, 2, 3, 4] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + See Also + -------- + floyd_warshall, all_pairs_bellman_ford_path + + """ + path = single_source_dijkstra_path + # TODO This can be trivially parallelized. + for n in G: + yield (n, path(G, n, cutoff=cutoff, weight=weight)) + + +@nx._dispatchable(edge_attrs="weight") +def bellman_ford_predecessor_and_distance( + G, source, target=None, weight="weight", heuristic=False +): + """Compute shortest path lengths and predecessors on shortest paths + in weighted graphs. + + The algorithm has a running time of $O(mn)$ where $n$ is the number of + nodes and $m$ is the number of edges. It is slower than Dijkstra but + can handle negative edge weights. + + If a negative cycle is detected, you can use :func:`find_negative_cycle` + to return the cycle and examine it. Shortest paths are not defined when + a negative cycle exists because once reached, the path can cycle forever + to build up arbitrarily low weights. + + Parameters + ---------- + G : NetworkX graph + The algorithm works for all types of graphs, including directed + graphs and multigraphs. + + source: node label + Starting node for path + + target : node label, optional + Ending node for path + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number. + + heuristic : bool + Determines whether to use a heuristic to early detect negative + cycles at a hopefully negligible cost. + + Returns + ------- + pred, dist : dictionaries + Returns two dictionaries keyed by node to predecessor in the + path and to the distance from the source respectively. + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + NetworkXUnbounded + If the (di)graph contains a negative (di)cycle, the + algorithm raises an exception to indicate the presence of the + negative (di)cycle. Note: any negative weight edge in an + undirected graph is a negative cycle. + + Examples + -------- + >>> G = nx.path_graph(5, create_using=nx.DiGraph()) + >>> pred, dist = nx.bellman_ford_predecessor_and_distance(G, 0) + >>> sorted(pred.items()) + [(0, []), (1, [0]), (2, [1]), (3, [2]), (4, [3])] + >>> sorted(dist.items()) + [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)] + + >>> pred, dist = nx.bellman_ford_predecessor_and_distance(G, 0, 1) + >>> sorted(pred.items()) + [(0, []), (1, [0]), (2, [1]), (3, [2]), (4, [3])] + >>> sorted(dist.items()) + [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)] + + >>> G = nx.cycle_graph(5, create_using=nx.DiGraph()) + >>> G[1][2]["weight"] = -7 + >>> nx.bellman_ford_predecessor_and_distance(G, 0) + Traceback (most recent call last): + ... + networkx.exception.NetworkXUnbounded: Negative cycle detected. + + See Also + -------- + find_negative_cycle + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The dictionaries returned only have keys for nodes reachable from + the source. + + In the case where the (di)graph is not connected, if a component + not containing the source contains a negative (di)cycle, it + will not be detected. + + In NetworkX v2.1 and prior, the source node had predecessor `[None]`. + In NetworkX v2.2 this changed to the source node having predecessor `[]` + """ + if source not in G: + raise nx.NodeNotFound(f"Node {source} is not found in the graph") + weight = _weight_function(G, weight) + if G.is_multigraph(): + if any( + weight(u, v, {k: d}) < 0 + for u, v, k, d in nx.selfloop_edges(G, keys=True, data=True) + ): + raise nx.NetworkXUnbounded("Negative cycle detected.") + else: + if any(weight(u, v, d) < 0 for u, v, d in nx.selfloop_edges(G, data=True)): + raise nx.NetworkXUnbounded("Negative cycle detected.") + + dist = {source: 0} + pred = {source: []} + + if len(G) == 1: + return pred, dist + + weight = _weight_function(G, weight) + + dist = _bellman_ford( + G, [source], weight, pred=pred, dist=dist, target=target, heuristic=heuristic + ) + return (pred, dist) + + +def _bellman_ford( + G, + source, + weight, + pred=None, + paths=None, + dist=None, + target=None, + heuristic=True, +): + """Calls relaxation loop for Bellman–Ford algorithm and builds paths + + This is an implementation of the SPFA variant. + See https://en.wikipedia.org/wiki/Shortest_Path_Faster_Algorithm + + Parameters + ---------- + G : NetworkX graph + + source: list + List of source nodes. The shortest path from any of the source + nodes will be found if multiple sources are provided. + + weight : function + The weight of an edge is the value returned by the function. The + function must accept exactly three positional arguments: the two + endpoints of an edge and the dictionary of edge attributes for + that edge. The function must return a number. + + pred: dict of lists, optional (default=None) + dict to store a list of predecessors keyed by that node + If None, predecessors are not stored + + paths: dict, optional (default=None) + dict to store the path list from source to each node, keyed by node + If None, paths are not stored + + dist: dict, optional (default=None) + dict to store distance from source to the keyed node + If None, returned dist dict contents default to 0 for every node in the + source list + + target: node label, optional + Ending node for path. Path lengths to other destinations may (and + probably will) be incorrect. + + heuristic : bool + Determines whether to use a heuristic to early detect negative + cycles at a hopefully negligible cost. + + Returns + ------- + dist : dict + Returns a dict keyed by node to the distance from the source. + Dicts for paths and pred are in the mutated input dicts by those names. + + Raises + ------ + NodeNotFound + If any of `source` is not in `G`. + + NetworkXUnbounded + If the (di)graph contains a negative (di)cycle, the + algorithm raises an exception to indicate the presence of the + negative (di)cycle. Note: any negative weight edge in an + undirected graph is a negative cycle + """ + if pred is None: + pred = {v: [] for v in source} + + if dist is None: + dist = {v: 0 for v in source} + + negative_cycle_found = _inner_bellman_ford( + G, + source, + weight, + pred, + dist, + heuristic, + ) + if negative_cycle_found is not None: + raise nx.NetworkXUnbounded("Negative cycle detected.") + + if paths is not None: + sources = set(source) + dsts = [target] if target is not None else pred + for dst in dsts: + gen = _build_paths_from_predecessors(sources, dst, pred) + paths[dst] = next(gen) + + return dist + + +def _inner_bellman_ford( + G, + sources, + weight, + pred, + dist=None, + heuristic=True, +): + """Inner Relaxation loop for Bellman–Ford algorithm. + + This is an implementation of the SPFA variant. + See https://en.wikipedia.org/wiki/Shortest_Path_Faster_Algorithm + + Parameters + ---------- + G : NetworkX graph + + source: list + List of source nodes. The shortest path from any of the source + nodes will be found if multiple sources are provided. + + weight : function + The weight of an edge is the value returned by the function. The + function must accept exactly three positional arguments: the two + endpoints of an edge and the dictionary of edge attributes for + that edge. The function must return a number. + + pred: dict of lists + dict to store a list of predecessors keyed by that node + + dist: dict, optional (default=None) + dict to store distance from source to the keyed node + If None, returned dist dict contents default to 0 for every node in the + source list + + heuristic : bool + Determines whether to use a heuristic to early detect negative + cycles at a hopefully negligible cost. + + Returns + ------- + node or None + Return a node `v` where processing discovered a negative cycle. + If no negative cycle found, return None. + + Raises + ------ + NodeNotFound + If any of `source` is not in `G`. + """ + for s in sources: + if s not in G: + raise nx.NodeNotFound(f"Source {s} not in G") + + if pred is None: + pred = {v: [] for v in sources} + + if dist is None: + dist = {v: 0 for v in sources} + + # Heuristic Storage setup. Note: use None because nodes cannot be None + nonexistent_edge = (None, None) + pred_edge = {v: None for v in sources} + recent_update = {v: nonexistent_edge for v in sources} + + G_succ = G._adj # For speed-up (and works for both directed and undirected graphs) + inf = float("inf") + n = len(G) + + count = {} + q = deque(sources) + in_q = set(sources) + while q: + u = q.popleft() + in_q.remove(u) + + # Skip relaxations if any of the predecessors of u is in the queue. + if all(pred_u not in in_q for pred_u in pred[u]): + dist_u = dist[u] + for v, e in G_succ[u].items(): + dist_v = dist_u + weight(u, v, e) + + if dist_v < dist.get(v, inf): + # In this conditional branch we are updating the path with v. + # If it happens that some earlier update also added node v + # that implies the existence of a negative cycle since + # after the update node v would lie on the update path twice. + # The update path is stored up to one of the source nodes, + # therefore u is always in the dict recent_update + if heuristic: + if v in recent_update[u]: + # Negative cycle found! + pred[v].append(u) + return v + + # Transfer the recent update info from u to v if the + # same source node is the head of the update path. + # If the source node is responsible for the cost update, + # then clear the history and use it instead. + if v in pred_edge and pred_edge[v] == u: + recent_update[v] = recent_update[u] + else: + recent_update[v] = (u, v) + + if v not in in_q: + q.append(v) + in_q.add(v) + count_v = count.get(v, 0) + 1 + if count_v == n: + # Negative cycle found! + return v + + count[v] = count_v + dist[v] = dist_v + pred[v] = [u] + pred_edge[v] = u + + elif dist.get(v) is not None and dist_v == dist.get(v): + pred[v].append(u) + + # successfully found shortest_path. No negative cycles found. + return None + + +@nx._dispatchable(edge_attrs="weight") +def bellman_ford_path(G, source, target, weight="weight"): + """Returns the shortest path from source to target in a weighted graph G. + + Parameters + ---------- + G : NetworkX graph + + source : node + Starting node + + target : node + Ending node + + weight : string or function (default="weight") + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number. + + Returns + ------- + path : list + List of nodes in a shortest path. + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + NetworkXNoPath + If no path exists between source and target. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> nx.bellman_ford_path(G, 0, 4) + [0, 1, 2, 3, 4] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + See Also + -------- + dijkstra_path, bellman_ford_path_length + """ + length, path = single_source_bellman_ford(G, source, target=target, weight=weight) + return path + + +@nx._dispatchable(edge_attrs="weight") +def bellman_ford_path_length(G, source, target, weight="weight"): + """Returns the shortest path length from source to target + in a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + source : node label + starting node for path + + target : node label + ending node for path + + weight : string or function (default="weight") + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number. + + Returns + ------- + length : number + Shortest path length. + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + NetworkXNoPath + If no path exists between source and target. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> nx.bellman_ford_path_length(G, 0, 4) + 4 + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + See Also + -------- + dijkstra_path_length, bellman_ford_path + """ + if source == target: + if source not in G: + raise nx.NodeNotFound(f"Node {source} not found in graph") + return 0 + + weight = _weight_function(G, weight) + + length = _bellman_ford(G, [source], weight, target=target) + + try: + return length[target] + except KeyError as err: + raise nx.NetworkXNoPath(f"node {target} not reachable from {source}") from err + + +@nx._dispatchable(edge_attrs="weight") +def single_source_bellman_ford_path(G, source, weight="weight"): + """Compute shortest path between source and all other reachable + nodes for a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + source : node + Starting node for path. + + weight : string or function (default="weight") + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number. + + Returns + ------- + paths : dictionary + Dictionary of shortest path lengths keyed by target. + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> path = nx.single_source_bellman_ford_path(G, 0) + >>> path[4] + [0, 1, 2, 3, 4] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + See Also + -------- + single_source_dijkstra, single_source_bellman_ford + + """ + (length, path) = single_source_bellman_ford(G, source, weight=weight) + return path + + +@nx._dispatchable(edge_attrs="weight") +def single_source_bellman_ford_path_length(G, source, weight="weight"): + """Compute the shortest path length between source and all other + reachable nodes for a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + source : node label + Starting node for path + + weight : string or function (default="weight") + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number. + + Returns + ------- + length : dictionary + Dictionary of shortest path length keyed by target + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> length = nx.single_source_bellman_ford_path_length(G, 0) + >>> length[4] + 4 + >>> for node in [0, 1, 2, 3, 4]: + ... print(f"{node}: {length[node]}") + 0: 0 + 1: 1 + 2: 2 + 3: 3 + 4: 4 + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + See Also + -------- + single_source_dijkstra, single_source_bellman_ford + + """ + weight = _weight_function(G, weight) + return _bellman_ford(G, [source], weight) + + +@nx._dispatchable(edge_attrs="weight") +def single_source_bellman_ford(G, source, target=None, weight="weight"): + """Compute shortest paths and lengths in a weighted graph G. + + Uses Bellman-Ford algorithm for shortest paths. + + Parameters + ---------- + G : NetworkX graph + + source : node label + Starting node for path + + target : node label, optional + Ending node for path + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number. + + Returns + ------- + distance, path : pair of dictionaries, or numeric and list + If target is None, returns a tuple of two dictionaries keyed by node. + The first dictionary stores distance from one of the source nodes. + The second stores the path from one of the sources to that node. + If target is not None, returns a tuple of (distance, path) where + distance is the distance from source to target and path is a list + representing the path from source to target. + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> length, path = nx.single_source_bellman_ford(G, 0) + >>> length[4] + 4 + >>> for node in [0, 1, 2, 3, 4]: + ... print(f"{node}: {length[node]}") + 0: 0 + 1: 1 + 2: 2 + 3: 3 + 4: 4 + >>> path[4] + [0, 1, 2, 3, 4] + >>> length, path = nx.single_source_bellman_ford(G, 0, 1) + >>> length + 1 + >>> path + [0, 1] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + See Also + -------- + single_source_dijkstra + single_source_bellman_ford_path + single_source_bellman_ford_path_length + """ + if source == target: + if source not in G: + raise nx.NodeNotFound(f"Node {source} is not found in the graph") + return (0, [source]) + + weight = _weight_function(G, weight) + + paths = {source: [source]} # dictionary of paths + dist = _bellman_ford(G, [source], weight, paths=paths, target=target) + if target is None: + return (dist, paths) + try: + return (dist[target], paths[target]) + except KeyError as err: + msg = f"Node {target} not reachable from {source}" + raise nx.NetworkXNoPath(msg) from err + + +@nx._dispatchable(edge_attrs="weight") +def all_pairs_bellman_ford_path_length(G, weight="weight"): + """Compute shortest path lengths between all nodes in a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + weight : string or function (default="weight") + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number. + + Returns + ------- + distance : iterator + (source, dictionary) iterator with dictionary keyed by target and + shortest path length as the key value. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> length = dict(nx.all_pairs_bellman_ford_path_length(G)) + >>> for node in [0, 1, 2, 3, 4]: + ... print(f"1 - {node}: {length[1][node]}") + 1 - 0: 1 + 1 - 1: 0 + 1 - 2: 1 + 1 - 3: 2 + 1 - 4: 3 + >>> length[3][2] + 1 + >>> length[2][2] + 0 + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The dictionary returned only has keys for reachable node pairs. + """ + length = single_source_bellman_ford_path_length + for n in G: + yield (n, dict(length(G, n, weight=weight))) + + +@nx._dispatchable(edge_attrs="weight") +def all_pairs_bellman_ford_path(G, weight="weight"): + """Compute shortest paths between all nodes in a weighted graph. + + Parameters + ---------- + G : NetworkX graph + + weight : string or function (default="weight") + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number. + + Returns + ------- + paths : iterator + (source, dictionary) iterator with dictionary keyed by target and + shortest path as the key value. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> path = dict(nx.all_pairs_bellman_ford_path(G)) + >>> path[0][4] + [0, 1, 2, 3, 4] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + See Also + -------- + floyd_warshall, all_pairs_dijkstra_path + + """ + path = single_source_bellman_ford_path + for n in G: + yield (n, path(G, n, weight=weight)) + + +@nx._dispatchable(edge_attrs="weight") +def goldberg_radzik(G, source, weight="weight"): + """Compute shortest path lengths and predecessors on shortest paths + in weighted graphs. + + The algorithm has a running time of $O(mn)$ where $n$ is the number of + nodes and $m$ is the number of edges. It is slower than Dijkstra but + can handle negative edge weights. + + Parameters + ---------- + G : NetworkX graph + The algorithm works for all types of graphs, including directed + graphs and multigraphs. + + source: node label + Starting node for path + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number. + + Returns + ------- + pred, dist : dictionaries + Returns two dictionaries keyed by node to predecessor in the + path and to the distance from the source respectively. + + Raises + ------ + NodeNotFound + If `source` is not in `G`. + + NetworkXUnbounded + If the (di)graph contains a negative (di)cycle, the + algorithm raises an exception to indicate the presence of the + negative (di)cycle. Note: any negative weight edge in an + undirected graph is a negative cycle. + + As of NetworkX v3.2, a zero weight cycle is no longer + incorrectly reported as a negative weight cycle. + + + Examples + -------- + >>> G = nx.path_graph(5, create_using=nx.DiGraph()) + >>> pred, dist = nx.goldberg_radzik(G, 0) + >>> sorted(pred.items()) + [(0, None), (1, 0), (2, 1), (3, 2), (4, 3)] + >>> sorted(dist.items()) + [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)] + + >>> G = nx.cycle_graph(5, create_using=nx.DiGraph()) + >>> G[1][2]["weight"] = -7 + >>> nx.goldberg_radzik(G, 0) + Traceback (most recent call last): + ... + networkx.exception.NetworkXUnbounded: Negative cycle detected. + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The dictionaries returned only have keys for nodes reachable from + the source. + + In the case where the (di)graph is not connected, if a component + not containing the source contains a negative (di)cycle, it + will not be detected. + + """ + if source not in G: + raise nx.NodeNotFound(f"Node {source} is not found in the graph") + weight = _weight_function(G, weight) + if G.is_multigraph(): + if any( + weight(u, v, {k: d}) < 0 + for u, v, k, d in nx.selfloop_edges(G, keys=True, data=True) + ): + raise nx.NetworkXUnbounded("Negative cycle detected.") + else: + if any(weight(u, v, d) < 0 for u, v, d in nx.selfloop_edges(G, data=True)): + raise nx.NetworkXUnbounded("Negative cycle detected.") + + if len(G) == 1: + return {source: None}, {source: 0} + + G_succ = G._adj # For speed-up (and works for both directed and undirected graphs) + + inf = float("inf") + d = {u: inf for u in G} + d[source] = 0 + pred = {source: None} + + def topo_sort(relabeled): + """Topologically sort nodes relabeled in the previous round and detect + negative cycles. + """ + # List of nodes to scan in this round. Denoted by A in Goldberg and + # Radzik's paper. + to_scan = [] + # In the DFS in the loop below, neg_count records for each node the + # number of edges of negative reduced costs on the path from a DFS root + # to the node in the DFS forest. The reduced cost of an edge (u, v) is + # defined as d[u] + weight[u][v] - d[v]. + # + # neg_count also doubles as the DFS visit marker array. + neg_count = {} + for u in relabeled: + # Skip visited nodes. + if u in neg_count: + continue + d_u = d[u] + # Skip nodes without out-edges of negative reduced costs. + if all(d_u + weight(u, v, e) >= d[v] for v, e in G_succ[u].items()): + continue + # Nonrecursive DFS that inserts nodes reachable from u via edges of + # nonpositive reduced costs into to_scan in (reverse) topological + # order. + stack = [(u, iter(G_succ[u].items()))] + in_stack = {u} + neg_count[u] = 0 + while stack: + u, it = stack[-1] + try: + v, e = next(it) + except StopIteration: + to_scan.append(u) + stack.pop() + in_stack.remove(u) + continue + t = d[u] + weight(u, v, e) + d_v = d[v] + if t < d_v: + is_neg = t < d_v + d[v] = t + pred[v] = u + if v not in neg_count: + neg_count[v] = neg_count[u] + int(is_neg) + stack.append((v, iter(G_succ[v].items()))) + in_stack.add(v) + elif v in in_stack and neg_count[u] + int(is_neg) > neg_count[v]: + # (u, v) is a back edge, and the cycle formed by the + # path v to u and (u, v) contains at least one edge of + # negative reduced cost. The cycle must be of negative + # cost. + raise nx.NetworkXUnbounded("Negative cycle detected.") + to_scan.reverse() + return to_scan + + def relax(to_scan): + """Relax out-edges of relabeled nodes.""" + relabeled = set() + # Scan nodes in to_scan in topological order and relax incident + # out-edges. Add the relabled nodes to labeled. + for u in to_scan: + d_u = d[u] + for v, e in G_succ[u].items(): + w_e = weight(u, v, e) + if d_u + w_e < d[v]: + d[v] = d_u + w_e + pred[v] = u + relabeled.add(v) + return relabeled + + # Set of nodes relabled in the last round of scan operations. Denoted by B + # in Goldberg and Radzik's paper. + relabeled = {source} + + while relabeled: + to_scan = topo_sort(relabeled) + relabeled = relax(to_scan) + + d = {u: d[u] for u in pred} + return pred, d + + +@nx._dispatchable(edge_attrs="weight") +def negative_edge_cycle(G, weight="weight", heuristic=True): + """Returns True if there exists a negative edge cycle anywhere in G. + + Parameters + ---------- + G : NetworkX graph + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number. + + heuristic : bool + Determines whether to use a heuristic to early detect negative + cycles at a negligible cost. In case of graphs with a negative cycle, + the performance of detection increases by at least an order of magnitude. + + Returns + ------- + negative_cycle : bool + True if a negative edge cycle exists, otherwise False. + + Examples + -------- + >>> G = nx.cycle_graph(5, create_using=nx.DiGraph()) + >>> print(nx.negative_edge_cycle(G)) + False + >>> G[1][2]["weight"] = -7 + >>> print(nx.negative_edge_cycle(G)) + True + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + This algorithm uses bellman_ford_predecessor_and_distance() but finds + negative cycles on any component by first adding a new node connected to + every node, and starting bellman_ford_predecessor_and_distance on that + node. It then removes that extra node. + """ + if G.size() == 0: + return False + + # find unused node to use temporarily + newnode = -1 + while newnode in G: + newnode -= 1 + # connect it to all nodes + G.add_edges_from([(newnode, n) for n in G]) + + try: + bellman_ford_predecessor_and_distance( + G, newnode, weight=weight, heuristic=heuristic + ) + except nx.NetworkXUnbounded: + return True + finally: + G.remove_node(newnode) + return False + + +@nx._dispatchable(edge_attrs="weight") +def find_negative_cycle(G, source, weight="weight"): + """Returns a cycle with negative total weight if it exists. + + Bellman-Ford is used to find shortest_paths. That algorithm + stops if there exists a negative cycle. This algorithm + picks up from there and returns the found negative cycle. + + The cycle consists of a list of nodes in the cycle order. The last + node equals the first to make it a cycle. + You can look up the edge weights in the original graph. In the case + of multigraphs the relevant edge is the minimal weight edge between + the nodes in the 2-tuple. + + If the graph has no negative cycle, a NetworkXError is raised. + + Parameters + ---------- + G : NetworkX graph + + source: node label + The search for the negative cycle will start from this node. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number. + + Examples + -------- + >>> G = nx.DiGraph() + >>> G.add_weighted_edges_from( + ... [(0, 1, 2), (1, 2, 2), (2, 0, 1), (1, 4, 2), (4, 0, -5)] + ... ) + >>> nx.find_negative_cycle(G, 0) + [4, 0, 1, 4] + + Returns + ------- + cycle : list + A list of nodes in the order of the cycle found. The last node + equals the first to indicate a cycle. + + Raises + ------ + NetworkXError + If no negative cycle is found. + """ + weight = _weight_function(G, weight) + pred = {source: []} + + v = _inner_bellman_ford(G, [source], weight, pred=pred) + if v is None: + raise nx.NetworkXError("No negative cycles detected.") + + # negative cycle detected... find it + neg_cycle = [] + stack = [(v, list(pred[v]))] + seen = {v} + while stack: + node, preds = stack[-1] + if v in preds: + # found the cycle + neg_cycle.extend([node, v]) + neg_cycle = list(reversed(neg_cycle)) + return neg_cycle + + if preds: + nbr = preds.pop() + if nbr not in seen: + stack.append((nbr, list(pred[nbr]))) + neg_cycle.append(node) + seen.add(nbr) + else: + stack.pop() + if neg_cycle: + neg_cycle.pop() + else: + if v in G[v] and weight(G, v, v) < 0: + return [v, v] + # should not reach here + raise nx.NetworkXError("Negative cycle is detected but not found") + # should not get here... + msg = "negative cycle detected but not identified" + raise nx.NetworkXUnbounded(msg) + + +@nx._dispatchable(edge_attrs="weight") +def bidirectional_dijkstra(G, source, target, weight="weight"): + r"""Dijkstra's algorithm for shortest paths using bidirectional search. + + Parameters + ---------- + G : NetworkX graph + + source : node + Starting node. + + target : node + Ending node. + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number or None to indicate a hidden edge. + + Returns + ------- + length, path : number and list + length is the distance from source to target. + path is a list of nodes on a path from source to target. + + Raises + ------ + NodeNotFound + If `source` or `target` is not in `G`. + + NetworkXNoPath + If no path exists between source and target. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> length, path = nx.bidirectional_dijkstra(G, 0, 4) + >>> print(length) + 4 + >>> print(path) + [0, 1, 2, 3, 4] + + Notes + ----- + Edge weight attributes must be numerical. + Distances are calculated as sums of weighted edges traversed. + + The weight function can be used to hide edges by returning None. + So ``weight = lambda u, v, d: 1 if d['color']=="red" else None`` + will find the shortest red path. + + In practice bidirectional Dijkstra is much more than twice as fast as + ordinary Dijkstra. + + Ordinary Dijkstra expands nodes in a sphere-like manner from the + source. The radius of this sphere will eventually be the length + of the shortest path. Bidirectional Dijkstra will expand nodes + from both the source and the target, making two spheres of half + this radius. Volume of the first sphere is `\pi*r*r` while the + others are `2*\pi*r/2*r/2`, making up half the volume. + + This algorithm is not guaranteed to work if edge weights + are negative or are floating point numbers + (overflows and roundoff errors can cause problems). + + See Also + -------- + shortest_path + shortest_path_length + """ + if source not in G: + raise nx.NodeNotFound(f"Source {source} is not in G") + + if target not in G: + raise nx.NodeNotFound(f"Target {target} is not in G") + + if source == target: + return (0, [source]) + + weight = _weight_function(G, weight) + push = heappush + pop = heappop + # Init: [Forward, Backward] + dists = [{}, {}] # dictionary of final distances + paths = [{source: [source]}, {target: [target]}] # dictionary of paths + fringe = [[], []] # heap of (distance, node) for choosing node to expand + seen = [{source: 0}, {target: 0}] # dict of distances to seen nodes + c = count() + # initialize fringe heap + push(fringe[0], (0, next(c), source)) + push(fringe[1], (0, next(c), target)) + # neighs for extracting correct neighbor information + if G.is_directed(): + neighs = [G._succ, G._pred] + else: + neighs = [G._adj, G._adj] + # variables to hold shortest discovered path + # finaldist = 1e30000 + finalpath = [] + dir = 1 + while fringe[0] and fringe[1]: + # choose direction + # dir == 0 is forward direction and dir == 1 is back + dir = 1 - dir + # extract closest to expand + (dist, _, v) = pop(fringe[dir]) + if v in dists[dir]: + # Shortest path to v has already been found + continue + # update distance + dists[dir][v] = dist # equal to seen[dir][v] + if v in dists[1 - dir]: + # if we have scanned v in both directions we are done + # we have now discovered the shortest path + return (finaldist, finalpath) + + for w, d in neighs[dir][v].items(): + # weight(v, w, d) for forward and weight(w, v, d) for back direction + cost = weight(v, w, d) if dir == 0 else weight(w, v, d) + if cost is None: + continue + vwLength = dists[dir][v] + cost + if w in dists[dir]: + if vwLength < dists[dir][w]: + raise ValueError("Contradictory paths found: negative weights?") + elif w not in seen[dir] or vwLength < seen[dir][w]: + # relaxing + seen[dir][w] = vwLength + push(fringe[dir], (vwLength, next(c), w)) + paths[dir][w] = paths[dir][v] + [w] + if w in seen[0] and w in seen[1]: + # see if this path is better than the already + # discovered shortest path + totaldist = seen[0][w] + seen[1][w] + if finalpath == [] or finaldist > totaldist: + finaldist = totaldist + revpath = paths[1][w][:] + revpath.reverse() + finalpath = paths[0][w] + revpath[1:] + raise nx.NetworkXNoPath(f"No path between {source} and {target}.") + + +@nx._dispatchable(edge_attrs="weight") +def johnson(G, weight="weight"): + r"""Uses Johnson's Algorithm to compute shortest paths. + + Johnson's Algorithm finds a shortest path between each pair of + nodes in a weighted graph even if negative weights are present. + + Parameters + ---------- + G : NetworkX graph + + weight : string or function + If this is a string, then edge weights will be accessed via the + edge attribute with this key (that is, the weight of the edge + joining `u` to `v` will be ``G.edges[u, v][weight]``). If no + such edge attribute exists, the weight of the edge is assumed to + be one. + + If this is a function, the weight of an edge is the value + returned by the function. The function must accept exactly three + positional arguments: the two endpoints of an edge and the + dictionary of edge attributes for that edge. The function must + return a number. + + Returns + ------- + distance : dictionary + Dictionary, keyed by source and target, of shortest paths. + + Examples + -------- + >>> graph = nx.DiGraph() + >>> graph.add_weighted_edges_from( + ... [("0", "3", 3), ("0", "1", -5), ("0", "2", 2), ("1", "2", 4), ("2", "3", 1)] + ... ) + >>> paths = nx.johnson(graph, weight="weight") + >>> paths["0"]["2"] + ['0', '1', '2'] + + Notes + ----- + Johnson's algorithm is suitable even for graphs with negative weights. It + works by using the Bellman–Ford algorithm to compute a transformation of + the input graph that removes all negative weights, allowing Dijkstra's + algorithm to be used on the transformed graph. + + The time complexity of this algorithm is $O(n^2 \log n + n m)$, + where $n$ is the number of nodes and $m$ the number of edges in the + graph. For dense graphs, this may be faster than the Floyd–Warshall + algorithm. + + See Also + -------- + floyd_warshall_predecessor_and_distance + floyd_warshall_numpy + all_pairs_shortest_path + all_pairs_shortest_path_length + all_pairs_dijkstra_path + bellman_ford_predecessor_and_distance + all_pairs_bellman_ford_path + all_pairs_bellman_ford_path_length + + """ + dist = {v: 0 for v in G} + pred = {v: [] for v in G} + weight = _weight_function(G, weight) + + # Calculate distance of shortest paths + dist_bellman = _bellman_ford(G, list(G), weight, pred=pred, dist=dist) + + # Update the weight function to take into account the Bellman--Ford + # relaxation distances. + def new_weight(u, v, d): + return weight(u, v, d) + dist_bellman[u] - dist_bellman[v] + + def dist_path(v): + paths = {v: [v]} + _dijkstra(G, v, new_weight, paths=paths) + return paths + + return {v: dist_path(v) for v in G} diff --git a/wemm/lib/python3.10/site-packages/networkx/algorithms/smetric.py b/wemm/lib/python3.10/site-packages/networkx/algorithms/smetric.py new file mode 100644 index 0000000000000000000000000000000000000000..d985aa805b4fb21300680afe389aae4732793a73 --- /dev/null +++ b/wemm/lib/python3.10/site-packages/networkx/algorithms/smetric.py @@ -0,0 +1,30 @@ +import networkx as nx + +__all__ = ["s_metric"] + + +@nx._dispatchable +def s_metric(G): + """Returns the s-metric [1]_ of graph. + + The s-metric is defined as the sum of the products ``deg(u) * deg(v)`` + for every edge ``(u, v)`` in `G`. + + Parameters + ---------- + G : graph + The graph used to compute the s-metric. + + Returns + ------- + s : float + The s-metric of the graph. + + References + ---------- + .. [1] Lun Li, David Alderson, John C. Doyle, and Walter Willinger, + Towards a Theory of Scale-Free Graphs: + Definition, Properties, and Implications (Extended Version), 2005. + https://arxiv.org/abs/cond-mat/0501169 + """ + return float(sum(G.degree(u) * G.degree(v) for (u, v) in G.edges())) diff --git a/wemm/lib/python3.10/site-packages/pillow.libs/libwebpdemux-e5426797.so.2.0.16 b/wemm/lib/python3.10/site-packages/pillow.libs/libwebpdemux-e5426797.so.2.0.16 new file mode 100644 index 0000000000000000000000000000000000000000..cbc1295264df9937063b0bd4ac00ab2f97c344a1 Binary files /dev/null and b/wemm/lib/python3.10/site-packages/pillow.libs/libwebpdemux-e5426797.so.2.0.16 differ