diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/__init__.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..7839db96a712bd5db28c29112ac20864c15d9539 --- /dev/null +++ b/.venv/lib/python3.11/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 * 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import connected_components +from networkx.exception import AmbiguousSolution + +__all__ = [ + "is_bipartite", + "is_bipartite_node_set", + "color", + "sets", + "density", + "degrees", +] + + +@nx._dispatchable +def color(G): + """Returns a two-coloring of the graph. + + Raises an exception if the graph is not bipartite. + + Parameters + ---------- + G : NetworkX graph + + Returns + ------- + color : dictionary + A dictionary keyed by node with a 1 or 0 as data for each node color. + + Raises + ------ + NetworkXError + If the graph is not two-colorable. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> G = nx.path_graph(4) + >>> c = bipartite.color(G) + >>> print(c) + {0: 1, 1: 0, 2: 1, 3: 0} + + You can use this to set a node attribute indicating the bipartite set: + + >>> nx.set_node_attributes(G, c, "bipartite") + >>> print(G.nodes[0]["bipartite"]) + 1 + >>> print(G.nodes[1]["bipartite"]) + 0 + """ + if G.is_directed(): + import itertools + + def neighbors(v): + return itertools.chain.from_iterable([G.predecessors(v), G.successors(v)]) + + else: + neighbors = G.neighbors + + color = {} + for n in G: # handle disconnected graphs + if n in color or len(G[n]) == 0: # skip isolates + continue + queue = [n] + color[n] = 1 # nodes seen with color (1 or 0) + while queue: + v = queue.pop() + c = 1 - color[v] # opposite color of node v + for w in neighbors(v): + if w in color: + if color[w] == color[v]: + raise nx.NetworkXError("Graph is not bipartite.") + else: + color[w] = c + queue.append(w) + # color isolates with 0 + color.update(dict.fromkeys(nx.isolates(G), 0)) + return color + + +@nx._dispatchable +def is_bipartite(G): + """Returns True if graph G is bipartite, False if not. + + Parameters + ---------- + G : NetworkX graph + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> G = nx.path_graph(4) + >>> print(bipartite.is_bipartite(G)) + True + + See Also + -------- + color, is_bipartite_node_set + """ + try: + color(G) + return True + except nx.NetworkXError: + return False + + +@nx._dispatchable +def is_bipartite_node_set(G, nodes): + """Returns True if nodes and G/nodes are a bipartition of G. + + Parameters + ---------- + G : NetworkX graph + + nodes: list or container + Check if nodes are a one of a bipartite set. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> G = nx.path_graph(4) + >>> X = set([1, 3]) + >>> bipartite.is_bipartite_node_set(G, X) + True + + Notes + ----- + An exception is raised if the input nodes are not distinct, because in this + case some bipartite algorithms will yield incorrect results. + For connected graphs the bipartite sets are unique. This function handles + disconnected graphs. + """ + S = set(nodes) + + if len(S) < len(nodes): + # this should maybe just return False? + raise AmbiguousSolution( + "The input node set contains duplicates.\n" + "This may lead to incorrect results when using it in bipartite algorithms.\n" + "Consider using set(nodes) as the input" + ) + + for CC in (G.subgraph(c).copy() for c in connected_components(G)): + X, Y = sets(CC) + if not ( + (X.issubset(S) and Y.isdisjoint(S)) or (Y.issubset(S) and X.isdisjoint(S)) + ): + return False + return True + + +@nx._dispatchable +def sets(G, top_nodes=None): + """Returns bipartite node sets of graph G. + + Raises an exception if the graph is not bipartite or if the input + graph is disconnected and thus more than one valid solution exists. + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + Parameters + ---------- + G : NetworkX graph + + top_nodes : container, optional + Container with all nodes in one bipartite node set. If not supplied + it will be computed. But if more than one solution exists an exception + will be raised. + + Returns + ------- + X : set + Nodes from one side of the bipartite graph. + Y : set + Nodes from the other side. + + Raises + ------ + AmbiguousSolution + Raised if the input bipartite graph is disconnected and no container + with all nodes in one bipartite set is provided. When determining + the nodes in each bipartite set more than one valid solution is + possible if the input graph is disconnected. + NetworkXError + Raised if the input graph is not bipartite. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> G = nx.path_graph(4) + >>> X, Y = bipartite.sets(G) + >>> list(X) + [0, 2] + >>> list(Y) + [1, 3] + + See Also + -------- + color + + """ + if G.is_directed(): + is_connected = nx.is_weakly_connected + else: + is_connected = nx.is_connected + if top_nodes is not None: + X = set(top_nodes) + Y = set(G) - X + else: + if not is_connected(G): + msg = "Disconnected graph: Ambiguous solution for bipartite sets." + raise nx.AmbiguousSolution(msg) + c = color(G) + X = {n for n, is_top in c.items() if is_top} + Y = {n for n, is_top in c.items() if not is_top} + return (X, Y) + + +@nx._dispatchable(graphs="B") +def density(B, nodes): + """Returns density of bipartite graph B. + + Parameters + ---------- + B : NetworkX graph + + nodes: list or container + Nodes in one node set of the bipartite graph. + + Returns + ------- + d : float + The bipartite density + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> G = nx.complete_bipartite_graph(3, 2) + >>> X = set([0, 1, 2]) + >>> bipartite.density(G, X) + 1.0 + >>> Y = set([3, 4]) + >>> bipartite.density(G, Y) + 1.0 + + Notes + ----- + The container of nodes passed as argument must contain all nodes + in one of the two bipartite node sets to avoid ambiguity in the + case of disconnected graphs. + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + See Also + -------- + color + """ + n = len(B) + m = nx.number_of_edges(B) + nb = len(nodes) + nt = n - nb + if m == 0: # includes cases n==0 and n==1 + d = 0.0 + else: + if B.is_directed(): + d = m / (2 * nb * nt) + else: + d = m / (nb * nt) + return d + + +@nx._dispatchable(graphs="B", edge_attrs="weight") +def degrees(B, nodes, weight=None): + """Returns the degrees of the two node sets in the bipartite graph B. + + Parameters + ---------- + B : NetworkX graph + + nodes: list or container + Nodes in one node set of the bipartite graph. + + weight : string or None, optional (default=None) + The edge attribute that holds the numerical value used as a weight. + If None, then each edge has weight 1. + The degree is the sum of the edge weights adjacent to the node. + + Returns + ------- + (degX,degY) : tuple of dictionaries + The degrees of the two bipartite sets as dictionaries keyed by node. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> G = nx.complete_bipartite_graph(3, 2) + >>> Y = set([3, 4]) + >>> degX, degY = bipartite.degrees(G, Y) + >>> dict(degX) + {0: 2, 1: 2, 2: 2} + + Notes + ----- + The container of nodes passed as argument must contain all nodes + in one of the two bipartite node sets to avoid ambiguity in the + case of disconnected graphs. + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + See Also + -------- + color, density + """ + bottom = set(nodes) + top = set(B) - bottom + return (B.degree(top, weight), B.degree(bottom, weight)) diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/centrality.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/centrality.py new file mode 100644 index 0000000000000000000000000000000000000000..42d7270ee7d0bb18b56a55dc4c17dc19f5dc77a7 --- /dev/null +++ b/.venv/lib/python3.11/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/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/cluster.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/cluster.py new file mode 100644 index 0000000000000000000000000000000000000000..5b66b2802c97b44d956b158656cb58f22429b789 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/cluster.py @@ -0,0 +1,278 @@ +"""Functions for computing clustering of pairs""" + +import itertools + +import networkx as nx + +__all__ = [ + "clustering", + "average_clustering", + "latapy_clustering", + "robins_alexander_clustering", +] + + +def cc_dot(nu, nv): + return len(nu & nv) / len(nu | nv) + + +def cc_max(nu, nv): + return len(nu & nv) / max(len(nu), len(nv)) + + +def cc_min(nu, nv): + return len(nu & nv) / min(len(nu), len(nv)) + + +modes = {"dot": cc_dot, "min": cc_min, "max": cc_max} + + +@nx._dispatchable +def latapy_clustering(G, nodes=None, mode="dot"): + r"""Compute a bipartite clustering coefficient for nodes. + + The bipartite clustering coefficient is a measure of local density + of connections defined as [1]_: + + .. math:: + + c_u = \frac{\sum_{v \in N(N(u))} c_{uv} }{|N(N(u))|} + + where `N(N(u))` are the second order neighbors of `u` in `G` excluding `u`, + and `c_{uv}` is the pairwise clustering coefficient between nodes + `u` and `v`. + + The mode selects the function for `c_{uv}` which can be: + + `dot`: + + .. math:: + + c_{uv}=\frac{|N(u)\cap N(v)|}{|N(u) \cup N(v)|} + + `min`: + + .. math:: + + c_{uv}=\frac{|N(u)\cap N(v)|}{min(|N(u)|,|N(v)|)} + + `max`: + + .. math:: + + c_{uv}=\frac{|N(u)\cap N(v)|}{max(|N(u)|,|N(v)|)} + + + Parameters + ---------- + G : graph + A bipartite graph + + nodes : list or iterable (optional) + Compute bipartite clustering for these nodes. The default + is all nodes in G. + + mode : string + The pairwise bipartite clustering method to be used in the computation. + It must be "dot", "max", or "min". + + Returns + ------- + clustering : dictionary + A dictionary keyed by node with the clustering coefficient value. + + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> G = nx.path_graph(4) # path graphs are bipartite + >>> c = bipartite.clustering(G) + >>> c[0] + 0.5 + >>> c = bipartite.clustering(G, mode="min") + >>> c[0] + 1.0 + + See Also + -------- + robins_alexander_clustering + average_clustering + networkx.algorithms.cluster.square_clustering + + 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 not nx.algorithms.bipartite.is_bipartite(G): + raise nx.NetworkXError("Graph is not bipartite") + + try: + cc_func = modes[mode] + except KeyError as err: + raise nx.NetworkXError( + "Mode for bipartite clustering must be: dot, min or max" + ) from err + + if nodes is None: + nodes = G + ccs = {} + for v in nodes: + cc = 0.0 + nbrs2 = {u for nbr in G[v] for u in G[nbr]} - {v} + for u in nbrs2: + cc += cc_func(set(G[u]), set(G[v])) + if cc > 0.0: # len(nbrs2)>0 + cc /= len(nbrs2) + ccs[v] = cc + return ccs + + +clustering = latapy_clustering + + +@nx._dispatchable(name="bipartite_average_clustering") +def average_clustering(G, nodes=None, mode="dot"): + r"""Compute the average bipartite clustering coefficient. + + A clustering coefficient for the whole graph is the average, + + .. math:: + + C = \frac{1}{n}\sum_{v \in G} c_v, + + where `n` is the number of nodes in `G`. + + Similar measures for the two bipartite sets can be defined [1]_ + + .. math:: + + C_X = \frac{1}{|X|}\sum_{v \in X} c_v, + + where `X` is a bipartite set of `G`. + + Parameters + ---------- + G : graph + a bipartite graph + + nodes : list or iterable, optional + A container of nodes to use in computing the average. + The nodes should be either the entire graph (the default) or one of the + bipartite sets. + + mode : string + The pairwise bipartite clustering method. + It must be "dot", "max", or "min" + + Returns + ------- + clustering : float + The average bipartite clustering for the given set of nodes or the + entire graph if no nodes are specified. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> G = nx.star_graph(3) # star graphs are bipartite + >>> bipartite.average_clustering(G) + 0.75 + >>> X, Y = bipartite.sets(G) + >>> bipartite.average_clustering(G, X) + 0.0 + >>> bipartite.average_clustering(G, Y) + 1.0 + + See Also + -------- + clustering + + Notes + ----- + The container of nodes passed to this function must contain all of the nodes + in one of the bipartite sets ("top" or "bottom") in order to compute + the correct average bipartite clustering coefficients. + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + + 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 + ccs = latapy_clustering(G, nodes=nodes, mode=mode) + return sum(ccs[v] for v in nodes) / len(nodes) + + +@nx._dispatchable +def robins_alexander_clustering(G): + r"""Compute the bipartite clustering of G. + + Robins and Alexander [1]_ defined bipartite clustering coefficient as + four times the number of four cycles `C_4` divided by the number of + three paths `L_3` in a bipartite graph: + + .. math:: + + CC_4 = \frac{4 * C_4}{L_3} + + Parameters + ---------- + G : graph + a bipartite graph + + Returns + ------- + clustering : float + The Robins and Alexander bipartite clustering for the input graph. + + Examples + -------- + >>> from networkx.algorithms import bipartite + >>> G = nx.davis_southern_women_graph() + >>> print(round(bipartite.robins_alexander_clustering(G), 3)) + 0.468 + + See Also + -------- + latapy_clustering + networkx.algorithms.cluster.square_clustering + + References + ---------- + .. [1] Robins, G. and M. Alexander (2004). Small worlds among interlocking + directors: Network structure and distance in bipartite graphs. + Computational & Mathematical Organization Theory 10(1), 69–94. + + """ + if G.order() < 4 or G.size() < 3: + return 0 + L_3 = _threepaths(G) + if L_3 == 0: + return 0 + C_4 = _four_cycles(G) + return (4.0 * C_4) / L_3 + + +def _four_cycles(G): + cycles = 0 + for v in G: + for u, w in itertools.combinations(G[v], 2): + cycles += len((set(G[u]) & set(G[w])) - {v}) + return cycles / 4 + + +def _threepaths(G): + paths = 0 + for v in G: + for u in G[v]: + for w in set(G[u]) - {v}: + paths += len(set(G[w]) - {v, u}) + # Divide by two because we count each three path twice + # one for each possible starting point + return paths / 2 diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/covering.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/covering.py new file mode 100644 index 0000000000000000000000000000000000000000..f937903e5576ec7313a774863c8470a4a271a252 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/covering.py @@ -0,0 +1,57 @@ +"""Functions related to graph covers.""" + +import networkx as nx +from networkx.algorithms.bipartite.matching import hopcroft_karp_matching +from networkx.algorithms.covering import min_edge_cover as _min_edge_cover +from networkx.utils import not_implemented_for + +__all__ = ["min_edge_cover"] + + +@not_implemented_for("directed") +@not_implemented_for("multigraph") +@nx._dispatchable(name="bipartite_min_edge_cover") +def min_edge_cover(G, matching_algorithm=None): + """Returns a set of edges which constitutes + the minimum edge cover of the graph. + + The smallest edge cover can be found in polynomial time by finding + a maximum matching and extending it greedily so that all nodes + are covered. + + Parameters + ---------- + G : NetworkX graph + An undirected bipartite graph. + + matching_algorithm : function + A function that returns a maximum cardinality matching in a + given bipartite graph. The function must take one input, the + graph ``G``, and return a dictionary mapping each node to its + mate. If not specified, + :func:`~networkx.algorithms.bipartite.matching.hopcroft_karp_matching` + will be used. Other possibilities include + :func:`~networkx.algorithms.bipartite.matching.eppstein_matching`, + + Returns + ------- + set + A set of the edges in a minimum edge cover of the graph, given as + pairs of nodes. It contains both the edges `(u, v)` and `(v, u)` + for given nodes `u` and `v` among the edges of minimum edge cover. + + Notes + ----- + An edge cover of a graph is a set of edges such that every node of + the graph is incident to at least one edge of the set. + A minimum edge cover is an edge covering of smallest cardinality. + + Due to its implementation, the worst-case running time of this algorithm + is bounded by the worst-case running time of the function + ``matching_algorithm``. + """ + if G.order() == 0: # Special case for the empty graph + return set() + if matching_algorithm is None: + matching_algorithm = hopcroft_karp_matching + return _min_edge_cover(G, matching_algorithm=matching_algorithm) diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/edgelist.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/edgelist.py new file mode 100644 index 0000000000000000000000000000000000000000..db6ef9d8e2773de9ec698db151661fac28adc326 --- /dev/null +++ b/.venv/lib/python3.11/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/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/extendability.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/extendability.py new file mode 100644 index 0000000000000000000000000000000000000000..61d8d067d9792659ed7097340c5ece28d9dc2e8c --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/extendability.py @@ -0,0 +1,105 @@ +"""Provides a function for computing the extendability of a graph which is +undirected, simple, connected and bipartite and contains at least one perfect matching.""" + +import networkx as nx +from networkx.utils import not_implemented_for + +__all__ = ["maximal_extendability"] + + +@not_implemented_for("directed") +@not_implemented_for("multigraph") +@nx._dispatchable +def maximal_extendability(G): + """Computes the extendability of a graph. + + The extendability of a graph is defined as the maximum $k$ for which `G` + is $k$-extendable. Graph `G` is $k$-extendable if and only if `G` has a + perfect matching and every set of $k$ independent edges can be extended + to a perfect matching in `G`. + + Parameters + ---------- + G : NetworkX Graph + A fully-connected bipartite graph without self-loops + + Returns + ------- + extendability : int + + Raises + ------ + NetworkXError + If the graph `G` is disconnected. + If the graph `G` is not bipartite. + If the graph `G` does not contain a perfect matching. + If the residual graph of `G` is not strongly connected. + + Notes + ----- + Definition: + Let `G` be a simple, connected, undirected and bipartite graph with a perfect + matching M and bipartition (U,V). The residual graph of `G`, denoted by $G_M$, + is the graph obtained from G by directing the edges of M from V to U and the + edges that do not belong to M from U to V. + + Lemma [1]_ : + Let M be a perfect matching of `G`. `G` is $k$-extendable if and only if its residual + graph $G_M$ is strongly connected and there are $k$ vertex-disjoint directed + paths between every vertex of U and every vertex of V. + + Assuming that input graph `G` is undirected, simple, connected, bipartite and contains + a perfect matching M, this function constructs the residual graph $G_M$ of G and + returns the minimum value among the maximum vertex-disjoint directed paths between + every vertex of U and every vertex of V in $G_M$. By combining the definitions + and the lemma, this value represents the extendability of the graph `G`. + + Time complexity O($n^3$ $m^2$)) where $n$ is the number of vertices + and $m$ is the number of edges. + + References + ---------- + .. [1] "A polynomial algorithm for the extendability problem in bipartite graphs", + J. Lakhal, L. Litzler, Information Processing Letters, 1998. + .. [2] "On n-extendible graphs", M. D. Plummer, Discrete Mathematics, 31:201–210, 1980 + https://doi.org/10.1016/0012-365X(80)90037-0 + + """ + if not nx.is_connected(G): + raise nx.NetworkXError("Graph G is not connected") + + if not nx.bipartite.is_bipartite(G): + raise nx.NetworkXError("Graph G is not bipartite") + + U, V = nx.bipartite.sets(G) + + maximum_matching = nx.bipartite.hopcroft_karp_matching(G) + + if not nx.is_perfect_matching(G, maximum_matching): + raise nx.NetworkXError("Graph G does not contain a perfect matching") + + # list of edges in perfect matching, directed from V to U + pm = [(node, maximum_matching[node]) for node in V & maximum_matching.keys()] + + # Direct all the edges of G, from V to U if in matching, else from U to V + directed_edges = [ + (x, y) if (x in V and (x, y) in pm) or (x in U and (y, x) not in pm) else (y, x) + for x, y in G.edges + ] + + # Construct the residual graph of G + residual_G = nx.DiGraph() + residual_G.add_nodes_from(G) + residual_G.add_edges_from(directed_edges) + + if not nx.is_strongly_connected(residual_G): + raise nx.NetworkXError("The residual graph of G is not strongly connected") + + # For node-pairs between V & U, keep min of max number of node-disjoint paths + # Variable $k$ stands for the extendability of graph G + k = float("inf") + for u in U: + for v in V: + num_paths = sum(1 for _ in nx.node_disjoint_paths(residual_G, u, v)) + k = k if k < num_paths else num_paths + return k diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/generators.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/generators.py new file mode 100644 index 0000000000000000000000000000000000000000..e8428f6bc77c4ec550f495477f7429b43129226d --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/generators.py @@ -0,0 +1,604 @@ +""" +Generators and functions for bipartite graphs. +""" + +import math +import numbers +from functools import reduce + +import networkx as nx +from networkx.utils import nodes_or_number, py_random_state + +__all__ = [ + "configuration_model", + "havel_hakimi_graph", + "reverse_havel_hakimi_graph", + "alternating_havel_hakimi_graph", + "preferential_attachment_graph", + "random_graph", + "gnmk_random_graph", + "complete_bipartite_graph", +] + + +@nx._dispatchable(graphs=None, returns_graph=True) +@nodes_or_number([0, 1]) +def complete_bipartite_graph(n1, n2, create_using=None): + """Returns the complete bipartite graph `K_{n_1,n_2}`. + + The graph is composed of two partitions with nodes 0 to (n1 - 1) + in the first and nodes n1 to (n1 + n2 - 1) in the second. + Each node in the first is connected to each node in the second. + + Parameters + ---------- + n1, n2 : integer or iterable container of nodes + If integers, nodes are from `range(n1)` and `range(n1, n1 + n2)`. + If a container, the elements are the nodes. + create_using : NetworkX graph instance, (default: nx.Graph) + Return graph of this type. + + Notes + ----- + Nodes are the integers 0 to `n1 + n2 - 1` unless either n1 or n2 are + containers of nodes. If only one of n1 or n2 are integers, that + integer is replaced by `range` of that integer. + + The nodes are assigned the attribute 'bipartite' with the value 0 or 1 + to indicate which bipartite set the node belongs to. + + This function is not imported in the main namespace. + To use it use nx.bipartite.complete_bipartite_graph + """ + G = nx.empty_graph(0, create_using) + if G.is_directed(): + raise nx.NetworkXError("Directed Graph not supported") + + n1, top = n1 + n2, bottom = n2 + if isinstance(n1, numbers.Integral) and isinstance(n2, numbers.Integral): + bottom = [n1 + i for i in bottom] + G.add_nodes_from(top, bipartite=0) + G.add_nodes_from(bottom, bipartite=1) + if len(G) != len(top) + len(bottom): + raise nx.NetworkXError("Inputs n1 and n2 must contain distinct nodes") + G.add_edges_from((u, v) for u in top for v in bottom) + G.graph["name"] = f"complete_bipartite_graph({len(top)}, {len(bottom)})" + return G + + +@py_random_state(3) +@nx._dispatchable(name="bipartite_configuration_model", graphs=None, returns_graph=True) +def configuration_model(aseq, bseq, create_using=None, seed=None): + """Returns a random bipartite graph from two given degree sequences. + + Parameters + ---------- + aseq : list + Degree sequence for node set A. + bseq : list + Degree sequence for node set B. + create_using : NetworkX graph instance, optional + Return graph of this type. + seed : integer, random_state, or None (default) + Indicator of random number generation state. + See :ref:`Randomness`. + + The graph is composed of two partitions. Set A has nodes 0 to + (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). + Nodes from set A are connected to nodes in set B by choosing + randomly from the possible free stubs, one in A and one in B. + + Notes + ----- + The sum of the two sequences must be equal: sum(aseq)=sum(bseq) + If no graph type is specified use MultiGraph with parallel edges. + If you want a graph with no parallel edges use create_using=Graph() + but then the resulting degree sequences might not be exact. + + The nodes are assigned the attribute 'bipartite' with the value 0 or 1 + to indicate which bipartite set the node belongs to. + + This function is not imported in the main namespace. + To use it use nx.bipartite.configuration_model + """ + G = nx.empty_graph(0, create_using, default=nx.MultiGraph) + if G.is_directed(): + raise nx.NetworkXError("Directed Graph not supported") + + # length and sum of each sequence + lena = len(aseq) + lenb = len(bseq) + suma = sum(aseq) + sumb = sum(bseq) + + if not suma == sumb: + raise nx.NetworkXError( + f"invalid degree sequences, sum(aseq)!=sum(bseq),{suma},{sumb}" + ) + + G = _add_nodes_with_bipartite_label(G, lena, lenb) + + if len(aseq) == 0 or max(aseq) == 0: + return G # done if no edges + + # build lists of degree-repeated vertex numbers + stubs = [[v] * aseq[v] for v in range(lena)] + astubs = [x for subseq in stubs for x in subseq] + + stubs = [[v] * bseq[v - lena] for v in range(lena, lena + lenb)] + bstubs = [x for subseq in stubs for x in subseq] + + # shuffle lists + seed.shuffle(astubs) + seed.shuffle(bstubs) + + G.add_edges_from([astubs[i], bstubs[i]] for i in range(suma)) + + G.name = "bipartite_configuration_model" + return G + + +@nx._dispatchable(name="bipartite_havel_hakimi_graph", graphs=None, returns_graph=True) +def havel_hakimi_graph(aseq, bseq, create_using=None): + """Returns a bipartite graph from two given degree sequences using a + Havel-Hakimi style construction. + + The graph is composed of two partitions. Set A has nodes 0 to + (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). + Nodes from the set A are connected to nodes in the set B by + connecting the highest degree nodes in set A to the highest degree + nodes in set B until all stubs are connected. + + Parameters + ---------- + aseq : list + Degree sequence for node set A. + bseq : list + Degree sequence for node set B. + create_using : NetworkX graph instance, optional + Return graph of this type. + + Notes + ----- + The sum of the two sequences must be equal: sum(aseq)=sum(bseq) + If no graph type is specified use MultiGraph with parallel edges. + If you want a graph with no parallel edges use create_using=Graph() + but then the resulting degree sequences might not be exact. + + The nodes are assigned the attribute 'bipartite' with the value 0 or 1 + to indicate which bipartite set the node belongs to. + + This function is not imported in the main namespace. + To use it use nx.bipartite.havel_hakimi_graph + """ + G = nx.empty_graph(0, create_using, default=nx.MultiGraph) + if G.is_directed(): + raise nx.NetworkXError("Directed Graph not supported") + + # length of the each sequence + naseq = len(aseq) + nbseq = len(bseq) + + suma = sum(aseq) + sumb = sum(bseq) + + if not suma == sumb: + raise nx.NetworkXError( + f"invalid degree sequences, sum(aseq)!=sum(bseq),{suma},{sumb}" + ) + + G = _add_nodes_with_bipartite_label(G, naseq, nbseq) + + if len(aseq) == 0 or max(aseq) == 0: + return G # done if no edges + + # build list of degree-repeated vertex numbers + astubs = [[aseq[v], v] for v in range(naseq)] + bstubs = [[bseq[v - naseq], v] for v in range(naseq, naseq + nbseq)] + astubs.sort() + while astubs: + (degree, u) = astubs.pop() # take of largest degree node in the a set + if degree == 0: + break # done, all are zero + # connect the source to largest degree nodes in the b set + bstubs.sort() + for target in bstubs[-degree:]: + v = target[1] + G.add_edge(u, v) + target[0] -= 1 # note this updates bstubs too. + if target[0] == 0: + bstubs.remove(target) + + G.name = "bipartite_havel_hakimi_graph" + return G + + +@nx._dispatchable(graphs=None, returns_graph=True) +def reverse_havel_hakimi_graph(aseq, bseq, create_using=None): + """Returns a bipartite graph from two given degree sequences using a + Havel-Hakimi style construction. + + The graph is composed of two partitions. Set A has nodes 0 to + (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). + Nodes from set A are connected to nodes in the set B by connecting + the highest degree nodes in set A to the lowest degree nodes in + set B until all stubs are connected. + + Parameters + ---------- + aseq : list + Degree sequence for node set A. + bseq : list + Degree sequence for node set B. + create_using : NetworkX graph instance, optional + Return graph of this type. + + Notes + ----- + The sum of the two sequences must be equal: sum(aseq)=sum(bseq) + If no graph type is specified use MultiGraph with parallel edges. + If you want a graph with no parallel edges use create_using=Graph() + but then the resulting degree sequences might not be exact. + + The nodes are assigned the attribute 'bipartite' with the value 0 or 1 + to indicate which bipartite set the node belongs to. + + This function is not imported in the main namespace. + To use it use nx.bipartite.reverse_havel_hakimi_graph + """ + G = nx.empty_graph(0, create_using, default=nx.MultiGraph) + if G.is_directed(): + raise nx.NetworkXError("Directed Graph not supported") + + # length of the each sequence + lena = len(aseq) + lenb = len(bseq) + suma = sum(aseq) + sumb = sum(bseq) + + if not suma == sumb: + raise nx.NetworkXError( + f"invalid degree sequences, sum(aseq)!=sum(bseq),{suma},{sumb}" + ) + + G = _add_nodes_with_bipartite_label(G, lena, lenb) + + if len(aseq) == 0 or max(aseq) == 0: + return G # done if no edges + + # build list of degree-repeated vertex numbers + astubs = [[aseq[v], v] for v in range(lena)] + bstubs = [[bseq[v - lena], v] for v in range(lena, lena + lenb)] + astubs.sort() + bstubs.sort() + while astubs: + (degree, u) = astubs.pop() # take of largest degree node in the a set + if degree == 0: + break # done, all are zero + # connect the source to the smallest degree nodes in the b set + for target in bstubs[0:degree]: + v = target[1] + G.add_edge(u, v) + target[0] -= 1 # note this updates bstubs too. + if target[0] == 0: + bstubs.remove(target) + + G.name = "bipartite_reverse_havel_hakimi_graph" + return G + + +@nx._dispatchable(graphs=None, returns_graph=True) +def alternating_havel_hakimi_graph(aseq, bseq, create_using=None): + """Returns a bipartite graph from two given degree sequences using + an alternating Havel-Hakimi style construction. + + The graph is composed of two partitions. Set A has nodes 0 to + (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1). + Nodes from the set A are connected to nodes in the set B by + connecting the highest degree nodes in set A to alternatively the + highest and the lowest degree nodes in set B until all stubs are + connected. + + Parameters + ---------- + aseq : list + Degree sequence for node set A. + bseq : list + Degree sequence for node set B. + create_using : NetworkX graph instance, optional + Return graph of this type. + + Notes + ----- + The sum of the two sequences must be equal: sum(aseq)=sum(bseq) + If no graph type is specified use MultiGraph with parallel edges. + If you want a graph with no parallel edges use create_using=Graph() + but then the resulting degree sequences might not be exact. + + The nodes are assigned the attribute 'bipartite' with the value 0 or 1 + to indicate which bipartite set the node belongs to. + + This function is not imported in the main namespace. + To use it use nx.bipartite.alternating_havel_hakimi_graph + """ + G = nx.empty_graph(0, create_using, default=nx.MultiGraph) + if G.is_directed(): + raise nx.NetworkXError("Directed Graph not supported") + + # length of the each sequence + naseq = len(aseq) + nbseq = len(bseq) + suma = sum(aseq) + sumb = sum(bseq) + + if not suma == sumb: + raise nx.NetworkXError( + f"invalid degree sequences, sum(aseq)!=sum(bseq),{suma},{sumb}" + ) + + G = _add_nodes_with_bipartite_label(G, naseq, nbseq) + + if len(aseq) == 0 or max(aseq) == 0: + return G # done if no edges + # build list of degree-repeated vertex numbers + astubs = [[aseq[v], v] for v in range(naseq)] + bstubs = [[bseq[v - naseq], v] for v in range(naseq, naseq + nbseq)] + while astubs: + astubs.sort() + (degree, u) = astubs.pop() # take of largest degree node in the a set + if degree == 0: + break # done, all are zero + bstubs.sort() + small = bstubs[0 : degree // 2] # add these low degree targets + large = bstubs[(-degree + degree // 2) :] # now high degree targets + stubs = [x for z in zip(large, small) for x in z] # combine, sorry + if len(stubs) < len(small) + len(large): # check for zip truncation + stubs.append(large.pop()) + for target in stubs: + v = target[1] + G.add_edge(u, v) + target[0] -= 1 # note this updates bstubs too. + if target[0] == 0: + bstubs.remove(target) + + G.name = "bipartite_alternating_havel_hakimi_graph" + return G + + +@py_random_state(3) +@nx._dispatchable(graphs=None, returns_graph=True) +def preferential_attachment_graph(aseq, p, create_using=None, seed=None): + """Create a bipartite graph with a preferential attachment model from + a given single degree sequence. + + The graph is composed of two partitions. Set A has nodes 0 to + (len(aseq) - 1) and set B has nodes starting with node len(aseq). + The number of nodes in set B is random. + + Parameters + ---------- + aseq : list + Degree sequence for node set A. + p : float + Probability that a new bottom node is added. + create_using : NetworkX graph instance, optional + Return graph of this type. + seed : integer, random_state, or None (default) + Indicator of random number generation state. + See :ref:`Randomness`. + + References + ---------- + .. [1] Guillaume, J.L. and Latapy, M., + Bipartite graphs as models of complex networks. + Physica A: Statistical Mechanics and its Applications, + 2006, 371(2), pp.795-813. + .. [2] Jean-Loup Guillaume and Matthieu Latapy, + Bipartite structure of all complex networks, + Inf. Process. Lett. 90, 2004, pg. 215-221 + https://doi.org/10.1016/j.ipl.2004.03.007 + + Notes + ----- + The nodes are assigned the attribute 'bipartite' with the value 0 or 1 + to indicate which bipartite set the node belongs to. + + This function is not imported in the main namespace. + To use it use nx.bipartite.preferential_attachment_graph + """ + G = nx.empty_graph(0, create_using, default=nx.MultiGraph) + if G.is_directed(): + raise nx.NetworkXError("Directed Graph not supported") + + if p > 1: + raise nx.NetworkXError(f"probability {p} > 1") + + naseq = len(aseq) + G = _add_nodes_with_bipartite_label(G, naseq, 0) + vv = [[v] * aseq[v] for v in range(naseq)] + while vv: + while vv[0]: + source = vv[0][0] + vv[0].remove(source) + if seed.random() < p or len(G) == naseq: + target = len(G) + G.add_node(target, bipartite=1) + G.add_edge(source, target) + else: + bb = [[b] * G.degree(b) for b in range(naseq, len(G))] + # flatten the list of lists into a list. + bbstubs = reduce(lambda x, y: x + y, bb) + # choose preferentially a bottom node. + target = seed.choice(bbstubs) + G.add_node(target, bipartite=1) + G.add_edge(source, target) + vv.remove(vv[0]) + G.name = "bipartite_preferential_attachment_model" + return G + + +@py_random_state(3) +@nx._dispatchable(graphs=None, returns_graph=True) +def random_graph(n, m, p, seed=None, directed=False): + """Returns a bipartite random graph. + + This is a bipartite version of the binomial (Erdős-Rényi) graph. + The graph is composed of two partitions. Set A has nodes 0 to + (n - 1) and set B has nodes n to (n + m - 1). + + Parameters + ---------- + n : int + The number of nodes in the first bipartite set. + m : int + The number of nodes in the second bipartite set. + p : float + Probability for edge creation. + seed : integer, random_state, or None (default) + Indicator of random number generation state. + See :ref:`Randomness`. + directed : bool, optional (default=False) + If True return a directed graph + + Notes + ----- + The bipartite random graph algorithm chooses each of the n*m (undirected) + or 2*nm (directed) possible edges with probability p. + + This algorithm is $O(n+m)$ where $m$ is the expected number of edges. + + The nodes are assigned the attribute 'bipartite' with the value 0 or 1 + to indicate which bipartite set the node belongs to. + + This function is not imported in the main namespace. + To use it use nx.bipartite.random_graph + + See Also + -------- + gnp_random_graph, configuration_model + + References + ---------- + .. [1] Vladimir Batagelj and Ulrik Brandes, + "Efficient generation of large random networks", + Phys. Rev. E, 71, 036113, 2005. + """ + G = nx.Graph() + G = _add_nodes_with_bipartite_label(G, n, m) + if directed: + G = nx.DiGraph(G) + G.name = f"fast_gnp_random_graph({n},{m},{p})" + + if p <= 0: + return G + if p >= 1: + return nx.complete_bipartite_graph(n, m) + + lp = math.log(1.0 - p) + + v = 0 + w = -1 + while v < n: + lr = math.log(1.0 - seed.random()) + w = w + 1 + int(lr / lp) + while w >= m and v < n: + w = w - m + v = v + 1 + if v < n: + G.add_edge(v, n + w) + + if directed: + # use the same algorithm to + # add edges from the "m" to "n" set + v = 0 + w = -1 + while v < n: + lr = math.log(1.0 - seed.random()) + w = w + 1 + int(lr / lp) + while w >= m and v < n: + w = w - m + v = v + 1 + if v < n: + G.add_edge(n + w, v) + + return G + + +@py_random_state(3) +@nx._dispatchable(graphs=None, returns_graph=True) +def gnmk_random_graph(n, m, k, seed=None, directed=False): + """Returns a random bipartite graph G_{n,m,k}. + + Produces a bipartite graph chosen randomly out of the set of all graphs + with n top nodes, m bottom nodes, and k edges. + The graph is composed of two sets of nodes. + Set A has nodes 0 to (n - 1) and set B has nodes n to (n + m - 1). + + Parameters + ---------- + n : int + The number of nodes in the first bipartite set. + m : int + The number of nodes in the second bipartite set. + k : int + The number of edges + seed : integer, random_state, or None (default) + Indicator of random number generation state. + See :ref:`Randomness`. + directed : bool, optional (default=False) + If True return a directed graph + + Examples + -------- + from nx.algorithms import bipartite + G = bipartite.gnmk_random_graph(10,20,50) + + See Also + -------- + gnm_random_graph + + Notes + ----- + If k > m * n then a complete bipartite graph is returned. + + This graph is a bipartite version of the `G_{nm}` random graph model. + + The nodes are assigned the attribute 'bipartite' with the value 0 or 1 + to indicate which bipartite set the node belongs to. + + This function is not imported in the main namespace. + To use it use nx.bipartite.gnmk_random_graph + """ + G = nx.Graph() + G = _add_nodes_with_bipartite_label(G, n, m) + if directed: + G = nx.DiGraph(G) + G.name = f"bipartite_gnm_random_graph({n},{m},{k})" + if n == 1 or m == 1: + return G + max_edges = n * m # max_edges for bipartite networks + if k >= max_edges: # Maybe we should raise an exception here + return nx.complete_bipartite_graph(n, m, create_using=G) + + top = [n for n, d in G.nodes(data=True) if d["bipartite"] == 0] + bottom = list(set(G) - set(top)) + edge_count = 0 + while edge_count < k: + # generate random edge,u,v + u = seed.choice(top) + v = seed.choice(bottom) + if v in G[u]: + continue + else: + G.add_edge(u, v) + edge_count += 1 + return G + + +def _add_nodes_with_bipartite_label(G, lena, lenb): + G.add_nodes_from(range(lena + lenb)) + b = dict(zip(range(lena), [0] * lena)) + b.update(dict(zip(range(lena, lena + lenb), [1] * lenb))) + nx.set_node_attributes(G, b, "bipartite") + return G diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/matching.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/matching.py new file mode 100644 index 0000000000000000000000000000000000000000..38a174780ac1eb7a42568aa6752b9adb82a2d984 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/matching.py @@ -0,0 +1,590 @@ +# This module uses material from the Wikipedia article Hopcroft--Karp algorithm +# , accessed on +# January 3, 2015, which is released under the Creative Commons +# Attribution-Share-Alike License 3.0 +# . That article includes +# pseudocode, which has been translated into the corresponding Python code. +# +# Portions of this module use code from David Eppstein's Python Algorithms and +# Data Structures (PADS) library, which is dedicated to the public domain (for +# proof, see ). +"""Provides functions for computing maximum cardinality matchings and minimum +weight full matchings in a bipartite graph. + +If you don't care about the particular implementation of the maximum matching +algorithm, simply use the :func:`maximum_matching`. If you do care, you can +import one of the named maximum matching algorithms directly. + +For example, to find a maximum matching in the complete bipartite graph with +two vertices on the left and three vertices on the right: + +>>> G = nx.complete_bipartite_graph(2, 3) +>>> left, right = nx.bipartite.sets(G) +>>> list(left) +[0, 1] +>>> list(right) +[2, 3, 4] +>>> nx.bipartite.maximum_matching(G) +{0: 2, 1: 3, 2: 0, 3: 1} + +The dictionary returned by :func:`maximum_matching` includes a mapping for +vertices in both the left and right vertex sets. + +Similarly, :func:`minimum_weight_full_matching` produces, for a complete +weighted bipartite graph, a matching whose cardinality is the cardinality of +the smaller of the two partitions, and for which the sum of the weights of the +edges included in the matching is minimal. + +""" + +import collections +import itertools + +import networkx as nx +from networkx.algorithms.bipartite import sets as bipartite_sets +from networkx.algorithms.bipartite.matrix import biadjacency_matrix + +__all__ = [ + "maximum_matching", + "hopcroft_karp_matching", + "eppstein_matching", + "to_vertex_cover", + "minimum_weight_full_matching", +] + +INFINITY = float("inf") + + +@nx._dispatchable +def hopcroft_karp_matching(G, top_nodes=None): + """Returns the maximum cardinality matching of the bipartite graph `G`. + + A matching is a set of edges that do not share any nodes. A maximum + cardinality matching is a matching with the most edges possible. It + is not always unique. Finding a matching in a bipartite graph can be + treated as a networkx flow problem. + + The functions ``hopcroft_karp_matching`` and ``maximum_matching`` + are aliases of the same function. + + Parameters + ---------- + G : NetworkX graph + + Undirected bipartite graph + + top_nodes : container of nodes + + Container with all nodes in one bipartite node set. If not supplied + it will be computed. But if more than one solution exists an exception + will be raised. + + Returns + ------- + matches : dictionary + + The matching is returned as a dictionary, `matches`, such that + ``matches[v] == w`` if node `v` is matched to node `w`. Unmatched + nodes do not occur as a key in `matches`. + + Raises + ------ + AmbiguousSolution + Raised if the input bipartite graph is disconnected and no container + with all nodes in one bipartite set is provided. When determining + the nodes in each bipartite set more than one valid solution is + possible if the input graph is disconnected. + + Notes + ----- + This function is implemented with the `Hopcroft--Karp matching algorithm + `_ for + bipartite graphs. + + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + See Also + -------- + maximum_matching + hopcroft_karp_matching + eppstein_matching + + References + ---------- + .. [1] John E. Hopcroft and Richard M. Karp. "An n^{5 / 2} Algorithm for + Maximum Matchings in Bipartite Graphs" In: **SIAM Journal of Computing** + 2.4 (1973), pp. 225--231. . + + """ + + # First we define some auxiliary search functions. + # + # If you are a human reading these auxiliary search functions, the "global" + # variables `leftmatches`, `rightmatches`, `distances`, etc. are defined + # below the functions, so that they are initialized close to the initial + # invocation of the search functions. + def breadth_first_search(): + for v in left: + if leftmatches[v] is None: + distances[v] = 0 + queue.append(v) + else: + distances[v] = INFINITY + distances[None] = INFINITY + while queue: + v = queue.popleft() + if distances[v] < distances[None]: + for u in G[v]: + if distances[rightmatches[u]] is INFINITY: + distances[rightmatches[u]] = distances[v] + 1 + queue.append(rightmatches[u]) + return distances[None] is not INFINITY + + def depth_first_search(v): + if v is not None: + for u in G[v]: + if distances[rightmatches[u]] == distances[v] + 1: + if depth_first_search(rightmatches[u]): + rightmatches[u] = v + leftmatches[v] = u + return True + distances[v] = INFINITY + return False + return True + + # Initialize the "global" variables that maintain state during the search. + left, right = bipartite_sets(G, top_nodes) + leftmatches = {v: None for v in left} + rightmatches = {v: None for v in right} + distances = {} + queue = collections.deque() + + # Implementation note: this counter is incremented as pairs are matched but + # it is currently not used elsewhere in the computation. + num_matched_pairs = 0 + while breadth_first_search(): + for v in left: + if leftmatches[v] is None: + if depth_first_search(v): + num_matched_pairs += 1 + + # Strip the entries matched to `None`. + leftmatches = {k: v for k, v in leftmatches.items() if v is not None} + rightmatches = {k: v for k, v in rightmatches.items() if v is not None} + + # At this point, the left matches and the right matches are inverses of one + # another. In other words, + # + # leftmatches == {v, k for k, v in rightmatches.items()} + # + # Finally, we combine both the left matches and right matches. + return dict(itertools.chain(leftmatches.items(), rightmatches.items())) + + +@nx._dispatchable +def eppstein_matching(G, top_nodes=None): + """Returns the maximum cardinality matching of the bipartite graph `G`. + + Parameters + ---------- + G : NetworkX graph + + Undirected bipartite graph + + top_nodes : container + + Container with all nodes in one bipartite node set. If not supplied + it will be computed. But if more than one solution exists an exception + will be raised. + + Returns + ------- + matches : dictionary + + The matching is returned as a dictionary, `matching`, such that + ``matching[v] == w`` if node `v` is matched to node `w`. Unmatched + nodes do not occur as a key in `matching`. + + Raises + ------ + AmbiguousSolution + Raised if the input bipartite graph is disconnected and no container + with all nodes in one bipartite set is provided. When determining + the nodes in each bipartite set more than one valid solution is + possible if the input graph is disconnected. + + Notes + ----- + This function is implemented with David Eppstein's version of the algorithm + Hopcroft--Karp algorithm (see :func:`hopcroft_karp_matching`), which + originally appeared in the `Python Algorithms and Data Structures library + (PADS) `_. + + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + See Also + -------- + + hopcroft_karp_matching + + """ + # Due to its original implementation, a directed graph is needed + # so that the two sets of bipartite nodes can be distinguished + left, right = bipartite_sets(G, top_nodes) + G = nx.DiGraph(G.edges(left)) + # initialize greedy matching (redundant, but faster than full search) + matching = {} + for u in G: + for v in G[u]: + if v not in matching: + matching[v] = u + break + while True: + # structure residual graph into layers + # pred[u] gives the neighbor in the previous layer for u in U + # preds[v] gives a list of neighbors in the previous layer for v in V + # unmatched gives a list of unmatched vertices in final layer of V, + # and is also used as a flag value for pred[u] when u is in the first + # layer + preds = {} + unmatched = [] + pred = {u: unmatched for u in G} + for v in matching: + del pred[matching[v]] + layer = list(pred) + + # repeatedly extend layering structure by another pair of layers + while layer and not unmatched: + newLayer = {} + for u in layer: + for v in G[u]: + if v not in preds: + newLayer.setdefault(v, []).append(u) + layer = [] + for v in newLayer: + preds[v] = newLayer[v] + if v in matching: + layer.append(matching[v]) + pred[matching[v]] = v + else: + unmatched.append(v) + + # did we finish layering without finding any alternating paths? + if not unmatched: + # TODO - The lines between --- were unused and were thus commented + # out. This whole commented chunk should be reviewed to determine + # whether it should be built upon or completely removed. + # --- + # unlayered = {} + # for u in G: + # # TODO Why is extra inner loop necessary? + # for v in G[u]: + # if v not in preds: + # unlayered[v] = None + # --- + # TODO Originally, this function returned a three-tuple: + # + # return (matching, list(pred), list(unlayered)) + # + # For some reason, the documentation for this function + # indicated that the second and third elements of the returned + # three-tuple would be the vertices in the left and right vertex + # sets, respectively, that are also in the maximum independent set. + # However, what I think the author meant was that the second + # element is the list of vertices that were unmatched and the third + # element was the list of vertices that were matched. Since that + # seems to be the case, they don't really need to be returned, + # since that information can be inferred from the matching + # dictionary. + + # All the matched nodes must be a key in the dictionary + for key in matching.copy(): + matching[matching[key]] = key + return matching + + # recursively search backward through layers to find alternating paths + # recursion returns true if found path, false otherwise + def recurse(v): + if v in preds: + L = preds.pop(v) + for u in L: + if u in pred: + pu = pred.pop(u) + if pu is unmatched or recurse(pu): + matching[v] = u + return True + return False + + for v in unmatched: + recurse(v) + + +def _is_connected_by_alternating_path(G, v, matched_edges, unmatched_edges, targets): + """Returns True if and only if the vertex `v` is connected to one of + the target vertices by an alternating path in `G`. + + An *alternating path* is a path in which every other edge is in the + specified maximum matching (and the remaining edges in the path are not in + the matching). An alternating path may have matched edges in the even + positions or in the odd positions, as long as the edges alternate between + 'matched' and 'unmatched'. + + `G` is an undirected bipartite NetworkX graph. + + `v` is a vertex in `G`. + + `matched_edges` is a set of edges present in a maximum matching in `G`. + + `unmatched_edges` is a set of edges not present in a maximum + matching in `G`. + + `targets` is a set of vertices. + + """ + + def _alternating_dfs(u, along_matched=True): + """Returns True if and only if `u` is connected to one of the + targets by an alternating path. + + `u` is a vertex in the graph `G`. + + If `along_matched` is True, this step of the depth-first search + will continue only through edges in the given matching. Otherwise, it + will continue only through edges *not* in the given matching. + + """ + visited = set() + # Follow matched edges when depth is even, + # and follow unmatched edges when depth is odd. + initial_depth = 0 if along_matched else 1 + stack = [(u, iter(G[u]), initial_depth)] + while stack: + parent, children, depth = stack[-1] + valid_edges = matched_edges if depth % 2 else unmatched_edges + try: + child = next(children) + if child not in visited: + if (parent, child) in valid_edges or (child, parent) in valid_edges: + if child in targets: + return True + visited.add(child) + stack.append((child, iter(G[child]), depth + 1)) + except StopIteration: + stack.pop() + return False + + # Check for alternating paths starting with edges in the matching, then + # check for alternating paths starting with edges not in the + # matching. + return _alternating_dfs(v, along_matched=True) or _alternating_dfs( + v, along_matched=False + ) + + +def _connected_by_alternating_paths(G, matching, targets): + """Returns the set of vertices that are connected to one of the target + vertices by an alternating path in `G` or are themselves a target. + + An *alternating path* is a path in which every other edge is in the + specified maximum matching (and the remaining edges in the path are not in + the matching). An alternating path may have matched edges in the even + positions or in the odd positions, as long as the edges alternate between + 'matched' and 'unmatched'. + + `G` is an undirected bipartite NetworkX graph. + + `matching` is a dictionary representing a maximum matching in `G`, as + returned by, for example, :func:`maximum_matching`. + + `targets` is a set of vertices. + + """ + # Get the set of matched edges and the set of unmatched edges. Only include + # one version of each undirected edge (for example, include edge (1, 2) but + # not edge (2, 1)). Using frozensets as an intermediary step we do not + # require nodes to be orderable. + edge_sets = {frozenset((u, v)) for u, v in matching.items()} + matched_edges = {tuple(edge) for edge in edge_sets} + unmatched_edges = { + (u, v) for (u, v) in G.edges() if frozenset((u, v)) not in edge_sets + } + + return { + v + for v in G + if v in targets + or _is_connected_by_alternating_path( + G, v, matched_edges, unmatched_edges, targets + ) + } + + +@nx._dispatchable +def to_vertex_cover(G, matching, top_nodes=None): + """Returns the minimum vertex cover corresponding to the given maximum + matching of the bipartite graph `G`. + + Parameters + ---------- + G : NetworkX graph + + Undirected bipartite graph + + matching : dictionary + + A dictionary whose keys are vertices in `G` and whose values are the + distinct neighbors comprising the maximum matching for `G`, as returned + by, for example, :func:`maximum_matching`. The dictionary *must* + represent the maximum matching. + + top_nodes : container + + Container with all nodes in one bipartite node set. If not supplied + it will be computed. But if more than one solution exists an exception + will be raised. + + Returns + ------- + vertex_cover : :class:`set` + + The minimum vertex cover in `G`. + + Raises + ------ + AmbiguousSolution + Raised if the input bipartite graph is disconnected and no container + with all nodes in one bipartite set is provided. When determining + the nodes in each bipartite set more than one valid solution is + possible if the input graph is disconnected. + + Notes + ----- + This function is implemented using the procedure guaranteed by `Konig's + theorem + `_, + which proves an equivalence between a maximum matching and a minimum vertex + cover in bipartite graphs. + + Since a minimum vertex cover is the complement of a maximum independent set + for any graph, one can compute the maximum independent set of a bipartite + graph this way: + + >>> G = nx.complete_bipartite_graph(2, 3) + >>> matching = nx.bipartite.maximum_matching(G) + >>> vertex_cover = nx.bipartite.to_vertex_cover(G, matching) + >>> independent_set = set(G) - vertex_cover + >>> print(list(independent_set)) + [2, 3, 4] + + See :mod:`bipartite documentation ` + for further details on how bipartite graphs are handled in NetworkX. + + """ + # This is a Python implementation of the algorithm described at + # . + L, R = bipartite_sets(G, top_nodes) + # Let U be the set of unmatched vertices in the left vertex set. + unmatched_vertices = set(G) - set(matching) + U = unmatched_vertices & L + # Let Z be the set of vertices that are either in U or are connected to U + # by alternating paths. + Z = _connected_by_alternating_paths(G, matching, U) + # At this point, every edge either has a right endpoint in Z or a left + # endpoint not in Z. This gives us the vertex cover. + return (L - Z) | (R & Z) + + +#: Returns the maximum cardinality matching in the given bipartite graph. +#: +#: This function is simply an alias for :func:`hopcroft_karp_matching`. +maximum_matching = hopcroft_karp_matching + + +@nx._dispatchable(edge_attrs="weight") +def minimum_weight_full_matching(G, top_nodes=None, weight="weight"): + r"""Returns a minimum weight full matching of the bipartite graph `G`. + + Let :math:`G = ((U, V), E)` be a weighted bipartite graph with real weights + :math:`w : E \to \mathbb{R}`. This function then produces a matching + :math:`M \subseteq E` with cardinality + + .. math:: + \lvert M \rvert = \min(\lvert U \rvert, \lvert V \rvert), + + which minimizes the sum of the weights of the edges included in the + matching, :math:`\sum_{e \in M} w(e)`, or raises an error if no such + matching exists. + + When :math:`\lvert U \rvert = \lvert V \rvert`, this is commonly + referred to as a perfect matching; here, since we allow + :math:`\lvert U \rvert` and :math:`\lvert V \rvert` to differ, we + follow Karp [1]_ and refer to the matching as *full*. + + Parameters + ---------- + G : NetworkX graph + + Undirected bipartite graph + + top_nodes : container + + Container with all nodes in one bipartite node set. If not supplied + it will be computed. + + weight : string, optional (default='weight') + + The edge data key used to provide each value in the matrix. + If None, then each edge has weight 1. + + Returns + ------- + matches : dictionary + + The matching is returned as a dictionary, `matches`, such that + ``matches[v] == w`` if node `v` is matched to node `w`. Unmatched + nodes do not occur as a key in `matches`. + + Raises + ------ + ValueError + Raised if no full matching exists. + + ImportError + Raised if SciPy is not available. + + Notes + ----- + The problem of determining a minimum weight full matching is also known as + the rectangular linear assignment problem. This implementation defers the + calculation of the assignment to SciPy. + + References + ---------- + .. [1] Richard Manning Karp: + An algorithm to Solve the m x n Assignment Problem in Expected Time + O(mn log n). + Networks, 10(2):143–152, 1980. + + """ + import numpy as np + import scipy as sp + + left, right = nx.bipartite.sets(G, top_nodes) + U = list(left) + V = list(right) + # We explicitly create the biadjacency matrix having infinities + # where edges are missing (as opposed to zeros, which is what one would + # get by using toarray on the sparse matrix). + weights_sparse = biadjacency_matrix( + G, row_order=U, column_order=V, weight=weight, format="coo" + ) + weights = np.full(weights_sparse.shape, np.inf) + weights[weights_sparse.row, weights_sparse.col] = weights_sparse.data + left_matches = sp.optimize.linear_sum_assignment(weights) + d = {U[u]: V[v] for u, v in zip(*left_matches)} + # d will contain the matching from edges in left to right; we need to + # add the ones from right to left as well. + d.update({v: u for u, v in d.items()}) + return d diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/matrix.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/matrix.py new file mode 100644 index 0000000000000000000000000000000000000000..bbfa47c70089bdc23dc5bb91f0221918e87d29db --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/matrix.py @@ -0,0 +1,168 @@ +""" +==================== +Biadjacency matrices +==================== +""" + +import itertools + +import networkx as nx +from networkx.convert_matrix import _generate_weighted_edges + +__all__ = ["biadjacency_matrix", "from_biadjacency_matrix"] + + +@nx._dispatchable(edge_attrs="weight") +def biadjacency_matrix( + G, row_order, column_order=None, dtype=None, weight="weight", format="csr" +): + r"""Returns the biadjacency matrix of the bipartite graph G. + + Let `G = (U, V, E)` be a bipartite graph with node sets + `U = u_{1},...,u_{r}` and `V = v_{1},...,v_{s}`. The biadjacency + matrix [1]_ is the `r` x `s` matrix `B` in which `b_{i,j} = 1` + if, and only if, `(u_i, v_j) \in E`. If the parameter `weight` is + not `None` and matches the name of an edge attribute, its value is + used instead of 1. + + Parameters + ---------- + G : graph + A NetworkX graph + + row_order : list of nodes + The rows of the matrix are ordered according to the list of nodes. + + column_order : list, optional + The columns of the matrix are ordered according to the list of nodes. + If column_order is None, then the ordering of columns is arbitrary. + + dtype : NumPy data-type, optional + A valid NumPy dtype used to initialize the array. If None, then the + NumPy default is used. + + weight : string or None, optional (default='weight') + The edge data key used to provide each value in the matrix. + If None, then each edge has weight 1. + + format : str in {'bsr', 'csr', 'csc', 'coo', 'lil', 'dia', 'dok'} + The type of the matrix to be returned (default 'csr'). For + some algorithms different implementations of sparse matrices + can perform better. See [2]_ for details. + + Returns + ------- + M : SciPy sparse array + Biadjacency matrix representation of the bipartite graph G. + + Notes + ----- + No attempt is made to check that the input graph is bipartite. + + For directed bipartite graphs only successors are considered as neighbors. + To obtain an adjacency matrix with ones (or weight values) for both + predecessors and successors you have to generate two biadjacency matrices + where the rows of one of them are the columns of the other, and then add + one to the transpose of the other. + + See Also + -------- + adjacency_matrix + from_biadjacency_matrix + + References + ---------- + .. [1] https://en.wikipedia.org/wiki/Adjacency_matrix#Adjacency_matrix_of_a_bipartite_graph + .. [2] Scipy Dev. References, "Sparse Matrices", + https://docs.scipy.org/doc/scipy/reference/sparse.html + """ + import scipy as sp + + nlen = len(row_order) + if nlen == 0: + raise nx.NetworkXError("row_order is empty list") + if len(row_order) != len(set(row_order)): + msg = "Ambiguous ordering: `row_order` contained duplicates." + raise nx.NetworkXError(msg) + if column_order is None: + column_order = list(set(G) - set(row_order)) + mlen = len(column_order) + if len(column_order) != len(set(column_order)): + msg = "Ambiguous ordering: `column_order` contained duplicates." + raise nx.NetworkXError(msg) + + row_index = dict(zip(row_order, itertools.count())) + col_index = dict(zip(column_order, itertools.count())) + + if G.number_of_edges() == 0: + row, col, data = [], [], [] + else: + row, col, data = zip( + *( + (row_index[u], col_index[v], d.get(weight, 1)) + for u, v, d in G.edges(row_order, data=True) + if u in row_index and v in col_index + ) + ) + A = sp.sparse.coo_array((data, (row, col)), shape=(nlen, mlen), dtype=dtype) + try: + return A.asformat(format) + except ValueError as err: + raise nx.NetworkXError(f"Unknown sparse array format: {format}") from err + + +@nx._dispatchable(graphs=None, returns_graph=True) +def from_biadjacency_matrix(A, create_using=None, edge_attribute="weight"): + r"""Creates a new bipartite graph from a biadjacency matrix given as a + SciPy sparse array. + + Parameters + ---------- + A: scipy sparse array + A biadjacency matrix representation of a graph + + create_using: NetworkX graph + Use specified graph for result. The default is Graph() + + edge_attribute: string + Name of edge attribute to store matrix numeric value. The data will + have the same type as the matrix entry (int, float, (real,imag)). + + Notes + ----- + The nodes are labeled with the attribute `bipartite` set to an integer + 0 or 1 representing membership in part 0 or part 1 of the bipartite graph. + + If `create_using` is an instance of :class:`networkx.MultiGraph` or + :class:`networkx.MultiDiGraph` and the entries of `A` are of + type :class:`int`, then this function returns a multigraph (of the same + type as `create_using`) with parallel edges. In this case, `edge_attribute` + will be ignored. + + See Also + -------- + biadjacency_matrix + from_numpy_array + + References + ---------- + [1] https://en.wikipedia.org/wiki/Adjacency_matrix#Adjacency_matrix_of_a_bipartite_graph + """ + G = nx.empty_graph(0, create_using) + n, m = A.shape + # Make sure we get even the isolated nodes of the graph. + G.add_nodes_from(range(n), bipartite=0) + G.add_nodes_from(range(n, n + m), bipartite=1) + # Create an iterable over (u, v, w) triples and for each triple, add an + # edge from u to v with weight w. + triples = ((u, n + v, d) for (u, v, d) in _generate_weighted_edges(A)) + # If the entries in the adjacency matrix are integers and the graph is a + # multigraph, then create parallel edges, each with weight 1, for each + # entry in the adjacency matrix. Otherwise, create one edge for each + # positive entry in the adjacency matrix and set the weight of that edge to + # be the entry in the matrix. + if A.dtype.kind in ("i", "u") and G.is_multigraph(): + chain = itertools.chain.from_iterable + triples = chain(((u, v, 1) for d in range(w)) for (u, v, w) in triples) + G.add_weighted_edges_from(triples, weight=edge_attribute) + return G diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/projection.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/projection.py new file mode 100644 index 0000000000000000000000000000000000000000..7c2a26cf73ddf39e51fbd20d442abe736acedddd --- /dev/null +++ b/.venv/lib/python3.11/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/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/redundancy.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/redundancy.py new file mode 100644 index 0000000000000000000000000000000000000000..b622b975f0255ee4ac4bc56031c127ac58592abf --- /dev/null +++ b/.venv/lib/python3.11/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/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/spectral.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/spectral.py new file mode 100644 index 0000000000000000000000000000000000000000..cb9388f6cb61cb3c5da865e22449f4e8f2d1e720 --- /dev/null +++ b/.venv/lib/python3.11/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/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/__pycache__/test_betweenness_centrality.cpython-311.pyc b/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/__pycache__/test_betweenness_centrality.cpython-311.pyc new file mode 100644 index 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a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/beamsearch.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/beamsearch.py new file mode 100644 index 0000000000000000000000000000000000000000..23fbe7bbb3f037eca4f7ede25b7edf6305356587 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/beamsearch.py @@ -0,0 +1,90 @@ +"""Basic algorithms for breadth-first searching the nodes of a graph.""" + +import networkx as nx + +__all__ = ["bfs_beam_edges"] + + +@nx._dispatchable +def bfs_beam_edges(G, source, value, width=None): + """Iterates over edges in a beam search. + + The beam search is a generalized breadth-first search in which only + the "best" *w* neighbors of the current node are enqueued, where *w* + is the beam width and "best" is an application-specific + heuristic. In general, a beam search with a small beam width might + not visit each node in the graph. + + .. note:: + + With the default value of ``width=None`` or `width` greater than the + maximum degree of the graph, this function equates to a slower + version of `~networkx.algorithms.traversal.breadth_first_search.bfs_edges`. + All nodes will be visited, though the order of the reported edges may + vary. In such cases, `value` has no effect - consider using `bfs_edges` + directly instead. + + Parameters + ---------- + G : NetworkX graph + + source : node + Starting node for the breadth-first search; this function + iterates over only those edges in the component reachable from + this node. + + value : function + A function that takes a node of the graph as input and returns a + real number indicating how "good" it is. A higher value means it + is more likely to be visited sooner during the search. When + visiting a new node, only the `width` neighbors with the highest + `value` are enqueued (in decreasing order of `value`). + + width : int (default = None) + The beam width for the search. This is the number of neighbors + (ordered by `value`) to enqueue when visiting each new node. + + Yields + ------ + edge + Edges in the beam search starting from `source`, given as a pair + of nodes. + + Examples + -------- + To give nodes with, for example, a higher centrality precedence + during the search, set the `value` function to return the centrality + value of the node: + + >>> G = nx.karate_club_graph() + >>> centrality = nx.eigenvector_centrality(G) + >>> list(nx.bfs_beam_edges(G, source=0, value=centrality.get, width=3)) + [(0, 2), (0, 1), (0, 8), (2, 32), (1, 13), (8, 33)] + """ + + if width is None: + width = len(G) + + def successors(v): + """Returns a list of the best neighbors of a node. + + `v` is a node in the graph `G`. + + The "best" neighbors are chosen according to the `value` + function (higher is better). Only the `width` best neighbors of + `v` are returned. + """ + # TODO The Python documentation states that for small values, it + # is better to use `heapq.nlargest`. We should determine the + # threshold at which its better to use `heapq.nlargest()` + # instead of `sorted()[:]` and apply that optimization here. + # + # If `width` is greater than the number of neighbors of `v`, all + # neighbors are returned by the semantics of slicing in + # Python. This occurs in the special case that the user did not + # specify a `width`: in this case all neighbors are always + # returned, so this is just a (slower) implementation of + # `bfs_edges(G, source)` but with a sorted enqueue step. + return iter(sorted(G.neighbors(v), key=value, reverse=True)[:width]) + + yield from nx.generic_bfs_edges(G, source, successors) diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/breadth_first_search.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/breadth_first_search.py new file mode 100644 index 0000000000000000000000000000000000000000..899dc92b723665f88eb76dc90a0c1aee87dde1f4 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/breadth_first_search.py @@ -0,0 +1,575 @@ +"""Basic algorithms for breadth-first searching the nodes of a graph.""" + +from collections import deque + +import networkx as nx + +__all__ = [ + "bfs_edges", + "bfs_tree", + "bfs_predecessors", + "bfs_successors", + "descendants_at_distance", + "bfs_layers", + "bfs_labeled_edges", + "generic_bfs_edges", +] + + +@nx._dispatchable +def generic_bfs_edges(G, source, neighbors=None, depth_limit=None): + """Iterate over edges in a breadth-first search. + + The breadth-first search begins at `source` and enqueues the + neighbors of newly visited nodes specified by the `neighbors` + function. + + Parameters + ---------- + G : NetworkX graph + + source : node + Starting node for the breadth-first search; this function + iterates over only those edges in the component reachable from + this node. + + neighbors : function + A function that takes a newly visited node of the graph as input + and returns an *iterator* (not just a list) of nodes that are + neighbors of that node with custom ordering. If not specified, this is + just the ``G.neighbors`` method, but in general it can be any function + that returns an iterator over some or all of the neighbors of a + given node, in any order. + + depth_limit : int, optional(default=len(G)) + Specify the maximum search depth. + + Yields + ------ + edge + Edges in the breadth-first search starting from `source`. + + Examples + -------- + >>> G = nx.path_graph(7) + >>> list(nx.generic_bfs_edges(G, source=0)) + [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6)] + >>> list(nx.generic_bfs_edges(G, source=2)) + [(2, 1), (2, 3), (1, 0), (3, 4), (4, 5), (5, 6)] + >>> list(nx.generic_bfs_edges(G, source=2, depth_limit=2)) + [(2, 1), (2, 3), (1, 0), (3, 4)] + + The `neighbors` param can be used to specify the visitation order of each + node's neighbors generically. In the following example, we modify the default + neighbor to return *odd* nodes first: + + >>> def odd_first(n): + ... return sorted(G.neighbors(n), key=lambda x: x % 2, reverse=True) + + >>> G = nx.star_graph(5) + >>> list(nx.generic_bfs_edges(G, source=0)) # Default neighbor ordering + [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)] + >>> list(nx.generic_bfs_edges(G, source=0, neighbors=odd_first)) + [(0, 1), (0, 3), (0, 5), (0, 2), (0, 4)] + + Notes + ----- + This implementation is from `PADS`_, which was in the public domain + when it was first accessed in July, 2004. The modifications + to allow depth limits are based on the Wikipedia article + "`Depth-limited-search`_". + + .. _PADS: http://www.ics.uci.edu/~eppstein/PADS/BFS.py + .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search + """ + if neighbors is None: + neighbors = G.neighbors + if depth_limit is None: + depth_limit = len(G) + + seen = {source} + n = len(G) + depth = 0 + next_parents_children = [(source, neighbors(source))] + while next_parents_children and depth < depth_limit: + this_parents_children = next_parents_children + next_parents_children = [] + for parent, children in this_parents_children: + for child in children: + if child not in seen: + seen.add(child) + next_parents_children.append((child, neighbors(child))) + yield parent, child + if len(seen) == n: + return + depth += 1 + + +@nx._dispatchable +def bfs_edges(G, source, reverse=False, depth_limit=None, sort_neighbors=None): + """Iterate over edges in a breadth-first-search starting at source. + + Parameters + ---------- + G : NetworkX graph + + source : node + Specify starting node for breadth-first search; this function + iterates over only those edges in the component reachable from + this node. + + reverse : bool, optional + If True traverse a directed graph in the reverse direction + + depth_limit : int, optional(default=len(G)) + Specify the maximum search depth + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Yields + ------ + edge: 2-tuple of nodes + Yields edges resulting from the breadth-first search. + + Examples + -------- + To get the edges in a breadth-first search:: + + >>> G = nx.path_graph(3) + >>> list(nx.bfs_edges(G, 0)) + [(0, 1), (1, 2)] + >>> list(nx.bfs_edges(G, source=0, depth_limit=1)) + [(0, 1)] + + To get the nodes in a breadth-first search order:: + + >>> G = nx.path_graph(3) + >>> root = 2 + >>> edges = nx.bfs_edges(G, root) + >>> nodes = [root] + [v for u, v in edges] + >>> nodes + [2, 1, 0] + + Notes + ----- + The naming of this function is very similar to + :func:`~networkx.algorithms.traversal.edgebfs.edge_bfs`. The difference + is that ``edge_bfs`` yields edges even if they extend back to an already + explored node while this generator yields the edges of the tree that results + from a breadth-first-search (BFS) so no edges are reported if they extend + to already explored nodes. That means ``edge_bfs`` reports all edges while + ``bfs_edges`` only reports those traversed by a node-based BFS. Yet another + description is that ``bfs_edges`` reports the edges traversed during BFS + while ``edge_bfs`` reports all edges in the order they are explored. + + Based on the breadth-first search implementation in PADS [1]_ + by D. Eppstein, July 2004; with modifications to allow depth limits + as described in [2]_. + + References + ---------- + .. [1] http://www.ics.uci.edu/~eppstein/PADS/BFS.py. + .. [2] https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + bfs_tree + :func:`~networkx.algorithms.traversal.depth_first_search.dfs_edges` + :func:`~networkx.algorithms.traversal.edgebfs.edge_bfs` + + """ + if reverse and G.is_directed(): + successors = G.predecessors + else: + successors = G.neighbors + + if sort_neighbors is not None: + yield from generic_bfs_edges( + G, source, lambda node: iter(sort_neighbors(successors(node))), depth_limit + ) + else: + yield from generic_bfs_edges(G, source, successors, depth_limit) + + +@nx._dispatchable(returns_graph=True) +def bfs_tree(G, source, reverse=False, depth_limit=None, sort_neighbors=None): + """Returns an oriented tree constructed from of a breadth-first-search + starting at source. + + Parameters + ---------- + G : NetworkX graph + + source : node + Specify starting node for breadth-first search + + reverse : bool, optional + If True traverse a directed graph in the reverse direction + + depth_limit : int, optional(default=len(G)) + Specify the maximum search depth + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Returns + ------- + T: NetworkX DiGraph + An oriented tree + + Examples + -------- + >>> G = nx.path_graph(3) + >>> list(nx.bfs_tree(G, 1).edges()) + [(1, 0), (1, 2)] + >>> H = nx.Graph() + >>> nx.add_path(H, [0, 1, 2, 3, 4, 5, 6]) + >>> nx.add_path(H, [2, 7, 8, 9, 10]) + >>> sorted(list(nx.bfs_tree(H, source=3, depth_limit=3).edges())) + [(1, 0), (2, 1), (2, 7), (3, 2), (3, 4), (4, 5), (5, 6), (7, 8)] + + + Notes + ----- + Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py + by D. Eppstein, July 2004. The modifications + to allow depth limits based on the Wikipedia article + "`Depth-limited-search`_". + + .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + dfs_tree + bfs_edges + edge_bfs + """ + T = nx.DiGraph() + T.add_node(source) + edges_gen = bfs_edges( + G, + source, + reverse=reverse, + depth_limit=depth_limit, + sort_neighbors=sort_neighbors, + ) + T.add_edges_from(edges_gen) + return T + + +@nx._dispatchable +def bfs_predecessors(G, source, depth_limit=None, sort_neighbors=None): + """Returns an iterator of predecessors in breadth-first-search from source. + + Parameters + ---------- + G : NetworkX graph + + source : node + Specify starting node for breadth-first search + + depth_limit : int, optional(default=len(G)) + Specify the maximum search depth + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Returns + ------- + pred: iterator + (node, predecessor) iterator where `predecessor` is the predecessor of + `node` in a breadth first search starting from `source`. + + Examples + -------- + >>> G = nx.path_graph(3) + >>> dict(nx.bfs_predecessors(G, 0)) + {1: 0, 2: 1} + >>> H = nx.Graph() + >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) + >>> dict(nx.bfs_predecessors(H, 0)) + {1: 0, 2: 0, 3: 1, 4: 1, 5: 2, 6: 2} + >>> M = nx.Graph() + >>> nx.add_path(M, [0, 1, 2, 3, 4, 5, 6]) + >>> nx.add_path(M, [2, 7, 8, 9, 10]) + >>> sorted(nx.bfs_predecessors(M, source=1, depth_limit=3)) + [(0, 1), (2, 1), (3, 2), (4, 3), (7, 2), (8, 7)] + >>> N = nx.DiGraph() + >>> nx.add_path(N, [0, 1, 2, 3, 4, 7]) + >>> nx.add_path(N, [3, 5, 6, 7]) + >>> sorted(nx.bfs_predecessors(N, source=2)) + [(3, 2), (4, 3), (5, 3), (6, 5), (7, 4)] + + Notes + ----- + Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py + by D. Eppstein, July 2004. The modifications + to allow depth limits based on the Wikipedia article + "`Depth-limited-search`_". + + .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + bfs_tree + bfs_edges + edge_bfs + """ + for s, t in bfs_edges( + G, source, depth_limit=depth_limit, sort_neighbors=sort_neighbors + ): + yield (t, s) + + +@nx._dispatchable +def bfs_successors(G, source, depth_limit=None, sort_neighbors=None): + """Returns an iterator of successors in breadth-first-search from source. + + Parameters + ---------- + G : NetworkX graph + + source : node + Specify starting node for breadth-first search + + depth_limit : int, optional(default=len(G)) + Specify the maximum search depth + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Returns + ------- + succ: iterator + (node, successors) iterator where `successors` is the non-empty list of + successors of `node` in a breadth first search from `source`. + To appear in the iterator, `node` must have successors. + + Examples + -------- + >>> G = nx.path_graph(3) + >>> dict(nx.bfs_successors(G, 0)) + {0: [1], 1: [2]} + >>> H = nx.Graph() + >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) + >>> dict(nx.bfs_successors(H, 0)) + {0: [1, 2], 1: [3, 4], 2: [5, 6]} + >>> G = nx.Graph() + >>> nx.add_path(G, [0, 1, 2, 3, 4, 5, 6]) + >>> nx.add_path(G, [2, 7, 8, 9, 10]) + >>> dict(nx.bfs_successors(G, source=1, depth_limit=3)) + {1: [0, 2], 2: [3, 7], 3: [4], 7: [8]} + >>> G = nx.DiGraph() + >>> nx.add_path(G, [0, 1, 2, 3, 4, 5]) + >>> dict(nx.bfs_successors(G, source=3)) + {3: [4], 4: [5]} + + Notes + ----- + Based on http://www.ics.uci.edu/~eppstein/PADS/BFS.py + by D. Eppstein, July 2004.The modifications + to allow depth limits based on the Wikipedia article + "`Depth-limited-search`_". + + .. _Depth-limited-search: https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + bfs_tree + bfs_edges + edge_bfs + """ + parent = source + children = [] + for p, c in bfs_edges( + G, source, depth_limit=depth_limit, sort_neighbors=sort_neighbors + ): + if p == parent: + children.append(c) + continue + yield (parent, children) + children = [c] + parent = p + yield (parent, children) + + +@nx._dispatchable +def bfs_layers(G, sources): + """Returns an iterator of all the layers in breadth-first search traversal. + + Parameters + ---------- + G : NetworkX graph + A graph over which to find the layers using breadth-first search. + + sources : node in `G` or list of nodes in `G` + Specify starting nodes for single source or multiple sources breadth-first search + + Yields + ------ + layer: list of nodes + Yields list of nodes at the same distance from sources + + Examples + -------- + >>> G = nx.path_graph(5) + >>> dict(enumerate(nx.bfs_layers(G, [0, 4]))) + {0: [0, 4], 1: [1, 3], 2: [2]} + >>> H = nx.Graph() + >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) + >>> dict(enumerate(nx.bfs_layers(H, [1]))) + {0: [1], 1: [0, 3, 4], 2: [2], 3: [5, 6]} + >>> dict(enumerate(nx.bfs_layers(H, [1, 6]))) + {0: [1, 6], 1: [0, 3, 4, 2], 2: [5]} + """ + if sources in G: + sources = [sources] + + current_layer = list(sources) + visited = set(sources) + + for source in current_layer: + if source not in G: + raise nx.NetworkXError(f"The node {source} is not in the graph.") + + # this is basically BFS, except that the current layer only stores the nodes at + # same distance from sources at each iteration + while current_layer: + yield current_layer + next_layer = [] + for node in current_layer: + for child in G[node]: + if child not in visited: + visited.add(child) + next_layer.append(child) + current_layer = next_layer + + +REVERSE_EDGE = "reverse" +TREE_EDGE = "tree" +FORWARD_EDGE = "forward" +LEVEL_EDGE = "level" + + +@nx._dispatchable +def bfs_labeled_edges(G, sources): + """Iterate over edges in a breadth-first search (BFS) labeled by type. + + We generate triple of the form (*u*, *v*, *d*), where (*u*, *v*) is the + edge being explored in the breadth-first search and *d* is one of the + strings 'tree', 'forward', 'level', or 'reverse'. A 'tree' edge is one in + which *v* is first discovered and placed into the layer below *u*. A + 'forward' edge is one in which *u* is on the layer above *v* and *v* has + already been discovered. A 'level' edge is one in which both *u* and *v* + occur on the same layer. A 'reverse' edge is one in which *u* is on a layer + below *v*. + + We emit each edge exactly once. In an undirected graph, 'reverse' edges do + not occur, because each is discovered either as a 'tree' or 'forward' edge. + + Parameters + ---------- + G : NetworkX graph + A graph over which to find the layers using breadth-first search. + + sources : node in `G` or list of nodes in `G` + Starting nodes for single source or multiple sources breadth-first search + + Yields + ------ + edges: generator + A generator of triples (*u*, *v*, *d*) where (*u*, *v*) is the edge being + explored and *d* is described above. + + Examples + -------- + >>> G = nx.cycle_graph(4, create_using=nx.DiGraph) + >>> list(nx.bfs_labeled_edges(G, 0)) + [(0, 1, 'tree'), (1, 2, 'tree'), (2, 3, 'tree'), (3, 0, 'reverse')] + >>> G = nx.complete_graph(3) + >>> list(nx.bfs_labeled_edges(G, 0)) + [(0, 1, 'tree'), (0, 2, 'tree'), (1, 2, 'level')] + >>> list(nx.bfs_labeled_edges(G, [0, 1])) + [(0, 1, 'level'), (0, 2, 'tree'), (1, 2, 'forward')] + """ + if sources in G: + sources = [sources] + + neighbors = G._adj + directed = G.is_directed() + visited = set() + visit = visited.discard if directed else visited.add + # We use visited in a negative sense, so the visited set stays empty for the + # directed case and level edges are reported on their first occurrence in + # the undirected case. Note our use of visited.discard -- this is built-in + # thus somewhat faster than a python-defined def nop(x): pass + depth = {s: 0 for s in sources} + queue = deque(depth.items()) + push = queue.append + pop = queue.popleft + while queue: + u, du = pop() + for v in neighbors[u]: + if v not in depth: + depth[v] = dv = du + 1 + push((v, dv)) + yield u, v, TREE_EDGE + else: + dv = depth[v] + if du == dv: + if v not in visited: + yield u, v, LEVEL_EDGE + elif du < dv: + yield u, v, FORWARD_EDGE + elif directed: + yield u, v, REVERSE_EDGE + visit(u) + + +@nx._dispatchable +def descendants_at_distance(G, source, distance): + """Returns all nodes at a fixed `distance` from `source` in `G`. + + Parameters + ---------- + G : NetworkX graph + A graph + source : node in `G` + distance : the distance of the wanted nodes from `source` + + Returns + ------- + set() + The descendants of `source` in `G` at the given `distance` from `source` + + Examples + -------- + >>> G = nx.path_graph(5) + >>> nx.descendants_at_distance(G, 2, 2) + {0, 4} + >>> H = nx.DiGraph() + >>> H.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)]) + >>> nx.descendants_at_distance(H, 0, 2) + {3, 4, 5, 6} + >>> nx.descendants_at_distance(H, 5, 0) + {5} + >>> nx.descendants_at_distance(H, 5, 1) + set() + """ + if source not in G: + raise nx.NetworkXError(f"The node {source} is not in the graph.") + + bfs_generator = nx.bfs_layers(G, source) + for i, layer in enumerate(bfs_generator): + if i == distance: + return set(layer) + return set() diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/depth_first_search.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/depth_first_search.py new file mode 100644 index 0000000000000000000000000000000000000000..5bac5ecfd1cbefcba5707cac2885ef32987ee98b --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/depth_first_search.py @@ -0,0 +1,529 @@ +"""Basic algorithms for depth-first searching the nodes of a graph.""" + +from collections import defaultdict + +import networkx as nx + +__all__ = [ + "dfs_edges", + "dfs_tree", + "dfs_predecessors", + "dfs_successors", + "dfs_preorder_nodes", + "dfs_postorder_nodes", + "dfs_labeled_edges", +] + + +@nx._dispatchable +def dfs_edges(G, source=None, depth_limit=None, *, sort_neighbors=None): + """Iterate over edges in a depth-first-search (DFS). + + Perform a depth-first-search over the nodes of `G` and yield + the edges in order. This may not generate all edges in `G` + (see `~networkx.algorithms.traversal.edgedfs.edge_dfs`). + + Parameters + ---------- + G : NetworkX graph + + source : node, optional + Specify starting node for depth-first search and yield edges in + the component reachable from source. + + depth_limit : int, optional (default=len(G)) + Specify the maximum search depth. + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Yields + ------ + edge: 2-tuple of nodes + Yields edges resulting from the depth-first-search. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> list(nx.dfs_edges(G, source=0)) + [(0, 1), (1, 2), (2, 3), (3, 4)] + >>> list(nx.dfs_edges(G, source=0, depth_limit=2)) + [(0, 1), (1, 2)] + + Notes + ----- + If a source is not specified then a source is chosen arbitrarily and + repeatedly until all components in the graph are searched. + + The implementation of this function is adapted from David Eppstein's + depth-first search function in PADS [1]_, with modifications + to allow depth limits based on the Wikipedia article + "Depth-limited search" [2]_. + + See Also + -------- + dfs_preorder_nodes + dfs_postorder_nodes + dfs_labeled_edges + :func:`~networkx.algorithms.traversal.edgedfs.edge_dfs` + :func:`~networkx.algorithms.traversal.breadth_first_search.bfs_edges` + + References + ---------- + .. [1] http://www.ics.uci.edu/~eppstein/PADS + .. [2] https://en.wikipedia.org/wiki/Depth-limited_search + """ + if source is None: + # edges for all components + nodes = G + else: + # edges for components with source + nodes = [source] + if depth_limit is None: + depth_limit = len(G) + + get_children = ( + G.neighbors + if sort_neighbors is None + else lambda n: iter(sort_neighbors(G.neighbors(n))) + ) + + visited = set() + for start in nodes: + if start in visited: + continue + visited.add(start) + stack = [(start, get_children(start))] + depth_now = 1 + while stack: + parent, children = stack[-1] + for child in children: + if child not in visited: + yield parent, child + visited.add(child) + if depth_now < depth_limit: + stack.append((child, get_children(child))) + depth_now += 1 + break + else: + stack.pop() + depth_now -= 1 + + +@nx._dispatchable(returns_graph=True) +def dfs_tree(G, source=None, depth_limit=None, *, sort_neighbors=None): + """Returns oriented tree constructed from a depth-first-search from source. + + Parameters + ---------- + G : NetworkX graph + + source : node, optional + Specify starting node for depth-first search. + + depth_limit : int, optional (default=len(G)) + Specify the maximum search depth. + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Returns + ------- + T : NetworkX DiGraph + An oriented tree + + Examples + -------- + >>> G = nx.path_graph(5) + >>> T = nx.dfs_tree(G, source=0, depth_limit=2) + >>> list(T.edges()) + [(0, 1), (1, 2)] + >>> T = nx.dfs_tree(G, source=0) + >>> list(T.edges()) + [(0, 1), (1, 2), (2, 3), (3, 4)] + + See Also + -------- + dfs_preorder_nodes + dfs_postorder_nodes + dfs_labeled_edges + :func:`~networkx.algorithms.traversal.edgedfs.edge_dfs` + :func:`~networkx.algorithms.traversal.breadth_first_search.bfs_tree` + """ + T = nx.DiGraph() + if source is None: + T.add_nodes_from(G) + else: + T.add_node(source) + T.add_edges_from(dfs_edges(G, source, depth_limit, sort_neighbors=sort_neighbors)) + return T + + +@nx._dispatchable +def dfs_predecessors(G, source=None, depth_limit=None, *, sort_neighbors=None): + """Returns dictionary of predecessors in depth-first-search from source. + + Parameters + ---------- + G : NetworkX graph + + source : node, optional + Specify starting node for depth-first search. + Note that you will get predecessors for all nodes in the + component containing `source`. This input only specifies + where the DFS starts. + + depth_limit : int, optional (default=len(G)) + Specify the maximum search depth. + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Returns + ------- + pred: dict + A dictionary with nodes as keys and predecessor nodes as values. + + Examples + -------- + >>> G = nx.path_graph(4) + >>> nx.dfs_predecessors(G, source=0) + {1: 0, 2: 1, 3: 2} + >>> nx.dfs_predecessors(G, source=0, depth_limit=2) + {1: 0, 2: 1} + + Notes + ----- + If a source is not specified then a source is chosen arbitrarily and + repeatedly until all components in the graph are searched. + + The implementation of this function is adapted from David Eppstein's + depth-first search function in `PADS`_, with modifications + to allow depth limits based on the Wikipedia article + "`Depth-limited search`_". + + .. _PADS: http://www.ics.uci.edu/~eppstein/PADS + .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + dfs_preorder_nodes + dfs_postorder_nodes + dfs_labeled_edges + :func:`~networkx.algorithms.traversal.edgedfs.edge_dfs` + :func:`~networkx.algorithms.traversal.breadth_first_search.bfs_tree` + """ + return { + t: s + for s, t in dfs_edges(G, source, depth_limit, sort_neighbors=sort_neighbors) + } + + +@nx._dispatchable +def dfs_successors(G, source=None, depth_limit=None, *, sort_neighbors=None): + """Returns dictionary of successors in depth-first-search from source. + + Parameters + ---------- + G : NetworkX graph + + source : node, optional + Specify starting node for depth-first search. + Note that you will get successors for all nodes in the + component containing `source`. This input only specifies + where the DFS starts. + + depth_limit : int, optional (default=len(G)) + Specify the maximum search depth. + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Returns + ------- + succ: dict + A dictionary with nodes as keys and list of successor nodes as values. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> nx.dfs_successors(G, source=0) + {0: [1], 1: [2], 2: [3], 3: [4]} + >>> nx.dfs_successors(G, source=0, depth_limit=2) + {0: [1], 1: [2]} + + Notes + ----- + If a source is not specified then a source is chosen arbitrarily and + repeatedly until all components in the graph are searched. + + The implementation of this function is adapted from David Eppstein's + depth-first search function in `PADS`_, with modifications + to allow depth limits based on the Wikipedia article + "`Depth-limited search`_". + + .. _PADS: http://www.ics.uci.edu/~eppstein/PADS + .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + dfs_preorder_nodes + dfs_postorder_nodes + dfs_labeled_edges + :func:`~networkx.algorithms.traversal.edgedfs.edge_dfs` + :func:`~networkx.algorithms.traversal.breadth_first_search.bfs_tree` + """ + d = defaultdict(list) + for s, t in dfs_edges( + G, + source=source, + depth_limit=depth_limit, + sort_neighbors=sort_neighbors, + ): + d[s].append(t) + return dict(d) + + +@nx._dispatchable +def dfs_postorder_nodes(G, source=None, depth_limit=None, *, sort_neighbors=None): + """Generate nodes in a depth-first-search post-ordering starting at source. + + Parameters + ---------- + G : NetworkX graph + + source : node, optional + Specify starting node for depth-first search. + + depth_limit : int, optional (default=len(G)) + Specify the maximum search depth. + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Returns + ------- + nodes: generator + A generator of nodes in a depth-first-search post-ordering. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> list(nx.dfs_postorder_nodes(G, source=0)) + [4, 3, 2, 1, 0] + >>> list(nx.dfs_postorder_nodes(G, source=0, depth_limit=2)) + [1, 0] + + Notes + ----- + If a source is not specified then a source is chosen arbitrarily and + repeatedly until all components in the graph are searched. + + The implementation of this function is adapted from David Eppstein's + depth-first search function in `PADS`_, with modifications + to allow depth limits based on the Wikipedia article + "`Depth-limited search`_". + + .. _PADS: http://www.ics.uci.edu/~eppstein/PADS + .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + dfs_edges + dfs_preorder_nodes + dfs_labeled_edges + :func:`~networkx.algorithms.traversal.edgedfs.edge_dfs` + :func:`~networkx.algorithms.traversal.breadth_first_search.bfs_tree` + """ + edges = nx.dfs_labeled_edges( + G, source=source, depth_limit=depth_limit, sort_neighbors=sort_neighbors + ) + return (v for u, v, d in edges if d == "reverse") + + +@nx._dispatchable +def dfs_preorder_nodes(G, source=None, depth_limit=None, *, sort_neighbors=None): + """Generate nodes in a depth-first-search pre-ordering starting at source. + + Parameters + ---------- + G : NetworkX graph + + source : node, optional + Specify starting node for depth-first search and return nodes in + the component reachable from source. + + depth_limit : int, optional (default=len(G)) + Specify the maximum search depth. + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Returns + ------- + nodes: generator + A generator of nodes in a depth-first-search pre-ordering. + + Examples + -------- + >>> G = nx.path_graph(5) + >>> list(nx.dfs_preorder_nodes(G, source=0)) + [0, 1, 2, 3, 4] + >>> list(nx.dfs_preorder_nodes(G, source=0, depth_limit=2)) + [0, 1, 2] + + Notes + ----- + If a source is not specified then a source is chosen arbitrarily and + repeatedly until all components in the graph are searched. + + The implementation of this function is adapted from David Eppstein's + depth-first search function in `PADS`_, with modifications + to allow depth limits based on the Wikipedia article + "`Depth-limited search`_". + + .. _PADS: http://www.ics.uci.edu/~eppstein/PADS + .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + dfs_edges + dfs_postorder_nodes + dfs_labeled_edges + :func:`~networkx.algorithms.traversal.breadth_first_search.bfs_edges` + """ + edges = nx.dfs_labeled_edges( + G, source=source, depth_limit=depth_limit, sort_neighbors=sort_neighbors + ) + return (v for u, v, d in edges if d == "forward") + + +@nx._dispatchable +def dfs_labeled_edges(G, source=None, depth_limit=None, *, sort_neighbors=None): + """Iterate over edges in a depth-first-search (DFS) labeled by type. + + Parameters + ---------- + G : NetworkX graph + + source : node, optional + Specify starting node for depth-first search and return edges in + the component reachable from source. + + depth_limit : int, optional (default=len(G)) + Specify the maximum search depth. + + sort_neighbors : function (default=None) + A function that takes an iterator over nodes as the input, and + returns an iterable of the same nodes with a custom ordering. + For example, `sorted` will sort the nodes in increasing order. + + Returns + ------- + edges: generator + A generator of triples of the form (*u*, *v*, *d*), where (*u*, + *v*) is the edge being explored in the depth-first search and *d* + is one of the strings 'forward', 'nontree', 'reverse', or 'reverse-depth_limit'. + A 'forward' edge is one in which *u* has been visited but *v* has + not. A 'nontree' edge is one in which both *u* and *v* have been + visited but the edge is not in the DFS tree. A 'reverse' edge is + one in which both *u* and *v* have been visited and the edge is in + the DFS tree. When the `depth_limit` is reached via a 'forward' edge, + a 'reverse' edge is immediately generated rather than the subtree + being explored. To indicate this flavor of 'reverse' edge, the string + yielded is 'reverse-depth_limit'. + + Examples + -------- + + The labels reveal the complete transcript of the depth-first search + algorithm in more detail than, for example, :func:`dfs_edges`:: + + >>> from pprint import pprint + >>> + >>> G = nx.DiGraph([(0, 1), (1, 2), (2, 1)]) + >>> pprint(list(nx.dfs_labeled_edges(G, source=0))) + [(0, 0, 'forward'), + (0, 1, 'forward'), + (1, 2, 'forward'), + (2, 1, 'nontree'), + (1, 2, 'reverse'), + (0, 1, 'reverse'), + (0, 0, 'reverse')] + + Notes + ----- + If a source is not specified then a source is chosen arbitrarily and + repeatedly until all components in the graph are searched. + + The implementation of this function is adapted from David Eppstein's + depth-first search function in `PADS`_, with modifications + to allow depth limits based on the Wikipedia article + "`Depth-limited search`_". + + .. _PADS: http://www.ics.uci.edu/~eppstein/PADS + .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search + + See Also + -------- + dfs_edges + dfs_preorder_nodes + dfs_postorder_nodes + """ + # Based on http://www.ics.uci.edu/~eppstein/PADS/DFS.py + # by D. Eppstein, July 2004. + if source is None: + # edges for all components + nodes = G + else: + # edges for components with source + nodes = [source] + if depth_limit is None: + depth_limit = len(G) + + get_children = ( + G.neighbors + if sort_neighbors is None + else lambda n: iter(sort_neighbors(G.neighbors(n))) + ) + + visited = set() + for start in nodes: + if start in visited: + continue + yield start, start, "forward" + visited.add(start) + stack = [(start, get_children(start))] + depth_now = 1 + while stack: + parent, children = stack[-1] + for child in children: + if child in visited: + yield parent, child, "nontree" + else: + yield parent, child, "forward" + visited.add(child) + if depth_now < depth_limit: + stack.append((child, iter(get_children(child)))) + depth_now += 1 + break + else: + yield parent, child, "reverse-depth_limit" + else: + stack.pop() + depth_now -= 1 + if stack: + yield stack[-1][0], parent, "reverse" + yield start, start, "reverse" diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/edgebfs.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/edgebfs.py new file mode 100644 index 0000000000000000000000000000000000000000..6320ddc2a683187136103dd1cb18036ae3088d03 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/edgebfs.py @@ -0,0 +1,178 @@ +""" +============================= +Breadth First Search on Edges +============================= + +Algorithms for a breadth-first traversal of edges in a graph. + +""" + +from collections import deque + +import networkx as nx + +FORWARD = "forward" +REVERSE = "reverse" + +__all__ = ["edge_bfs"] + + +@nx._dispatchable +def edge_bfs(G, source=None, orientation=None): + """A directed, breadth-first-search of edges in `G`, beginning at `source`. + + Yield the edges of G in a breadth-first-search order continuing until + all edges are generated. + + 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. + + Yields + ------ + edge : directed edge + A directed edge indicating the path taken by the breadth-first-search. + For graphs, `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, `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. + + Examples + -------- + >>> nodes = [0, 1, 2, 3] + >>> edges = [(0, 1), (1, 0), (1, 0), (2, 0), (2, 1), (3, 1)] + + >>> list(nx.edge_bfs(nx.Graph(edges), nodes)) + [(0, 1), (0, 2), (1, 2), (1, 3)] + + >>> list(nx.edge_bfs(nx.DiGraph(edges), nodes)) + [(0, 1), (1, 0), (2, 0), (2, 1), (3, 1)] + + >>> list(nx.edge_bfs(nx.MultiGraph(edges), nodes)) + [(0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 2, 0), (1, 2, 0), (1, 3, 0)] + + >>> list(nx.edge_bfs(nx.MultiDiGraph(edges), nodes)) + [(0, 1, 0), (1, 0, 0), (1, 0, 1), (2, 0, 0), (2, 1, 0), (3, 1, 0)] + + >>> list(nx.edge_bfs(nx.DiGraph(edges), nodes, orientation="ignore")) + [(0, 1, 'forward'), (1, 0, 'reverse'), (2, 0, 'reverse'), (2, 1, 'reverse'), (3, 1, 'reverse')] + + >>> list(nx.edge_bfs(nx.MultiDiGraph(edges), nodes, orientation="ignore")) + [(0, 1, 0, 'forward'), (1, 0, 0, 'reverse'), (1, 0, 1, 'reverse'), (2, 0, 0, 'reverse'), (2, 1, 0, 'reverse'), (3, 1, 0, 'reverse')] + + Notes + ----- + The goal of this function is to visit edges. It differs from the more + familiar breadth-first-search of nodes, as provided by + :func:`networkx.algorithms.traversal.breadth_first_search.bfs_edges`, in + that it does not stop once every node has been visited. In a directed graph + with edges [(0, 1), (1, 2), (2, 1)], the edge (2, 1) would not be visited + if not for the functionality provided by this function. + + The naming of this function is very similar to bfs_edges. The difference + is that 'edge_bfs' yields edges even if they extend back to an already + explored node while 'bfs_edges' yields the edges of the tree that results + from a breadth-first-search (BFS) so no edges are reported if they extend + to already explored nodes. That means 'edge_bfs' reports all edges while + 'bfs_edges' only report those traversed by a node-based BFS. Yet another + description is that 'bfs_edges' reports the edges traversed during BFS + while 'edge_bfs' reports all edges in the order they are explored. + + See Also + -------- + bfs_edges + bfs_tree + edge_dfs + + """ + nodes = list(G.nbunch_iter(source)) + if not nodes: + return + + directed = G.is_directed() + kwds = {"data": False} + if G.is_multigraph() is True: + kwds["keys"] = True + + # set up edge lookup + if orientation is None: + + def edges_from(node): + return iter(G.edges(node, **kwds)) + + elif not directed or orientation == "original": + + def edges_from(node): + for e in G.edges(node, **kwds): + yield e + (FORWARD,) + + elif orientation == "reverse": + + def edges_from(node): + for e in G.in_edges(node, **kwds): + yield e + (REVERSE,) + + elif orientation == "ignore": + + def edges_from(node): + for e in G.edges(node, **kwds): + yield e + (FORWARD,) + for e in G.in_edges(node, **kwds): + yield e + (REVERSE,) + + else: + raise nx.NetworkXError("invalid orientation argument.") + + if directed: + neighbors = G.successors + + def edge_id(edge): + # remove direction indicator + return edge[:-1] if orientation is not None else edge + + else: + neighbors = G.neighbors + + def edge_id(edge): + return (frozenset(edge[:2]),) + edge[2:] + + check_reverse = directed and orientation in ("reverse", "ignore") + + # start BFS + visited_nodes = set(nodes) + visited_edges = set() + queue = deque([(n, edges_from(n)) for n in nodes]) + while queue: + parent, children_edges = queue.popleft() + for edge in children_edges: + if check_reverse and edge[-1] == REVERSE: + child = edge[0] + else: + child = edge[1] + if child not in visited_nodes: + visited_nodes.add(child) + queue.append((child, edges_from(child))) + edgeid = edge_id(edge) + if edgeid not in visited_edges: + visited_edges.add(edgeid) + yield edge diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/edgedfs.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/edgedfs.py new file mode 100644 index 0000000000000000000000000000000000000000..8f657f39fdd8a24660772d7cc3cef0f641ed61c5 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/edgedfs.py @@ -0,0 +1,176 @@ +""" +=========================== +Depth First Search on Edges +=========================== + +Algorithms for a depth-first traversal of edges in a graph. + +""" + +import networkx as nx + +FORWARD = "forward" +REVERSE = "reverse" + +__all__ = ["edge_dfs"] + + +@nx._dispatchable +def edge_dfs(G, source=None, orientation=None): + """A directed, depth-first-search of edges in `G`, beginning at `source`. + + Yield the edges of G in a depth-first-search order continuing until + all edges are generated. + + 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. + + Yields + ------ + edge : directed edge + A directed edge indicating the path taken by the depth-first traversal. + For graphs, `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, `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. + + Examples + -------- + >>> nodes = [0, 1, 2, 3] + >>> edges = [(0, 1), (1, 0), (1, 0), (2, 1), (3, 1)] + + >>> list(nx.edge_dfs(nx.Graph(edges), nodes)) + [(0, 1), (1, 2), (1, 3)] + + >>> list(nx.edge_dfs(nx.DiGraph(edges), nodes)) + [(0, 1), (1, 0), (2, 1), (3, 1)] + + >>> list(nx.edge_dfs(nx.MultiGraph(edges), nodes)) + [(0, 1, 0), (1, 0, 1), (0, 1, 2), (1, 2, 0), (1, 3, 0)] + + >>> list(nx.edge_dfs(nx.MultiDiGraph(edges), nodes)) + [(0, 1, 0), (1, 0, 0), (1, 0, 1), (2, 1, 0), (3, 1, 0)] + + >>> list(nx.edge_dfs(nx.DiGraph(edges), nodes, orientation="ignore")) + [(0, 1, 'forward'), (1, 0, 'forward'), (2, 1, 'reverse'), (3, 1, 'reverse')] + + >>> list(nx.edge_dfs(nx.MultiDiGraph(edges), nodes, orientation="ignore")) + [(0, 1, 0, 'forward'), (1, 0, 0, 'forward'), (1, 0, 1, 'reverse'), (2, 1, 0, 'reverse'), (3, 1, 0, 'reverse')] + + Notes + ----- + The goal of this function is to visit edges. It differs from the more + familiar depth-first traversal of nodes, as provided by + :func:`~networkx.algorithms.traversal.depth_first_search.dfs_edges`, in + that it does not stop once every node has been visited. In a directed graph + with edges [(0, 1), (1, 2), (2, 1)], the edge (2, 1) would not be visited + if not for the functionality provided by this function. + + See Also + -------- + :func:`~networkx.algorithms.traversal.depth_first_search.dfs_edges` + + """ + nodes = list(G.nbunch_iter(source)) + if not nodes: + return + + directed = G.is_directed() + kwds = {"data": False} + if G.is_multigraph() is True: + kwds["keys"] = True + + # set up edge lookup + if orientation is None: + + def edges_from(node): + return iter(G.edges(node, **kwds)) + + elif not directed or orientation == "original": + + def edges_from(node): + for e in G.edges(node, **kwds): + yield e + (FORWARD,) + + elif orientation == "reverse": + + def edges_from(node): + for e in G.in_edges(node, **kwds): + yield e + (REVERSE,) + + elif orientation == "ignore": + + def edges_from(node): + for e in G.edges(node, **kwds): + yield e + (FORWARD,) + for e in G.in_edges(node, **kwds): + yield e + (REVERSE,) + + else: + raise nx.NetworkXError("invalid orientation argument.") + + # set up formation of edge_id to easily look up if edge already returned + if directed: + + def edge_id(edge): + # remove direction indicator + return edge[:-1] if orientation is not None else edge + + else: + + def edge_id(edge): + # single id for undirected requires frozenset on nodes + return (frozenset(edge[:2]),) + edge[2:] + + # Basic setup + check_reverse = directed and orientation in ("reverse", "ignore") + + visited_edges = set() + visited_nodes = set() + edges = {} + + # start DFS + for start_node in nodes: + stack = [start_node] + while stack: + current_node = stack[-1] + if current_node not in visited_nodes: + edges[current_node] = edges_from(current_node) + visited_nodes.add(current_node) + + try: + edge = next(edges[current_node]) + except StopIteration: + # No more edges from the current node. + stack.pop() + else: + edgeid = edge_id(edge) + if edgeid not in visited_edges: + visited_edges.add(edgeid) + # Mark the traversed "to" node as to-be-explored. + if check_reverse and edge[-1] == REVERSE: + stack.append(edge[0]) + else: + stack.append(edge[1]) + yield edge diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__init__.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/__init__.cpython-311.pyc b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/__init__.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..4e5cecb8090c81ca1a9efbcfa24f07e1d761650a Binary files /dev/null and b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/__init__.cpython-311.pyc differ diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_beamsearch.cpython-311.pyc b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_beamsearch.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..c874bd96f58315ff8d24b9186ae77692ba05db34 Binary files /dev/null and b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_beamsearch.cpython-311.pyc differ diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_bfs.cpython-311.pyc b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_bfs.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..15ff21467d22dc29126f88be3f4cc2943c9acdc0 Binary files /dev/null and b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_bfs.cpython-311.pyc differ diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_dfs.cpython-311.pyc b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_dfs.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..392e0371bb08a95c87026aa5c5316b8f921dda5c Binary files /dev/null and b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_dfs.cpython-311.pyc differ diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_edgebfs.cpython-311.pyc b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_edgebfs.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..fabb5137d11f4de7ed7fa7da9748e0ad291bd6ff Binary files /dev/null and b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_edgebfs.cpython-311.pyc differ diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_edgedfs.cpython-311.pyc b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_edgedfs.cpython-311.pyc new file mode 100644 index 0000000000000000000000000000000000000000..06bad84a8c0370564a0da3b91cde9bc51a1777ec Binary files /dev/null and b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/__pycache__/test_edgedfs.cpython-311.pyc differ diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_beamsearch.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_beamsearch.py new file mode 100644 index 0000000000000000000000000000000000000000..049f116b62fb595977d5ed94d01b9c15baf17fb3 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_beamsearch.py @@ -0,0 +1,25 @@ +"""Unit tests for the beam search functions.""" + +import pytest + +import networkx as nx + + +def test_narrow(): + """Tests that a narrow beam width may cause an incomplete search.""" + # In this search, we enqueue only the neighbor 3 at the first + # step, then only the neighbor 2 at the second step. Once at + # node 2, the search chooses node 3, since it has a higher value + # than node 1, but node 3 has already been visited, so the + # search terminates. + G = nx.cycle_graph(4) + edges = nx.bfs_beam_edges(G, source=0, value=lambda n: n, width=1) + assert list(edges) == [(0, 3), (3, 2)] + + +@pytest.mark.parametrize("width", (2, None)) +def test_wide(width): + """All nodes are searched when `width` is None or >= max degree""" + G = nx.cycle_graph(4) + edges = nx.bfs_beam_edges(G, source=0, value=lambda n: n, width=width) + assert list(edges) == [(0, 3), (0, 1), (3, 2)] diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_bfs.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_bfs.py new file mode 100644 index 0000000000000000000000000000000000000000..fcfbbc68dc113fe3363233a98faa3e99d44df689 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_bfs.py @@ -0,0 +1,203 @@ +from functools import partial + +import pytest + +import networkx as nx + + +class TestBFS: + @classmethod + def setup_class(cls): + # simple graph + G = nx.Graph() + G.add_edges_from([(0, 1), (1, 2), (1, 3), (2, 4), (3, 4)]) + cls.G = G + + def test_successor(self): + assert dict(nx.bfs_successors(self.G, source=0)) == {0: [1], 1: [2, 3], 2: [4]} + + def test_predecessor(self): + assert dict(nx.bfs_predecessors(self.G, source=0)) == {1: 0, 2: 1, 3: 1, 4: 2} + + def test_bfs_tree(self): + T = nx.bfs_tree(self.G, source=0) + assert sorted(T.nodes()) == sorted(self.G.nodes()) + assert sorted(T.edges()) == [(0, 1), (1, 2), (1, 3), (2, 4)] + + def test_bfs_edges(self): + edges = nx.bfs_edges(self.G, source=0) + assert list(edges) == [(0, 1), (1, 2), (1, 3), (2, 4)] + + def test_bfs_edges_reverse(self): + D = nx.DiGraph() + D.add_edges_from([(0, 1), (1, 2), (1, 3), (2, 4), (3, 4)]) + edges = nx.bfs_edges(D, source=4, reverse=True) + assert list(edges) == [(4, 2), (4, 3), (2, 1), (1, 0)] + + def test_bfs_edges_sorting(self): + D = nx.DiGraph() + D.add_edges_from([(0, 1), (0, 2), (1, 4), (1, 3), (2, 5)]) + sort_desc = partial(sorted, reverse=True) + edges_asc = nx.bfs_edges(D, source=0, sort_neighbors=sorted) + edges_desc = nx.bfs_edges(D, source=0, sort_neighbors=sort_desc) + assert list(edges_asc) == [(0, 1), (0, 2), (1, 3), (1, 4), (2, 5)] + assert list(edges_desc) == [(0, 2), (0, 1), (2, 5), (1, 4), (1, 3)] + + def test_bfs_tree_isolates(self): + G = nx.Graph() + G.add_node(1) + G.add_node(2) + T = nx.bfs_tree(G, source=1) + assert sorted(T.nodes()) == [1] + assert sorted(T.edges()) == [] + + def test_bfs_layers(self): + expected = { + 0: [0], + 1: [1], + 2: [2, 3], + 3: [4], + } + assert dict(enumerate(nx.bfs_layers(self.G, sources=[0]))) == expected + assert dict(enumerate(nx.bfs_layers(self.G, sources=0))) == expected + + def test_bfs_layers_missing_source(self): + with pytest.raises(nx.NetworkXError): + next(nx.bfs_layers(self.G, sources="abc")) + with pytest.raises(nx.NetworkXError): + next(nx.bfs_layers(self.G, sources=["abc"])) + + def test_descendants_at_distance(self): + for distance, descendants in enumerate([{0}, {1}, {2, 3}, {4}]): + assert nx.descendants_at_distance(self.G, 0, distance) == descendants + + def test_descendants_at_distance_missing_source(self): + with pytest.raises(nx.NetworkXError): + nx.descendants_at_distance(self.G, "abc", 0) + + def test_bfs_labeled_edges_directed(self): + D = nx.cycle_graph(5, create_using=nx.DiGraph) + expected = [ + (0, 1, "tree"), + (1, 2, "tree"), + (2, 3, "tree"), + (3, 4, "tree"), + (4, 0, "reverse"), + ] + answer = list(nx.bfs_labeled_edges(D, 0)) + assert expected == answer + + D.add_edge(4, 4) + expected.append((4, 4, "level")) + answer = list(nx.bfs_labeled_edges(D, 0)) + assert expected == answer + + D.add_edge(0, 2) + D.add_edge(1, 5) + D.add_edge(2, 5) + D.remove_edge(4, 4) + expected = [ + (0, 1, "tree"), + (0, 2, "tree"), + (1, 2, "level"), + (1, 5, "tree"), + (2, 3, "tree"), + (2, 5, "forward"), + (3, 4, "tree"), + (4, 0, "reverse"), + ] + answer = list(nx.bfs_labeled_edges(D, 0)) + assert expected == answer + + G = D.to_undirected() + G.add_edge(4, 4) + expected = [ + (0, 1, "tree"), + (0, 2, "tree"), + (0, 4, "tree"), + (1, 2, "level"), + (1, 5, "tree"), + (2, 3, "tree"), + (2, 5, "forward"), + (4, 3, "forward"), + (4, 4, "level"), + ] + answer = list(nx.bfs_labeled_edges(G, 0)) + assert expected == answer + + +class TestBreadthLimitedSearch: + @classmethod + def setup_class(cls): + # a tree + G = nx.Graph() + nx.add_path(G, [0, 1, 2, 3, 4, 5, 6]) + nx.add_path(G, [2, 7, 8, 9, 10]) + cls.G = G + # a disconnected graph + D = nx.Graph() + D.add_edges_from([(0, 1), (2, 3)]) + nx.add_path(D, [2, 7, 8, 9, 10]) + cls.D = D + + def test_limited_bfs_successor(self): + assert dict(nx.bfs_successors(self.G, source=1, depth_limit=3)) == { + 1: [0, 2], + 2: [3, 7], + 3: [4], + 7: [8], + } + result = { + n: sorted(s) for n, s in nx.bfs_successors(self.D, source=7, depth_limit=2) + } + assert result == {8: [9], 2: [3], 7: [2, 8]} + + def test_limited_bfs_predecessor(self): + assert dict(nx.bfs_predecessors(self.G, source=1, depth_limit=3)) == { + 0: 1, + 2: 1, + 3: 2, + 4: 3, + 7: 2, + 8: 7, + } + assert dict(nx.bfs_predecessors(self.D, source=7, depth_limit=2)) == { + 2: 7, + 3: 2, + 8: 7, + 9: 8, + } + + def test_limited_bfs_tree(self): + T = nx.bfs_tree(self.G, source=3, depth_limit=1) + assert sorted(T.edges()) == [(3, 2), (3, 4)] + + def test_limited_bfs_edges(self): + edges = nx.bfs_edges(self.G, source=9, depth_limit=4) + assert list(edges) == [(9, 8), (9, 10), (8, 7), (7, 2), (2, 1), (2, 3)] + + def test_limited_bfs_layers(self): + assert dict(enumerate(nx.bfs_layers(self.G, sources=[0]))) == { + 0: [0], + 1: [1], + 2: [2], + 3: [3, 7], + 4: [4, 8], + 5: [5, 9], + 6: [6, 10], + } + assert dict(enumerate(nx.bfs_layers(self.D, sources=2))) == { + 0: [2], + 1: [3, 7], + 2: [8], + 3: [9], + 4: [10], + } + + def test_limited_descendants_at_distance(self): + for distance, descendants in enumerate( + [{0}, {1}, {2}, {3, 7}, {4, 8}, {5, 9}, {6, 10}] + ): + assert nx.descendants_at_distance(self.G, 0, distance) == descendants + for distance, descendants in enumerate([{2}, {3, 7}, {8}, {9}, {10}]): + assert nx.descendants_at_distance(self.D, 2, distance) == descendants diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_dfs.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_dfs.py new file mode 100644 index 0000000000000000000000000000000000000000..e43d7d61629838aedc01b0a1624e018c0268fe11 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_dfs.py @@ -0,0 +1,305 @@ +import networkx as nx + + +class TestDFS: + @classmethod + def setup_class(cls): + # simple graph + G = nx.Graph() + G.add_edges_from([(0, 1), (1, 2), (1, 3), (2, 4), (3, 0), (0, 4)]) + cls.G = G + # simple graph, disconnected + D = nx.Graph() + D.add_edges_from([(0, 1), (2, 3)]) + cls.D = D + + def test_preorder_nodes(self): + assert list(nx.dfs_preorder_nodes(self.G, source=0)) == [0, 1, 2, 4, 3] + assert list(nx.dfs_preorder_nodes(self.D)) == [0, 1, 2, 3] + assert list(nx.dfs_preorder_nodes(self.D, source=2)) == [2, 3] + + def test_postorder_nodes(self): + assert list(nx.dfs_postorder_nodes(self.G, source=0)) == [4, 2, 3, 1, 0] + assert list(nx.dfs_postorder_nodes(self.D)) == [1, 0, 3, 2] + assert list(nx.dfs_postorder_nodes(self.D, source=0)) == [1, 0] + + def test_successor(self): + assert nx.dfs_successors(self.G, source=0) == {0: [1], 1: [2, 3], 2: [4]} + assert nx.dfs_successors(self.G, source=1) == {0: [3, 4], 1: [0], 4: [2]} + assert nx.dfs_successors(self.D) == {0: [1], 2: [3]} + assert nx.dfs_successors(self.D, source=1) == {1: [0]} + + def test_predecessor(self): + assert nx.dfs_predecessors(self.G, source=0) == {1: 0, 2: 1, 3: 1, 4: 2} + assert nx.dfs_predecessors(self.D) == {1: 0, 3: 2} + + def test_dfs_tree(self): + exp_nodes = sorted(self.G.nodes()) + exp_edges = [(0, 1), (1, 2), (1, 3), (2, 4)] + # Search from first node + T = nx.dfs_tree(self.G, source=0) + assert sorted(T.nodes()) == exp_nodes + assert sorted(T.edges()) == exp_edges + # Check source=None + T = nx.dfs_tree(self.G, source=None) + assert sorted(T.nodes()) == exp_nodes + assert sorted(T.edges()) == exp_edges + # Check source=None is the default + T = nx.dfs_tree(self.G) + assert sorted(T.nodes()) == exp_nodes + assert sorted(T.edges()) == exp_edges + + def test_dfs_edges(self): + edges = nx.dfs_edges(self.G, source=0) + assert list(edges) == [(0, 1), (1, 2), (2, 4), (1, 3)] + edges = nx.dfs_edges(self.D) + assert list(edges) == [(0, 1), (2, 3)] + + def test_dfs_edges_sorting(self): + G = nx.Graph([(0, 1), (1, 2), (1, 3), (2, 4), (3, 0), (0, 4)]) + edges_asc = nx.dfs_edges(G, source=0, sort_neighbors=sorted) + sorted_desc = lambda x: sorted(x, reverse=True) + edges_desc = nx.dfs_edges(G, source=0, sort_neighbors=sorted_desc) + assert list(edges_asc) == [(0, 1), (1, 2), (2, 4), (1, 3)] + assert list(edges_desc) == [(0, 4), (4, 2), (2, 1), (1, 3)] + + def test_dfs_labeled_edges(self): + edges = list(nx.dfs_labeled_edges(self.G, source=0)) + forward = [(u, v) for (u, v, d) in edges if d == "forward"] + assert forward == [(0, 0), (0, 1), (1, 2), (2, 4), (1, 3)] + assert edges == [ + (0, 0, "forward"), + (0, 1, "forward"), + (1, 0, "nontree"), + (1, 2, "forward"), + (2, 1, "nontree"), + (2, 4, "forward"), + (4, 2, "nontree"), + (4, 0, "nontree"), + (2, 4, "reverse"), + (1, 2, "reverse"), + (1, 3, "forward"), + (3, 1, "nontree"), + (3, 0, "nontree"), + (1, 3, "reverse"), + (0, 1, "reverse"), + (0, 3, "nontree"), + (0, 4, "nontree"), + (0, 0, "reverse"), + ] + + def test_dfs_labeled_edges_sorting(self): + G = nx.Graph([(0, 1), (1, 2), (1, 3), (2, 4), (3, 0), (0, 4)]) + edges_asc = nx.dfs_labeled_edges(G, source=0, sort_neighbors=sorted) + sorted_desc = lambda x: sorted(x, reverse=True) + edges_desc = nx.dfs_labeled_edges(G, source=0, sort_neighbors=sorted_desc) + assert list(edges_asc) == [ + (0, 0, "forward"), + (0, 1, "forward"), + (1, 0, "nontree"), + (1, 2, "forward"), + (2, 1, "nontree"), + (2, 4, "forward"), + (4, 0, "nontree"), + (4, 2, "nontree"), + (2, 4, "reverse"), + (1, 2, "reverse"), + (1, 3, "forward"), + (3, 0, "nontree"), + (3, 1, "nontree"), + (1, 3, "reverse"), + (0, 1, "reverse"), + (0, 3, "nontree"), + (0, 4, "nontree"), + (0, 0, "reverse"), + ] + assert list(edges_desc) == [ + (0, 0, "forward"), + (0, 4, "forward"), + (4, 2, "forward"), + (2, 4, "nontree"), + (2, 1, "forward"), + (1, 3, "forward"), + (3, 1, "nontree"), + (3, 0, "nontree"), + (1, 3, "reverse"), + (1, 2, "nontree"), + (1, 0, "nontree"), + (2, 1, "reverse"), + (4, 2, "reverse"), + (4, 0, "nontree"), + (0, 4, "reverse"), + (0, 3, "nontree"), + (0, 1, "nontree"), + (0, 0, "reverse"), + ] + + def test_dfs_labeled_disconnected_edges(self): + edges = list(nx.dfs_labeled_edges(self.D)) + forward = [(u, v) for (u, v, d) in edges if d == "forward"] + assert forward == [(0, 0), (0, 1), (2, 2), (2, 3)] + assert edges == [ + (0, 0, "forward"), + (0, 1, "forward"), + (1, 0, "nontree"), + (0, 1, "reverse"), + (0, 0, "reverse"), + (2, 2, "forward"), + (2, 3, "forward"), + (3, 2, "nontree"), + (2, 3, "reverse"), + (2, 2, "reverse"), + ] + + def test_dfs_tree_isolates(self): + G = nx.Graph() + G.add_node(1) + G.add_node(2) + T = nx.dfs_tree(G, source=1) + assert sorted(T.nodes()) == [1] + assert sorted(T.edges()) == [] + T = nx.dfs_tree(G, source=None) + assert sorted(T.nodes()) == [1, 2] + assert sorted(T.edges()) == [] + + +class TestDepthLimitedSearch: + @classmethod + def setup_class(cls): + # a tree + G = nx.Graph() + nx.add_path(G, [0, 1, 2, 3, 4, 5, 6]) + nx.add_path(G, [2, 7, 8, 9, 10]) + cls.G = G + # a disconnected graph + D = nx.Graph() + D.add_edges_from([(0, 1), (2, 3)]) + nx.add_path(D, [2, 7, 8, 9, 10]) + cls.D = D + + def test_dls_preorder_nodes(self): + assert list(nx.dfs_preorder_nodes(self.G, source=0, depth_limit=2)) == [0, 1, 2] + assert list(nx.dfs_preorder_nodes(self.D, source=1, depth_limit=2)) == ([1, 0]) + + def test_dls_postorder_nodes(self): + assert list(nx.dfs_postorder_nodes(self.G, source=3, depth_limit=3)) == [ + 1, + 7, + 2, + 5, + 4, + 3, + ] + assert list(nx.dfs_postorder_nodes(self.D, source=2, depth_limit=2)) == ( + [3, 7, 2] + ) + + def test_dls_successor(self): + result = nx.dfs_successors(self.G, source=4, depth_limit=3) + assert {n: set(v) for n, v in result.items()} == { + 2: {1, 7}, + 3: {2}, + 4: {3, 5}, + 5: {6}, + } + result = nx.dfs_successors(self.D, source=7, depth_limit=2) + assert {n: set(v) for n, v in result.items()} == {8: {9}, 2: {3}, 7: {8, 2}} + + def test_dls_predecessor(self): + assert nx.dfs_predecessors(self.G, source=0, depth_limit=3) == { + 1: 0, + 2: 1, + 3: 2, + 7: 2, + } + assert nx.dfs_predecessors(self.D, source=2, depth_limit=3) == { + 8: 7, + 9: 8, + 3: 2, + 7: 2, + } + + def test_dls_tree(self): + T = nx.dfs_tree(self.G, source=3, depth_limit=1) + assert sorted(T.edges()) == [(3, 2), (3, 4)] + + def test_dls_edges(self): + edges = nx.dfs_edges(self.G, source=9, depth_limit=4) + assert list(edges) == [(9, 8), (8, 7), (7, 2), (2, 1), (2, 3), (9, 10)] + + def test_dls_labeled_edges_depth_1(self): + edges = list(nx.dfs_labeled_edges(self.G, source=5, depth_limit=1)) + forward = [(u, v) for (u, v, d) in edges if d == "forward"] + assert forward == [(5, 5), (5, 4), (5, 6)] + # Note: reverse-depth_limit edge types were not reported before gh-6240 + assert edges == [ + (5, 5, "forward"), + (5, 4, "forward"), + (5, 4, "reverse-depth_limit"), + (5, 6, "forward"), + (5, 6, "reverse-depth_limit"), + (5, 5, "reverse"), + ] + + def test_dls_labeled_edges_depth_2(self): + edges = list(nx.dfs_labeled_edges(self.G, source=6, depth_limit=2)) + forward = [(u, v) for (u, v, d) in edges if d == "forward"] + assert forward == [(6, 6), (6, 5), (5, 4)] + assert edges == [ + (6, 6, "forward"), + (6, 5, "forward"), + (5, 4, "forward"), + (5, 4, "reverse-depth_limit"), + (5, 6, "nontree"), + (6, 5, "reverse"), + (6, 6, "reverse"), + ] + + def test_dls_labeled_disconnected_edges(self): + edges = list(nx.dfs_labeled_edges(self.D, depth_limit=1)) + assert edges == [ + (0, 0, "forward"), + (0, 1, "forward"), + (0, 1, "reverse-depth_limit"), + (0, 0, "reverse"), + (2, 2, "forward"), + (2, 3, "forward"), + (2, 3, "reverse-depth_limit"), + (2, 7, "forward"), + (2, 7, "reverse-depth_limit"), + (2, 2, "reverse"), + (8, 8, "forward"), + (8, 7, "nontree"), + (8, 9, "forward"), + (8, 9, "reverse-depth_limit"), + (8, 8, "reverse"), + (10, 10, "forward"), + (10, 9, "nontree"), + (10, 10, "reverse"), + ] + # large depth_limit has no impact + edges = list(nx.dfs_labeled_edges(self.D, depth_limit=19)) + assert edges == [ + (0, 0, "forward"), + (0, 1, "forward"), + (1, 0, "nontree"), + (0, 1, "reverse"), + (0, 0, "reverse"), + (2, 2, "forward"), + (2, 3, "forward"), + (3, 2, "nontree"), + (2, 3, "reverse"), + (2, 7, "forward"), + (7, 2, "nontree"), + (7, 8, "forward"), + (8, 7, "nontree"), + (8, 9, "forward"), + (9, 8, "nontree"), + (9, 10, "forward"), + (10, 9, "nontree"), + (9, 10, "reverse"), + (8, 9, "reverse"), + (7, 8, "reverse"), + (2, 7, "reverse"), + (2, 2, "reverse"), + ] diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_edgebfs.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_edgebfs.py new file mode 100644 index 0000000000000000000000000000000000000000..1bf3fae0bd067dd548281e3382a6125f6e50ee22 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_edgebfs.py @@ -0,0 +1,147 @@ +import pytest + +import networkx as nx +from networkx.algorithms.traversal.edgedfs import FORWARD, REVERSE + + +class TestEdgeBFS: + @classmethod + def setup_class(cls): + cls.nodes = [0, 1, 2, 3] + cls.edges = [(0, 1), (1, 0), (1, 0), (2, 0), (2, 1), (3, 1)] + + def test_empty(self): + G = nx.Graph() + edges = list(nx.edge_bfs(G)) + assert edges == [] + + def test_graph_single_source(self): + G = nx.Graph(self.edges) + G.add_edge(4, 5) + x = list(nx.edge_bfs(G, [0])) + x_ = [(0, 1), (0, 2), (1, 2), (1, 3)] + assert x == x_ + + def test_graph(self): + G = nx.Graph(self.edges) + x = list(nx.edge_bfs(G, self.nodes)) + x_ = [(0, 1), (0, 2), (1, 2), (1, 3)] + assert x == x_ + + def test_digraph(self): + G = nx.DiGraph(self.edges) + x = list(nx.edge_bfs(G, self.nodes)) + x_ = [(0, 1), (1, 0), (2, 0), (2, 1), (3, 1)] + assert x == x_ + + def test_digraph_orientation_invalid(self): + G = nx.DiGraph(self.edges) + edge_iterator = nx.edge_bfs(G, self.nodes, orientation="hello") + pytest.raises(nx.NetworkXError, list, edge_iterator) + + def test_digraph_orientation_none(self): + G = nx.DiGraph(self.edges) + x = list(nx.edge_bfs(G, self.nodes, orientation=None)) + x_ = [(0, 1), (1, 0), (2, 0), (2, 1), (3, 1)] + assert x == x_ + + def test_digraph_orientation_original(self): + G = nx.DiGraph(self.edges) + x = list(nx.edge_bfs(G, self.nodes, orientation="original")) + x_ = [ + (0, 1, FORWARD), + (1, 0, FORWARD), + (2, 0, FORWARD), + (2, 1, FORWARD), + (3, 1, FORWARD), + ] + assert x == x_ + + def test_digraph2(self): + G = nx.DiGraph() + nx.add_path(G, range(4)) + x = list(nx.edge_bfs(G, [0])) + x_ = [(0, 1), (1, 2), (2, 3)] + assert x == x_ + + def test_digraph_rev(self): + G = nx.DiGraph(self.edges) + x = list(nx.edge_bfs(G, self.nodes, orientation="reverse")) + x_ = [ + (1, 0, REVERSE), + (2, 0, REVERSE), + (0, 1, REVERSE), + (2, 1, REVERSE), + (3, 1, REVERSE), + ] + assert x == x_ + + def test_digraph_rev2(self): + G = nx.DiGraph() + nx.add_path(G, range(4)) + x = list(nx.edge_bfs(G, [3], orientation="reverse")) + x_ = [(2, 3, REVERSE), (1, 2, REVERSE), (0, 1, REVERSE)] + assert x == x_ + + def test_multigraph(self): + G = nx.MultiGraph(self.edges) + x = list(nx.edge_bfs(G, self.nodes)) + x_ = [(0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 2, 0), (1, 2, 0), (1, 3, 0)] + # This is an example of where hash randomization can break. + # There are 3! * 2 alternative outputs, such as: + # [(0, 1, 1), (1, 0, 0), (0, 1, 2), (1, 3, 0), (1, 2, 0)] + # But note, the edges (1,2,0) and (1,3,0) always follow the (0,1,k) + # edges. So the algorithm only guarantees a partial order. A total + # order is guaranteed only if the graph data structures are ordered. + assert x == x_ + + def test_multidigraph(self): + G = nx.MultiDiGraph(self.edges) + x = list(nx.edge_bfs(G, self.nodes)) + x_ = [(0, 1, 0), (1, 0, 0), (1, 0, 1), (2, 0, 0), (2, 1, 0), (3, 1, 0)] + assert x == x_ + + def test_multidigraph_rev(self): + G = nx.MultiDiGraph(self.edges) + x = list(nx.edge_bfs(G, self.nodes, orientation="reverse")) + x_ = [ + (1, 0, 0, REVERSE), + (1, 0, 1, REVERSE), + (2, 0, 0, REVERSE), + (0, 1, 0, REVERSE), + (2, 1, 0, REVERSE), + (3, 1, 0, REVERSE), + ] + assert x == x_ + + def test_digraph_ignore(self): + G = nx.DiGraph(self.edges) + x = list(nx.edge_bfs(G, self.nodes, orientation="ignore")) + x_ = [ + (0, 1, FORWARD), + (1, 0, REVERSE), + (2, 0, REVERSE), + (2, 1, REVERSE), + (3, 1, REVERSE), + ] + assert x == x_ + + def test_digraph_ignore2(self): + G = nx.DiGraph() + nx.add_path(G, range(4)) + x = list(nx.edge_bfs(G, [0], orientation="ignore")) + x_ = [(0, 1, FORWARD), (1, 2, FORWARD), (2, 3, FORWARD)] + assert x == x_ + + def test_multidigraph_ignore(self): + G = nx.MultiDiGraph(self.edges) + x = list(nx.edge_bfs(G, self.nodes, orientation="ignore")) + x_ = [ + (0, 1, 0, FORWARD), + (1, 0, 0, REVERSE), + (1, 0, 1, REVERSE), + (2, 0, 0, REVERSE), + (2, 1, 0, REVERSE), + (3, 1, 0, REVERSE), + ] + assert x == x_ diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_edgedfs.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_edgedfs.py new file mode 100644 index 0000000000000000000000000000000000000000..7c1967cce04b3a0c9db80f9af39d7b1dfd8ef4cb --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/traversal/tests/test_edgedfs.py @@ -0,0 +1,131 @@ +import pytest + +import networkx as nx +from networkx.algorithms import edge_dfs +from networkx.algorithms.traversal.edgedfs import FORWARD, REVERSE + +# These tests can fail with hash randomization. The easiest and clearest way +# to write these unit tests is for the edges to be output in an expected total +# order, but we cannot guarantee the order amongst outgoing edges from a node, +# unless each class uses an ordered data structure for neighbors. This is +# painful to do with the current API. The alternative is that the tests are +# written (IMO confusingly) so that there is not a total order over the edges, +# but only a partial order. Due to the small size of the graphs, hopefully +# failures due to hash randomization will not occur. For an example of how +# this can fail, see TestEdgeDFS.test_multigraph. + + +class TestEdgeDFS: + @classmethod + def setup_class(cls): + cls.nodes = [0, 1, 2, 3] + cls.edges = [(0, 1), (1, 0), (1, 0), (2, 1), (3, 1)] + + def test_empty(self): + G = nx.Graph() + edges = list(edge_dfs(G)) + assert edges == [] + + def test_graph(self): + G = nx.Graph(self.edges) + x = list(edge_dfs(G, self.nodes)) + x_ = [(0, 1), (1, 2), (1, 3)] + assert x == x_ + + def test_digraph(self): + G = nx.DiGraph(self.edges) + x = list(edge_dfs(G, self.nodes)) + x_ = [(0, 1), (1, 0), (2, 1), (3, 1)] + assert x == x_ + + def test_digraph_orientation_invalid(self): + G = nx.DiGraph(self.edges) + edge_iterator = edge_dfs(G, self.nodes, orientation="hello") + pytest.raises(nx.NetworkXError, list, edge_iterator) + + def test_digraph_orientation_none(self): + G = nx.DiGraph(self.edges) + x = list(edge_dfs(G, self.nodes, orientation=None)) + x_ = [(0, 1), (1, 0), (2, 1), (3, 1)] + assert x == x_ + + def test_digraph_orientation_original(self): + G = nx.DiGraph(self.edges) + x = list(edge_dfs(G, self.nodes, orientation="original")) + x_ = [(0, 1, FORWARD), (1, 0, FORWARD), (2, 1, FORWARD), (3, 1, FORWARD)] + assert x == x_ + + def test_digraph2(self): + G = nx.DiGraph() + nx.add_path(G, range(4)) + x = list(edge_dfs(G, [0])) + x_ = [(0, 1), (1, 2), (2, 3)] + assert x == x_ + + def test_digraph_rev(self): + G = nx.DiGraph(self.edges) + x = list(edge_dfs(G, self.nodes, orientation="reverse")) + x_ = [(1, 0, REVERSE), (0, 1, REVERSE), (2, 1, REVERSE), (3, 1, REVERSE)] + assert x == x_ + + def test_digraph_rev2(self): + G = nx.DiGraph() + nx.add_path(G, range(4)) + x = list(edge_dfs(G, [3], orientation="reverse")) + x_ = [(2, 3, REVERSE), (1, 2, REVERSE), (0, 1, REVERSE)] + assert x == x_ + + def test_multigraph(self): + G = nx.MultiGraph(self.edges) + x = list(edge_dfs(G, self.nodes)) + x_ = [(0, 1, 0), (1, 0, 1), (0, 1, 2), (1, 2, 0), (1, 3, 0)] + # This is an example of where hash randomization can break. + # There are 3! * 2 alternative outputs, such as: + # [(0, 1, 1), (1, 0, 0), (0, 1, 2), (1, 3, 0), (1, 2, 0)] + # But note, the edges (1,2,0) and (1,3,0) always follow the (0,1,k) + # edges. So the algorithm only guarantees a partial order. A total + # order is guaranteed only if the graph data structures are ordered. + assert x == x_ + + def test_multidigraph(self): + G = nx.MultiDiGraph(self.edges) + x = list(edge_dfs(G, self.nodes)) + x_ = [(0, 1, 0), (1, 0, 0), (1, 0, 1), (2, 1, 0), (3, 1, 0)] + assert x == x_ + + def test_multidigraph_rev(self): + G = nx.MultiDiGraph(self.edges) + x = list(edge_dfs(G, self.nodes, orientation="reverse")) + x_ = [ + (1, 0, 0, REVERSE), + (0, 1, 0, REVERSE), + (1, 0, 1, REVERSE), + (2, 1, 0, REVERSE), + (3, 1, 0, REVERSE), + ] + assert x == x_ + + def test_digraph_ignore(self): + G = nx.DiGraph(self.edges) + x = list(edge_dfs(G, self.nodes, orientation="ignore")) + x_ = [(0, 1, FORWARD), (1, 0, FORWARD), (2, 1, REVERSE), (3, 1, REVERSE)] + assert x == x_ + + def test_digraph_ignore2(self): + G = nx.DiGraph() + nx.add_path(G, range(4)) + x = list(edge_dfs(G, [0], orientation="ignore")) + x_ = [(0, 1, FORWARD), (1, 2, FORWARD), (2, 3, FORWARD)] + assert x == x_ + + def test_multidigraph_ignore(self): + G = nx.MultiDiGraph(self.edges) + x = list(edge_dfs(G, self.nodes, orientation="ignore")) + x_ = [ + (0, 1, 0, FORWARD), + (1, 0, 0, FORWARD), + (1, 0, 1, REVERSE), + (2, 1, 0, REVERSE), + (3, 1, 0, REVERSE), + ] + assert x == x_ diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/__init__.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..7120d4bc7ef25279b68eaa23690b6ff4574ed676 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/__init__.py @@ -0,0 +1,6 @@ +from .branchings import * +from .coding import * +from .mst import * +from .recognition import * +from .operations import * +from .decomposition import * diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/__pycache__/__init__.cpython-311.pyc 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0, 18, 0, 0], # 3 + [0, 0, 0, 0, 0, 0, 0, 12, 0], # 4 + [0, 0, 0, 0, 0, 0, 14, 0, 12], # 5 + [0, 0, 21, 0, 0, 0, 0, 0, 15], # 6 + [0, 0, 0, 19, 0, 0, 15, 0, 0], # 7 + [0, 0, 0, 0, 0, 0, 0, 18, 0], # 8 +], dtype=int) + +# Two copies of the graph from the original paper as disconnected components +G_big_array = np.zeros(np.array(G_array.shape) * 2, dtype=int) +G_big_array[:G_array.shape[0], :G_array.shape[1]] = G_array +G_big_array[G_array.shape[0]:, G_array.shape[1]:] = G_array + +# fmt: on + + +def G1(): + G = nx.from_numpy_array(G_array, create_using=nx.MultiDiGraph) + return G + + +def G2(): + # Now we shift all the weights by -10. + # Should not affect optimal arborescence, but does affect optimal branching. + Garr = G_array.copy() + Garr[np.nonzero(Garr)] -= 10 + G = nx.from_numpy_array(Garr, create_using=nx.MultiDiGraph) + return G + + +# An optimal branching for G1 that is also a spanning arborescence. So it is +# also an optimal spanning arborescence. +# +optimal_arborescence_1 = [ + (0, 2, 12), + (2, 1, 17), + (2, 3, 21), + (1, 5, 13), + (3, 4, 17), + (3, 6, 18), + (6, 8, 15), + (8, 7, 18), +] + +# For G2, the optimal branching of G1 (with shifted weights) is no longer +# an optimal branching, but it is still an optimal spanning arborescence +# (just with shifted weights). An optimal branching for G2 is similar to what +# appears in figure G (this is greedy_subopt_branching_1a below), but with the +# edge (3, 0, 5), which is now (3, 0, -5), removed. Thus, the optimal branching +# is not a spanning arborescence. The code finds optimal_branching_2a. +# An alternative and equivalent branching is optimal_branching_2b. We would +# need to modify the code to iterate through all equivalent optimal branchings. +# +# These are maximal branchings or arborescences. +optimal_branching_2a = [ + (5, 6, 4), + (6, 2, 11), + (6, 8, 5), + (8, 7, 8), + (2, 1, 7), + (2, 3, 11), + (3, 4, 7), +] +optimal_branching_2b = [ + (8, 7, 8), + (7, 3, 9), + (3, 4, 7), + (3, 6, 8), + (6, 2, 11), + (2, 1, 7), + (1, 5, 3), +] +optimal_arborescence_2 = [ + (0, 2, 2), + (2, 1, 7), + (2, 3, 11), + (1, 5, 3), + (3, 4, 7), + (3, 6, 8), + (6, 8, 5), + (8, 7, 8), +] + +# Two suboptimal maximal branchings on G1 obtained from a greedy algorithm. +# 1a matches what is shown in Figure G in Edmonds's paper. +greedy_subopt_branching_1a = [ + (5, 6, 14), + (6, 2, 21), + (6, 8, 15), + (8, 7, 18), + (2, 1, 17), + (2, 3, 21), + (3, 0, 5), + (3, 4, 17), +] +greedy_subopt_branching_1b = [ + (8, 7, 18), + (7, 6, 15), + (6, 2, 21), + (2, 1, 17), + (2, 3, 21), + (1, 5, 13), + (3, 0, 5), + (3, 4, 17), +] + + +def build_branching(edges, double=False): + G = nx.DiGraph() + for u, v, weight in edges: + G.add_edge(u, v, weight=weight) + if double: + G.add_edge(u + 9, v + 9, weight=weight) + return G + + +def sorted_edges(G, attr="weight", default=1): + edges = [(u, v, data.get(attr, default)) for (u, v, data) in G.edges(data=True)] + edges = sorted(edges, key=lambda x: (x[2], x[1], x[0])) + return edges + + +def assert_equal_branchings(G1, G2, attr="weight", default=1): + edges1 = list(G1.edges(data=True)) + edges2 = list(G2.edges(data=True)) + assert len(edges1) == len(edges2) + + # Grab the weights only. + e1 = sorted_edges(G1, attr, default) + e2 = sorted_edges(G2, attr, default) + + for a, b in zip(e1, e2): + assert a[:2] == b[:2] + np.testing.assert_almost_equal(a[2], b[2]) + + +################ + + +def test_optimal_branching1(): + G = build_branching(optimal_arborescence_1) + assert recognition.is_arborescence(G), True + assert branchings.branching_weight(G) == 131 + + +def test_optimal_branching2a(): + G = build_branching(optimal_branching_2a) + assert recognition.is_arborescence(G), True + assert branchings.branching_weight(G) == 53 + + +def test_optimal_branching2b(): + G = build_branching(optimal_branching_2b) + assert recognition.is_arborescence(G), True + assert branchings.branching_weight(G) == 53 + + +def test_optimal_arborescence2(): + G = build_branching(optimal_arborescence_2) + assert recognition.is_arborescence(G), True + assert branchings.branching_weight(G) == 51 + + +def test_greedy_suboptimal_branching1a(): + G = build_branching(greedy_subopt_branching_1a) + assert recognition.is_arborescence(G), True + assert branchings.branching_weight(G) == 128 + + +def test_greedy_suboptimal_branching1b(): + G = build_branching(greedy_subopt_branching_1b) + assert recognition.is_arborescence(G), True + assert branchings.branching_weight(G) == 127 + + +def test_greedy_max1(): + # Standard test. + # + G = G1() + B = branchings.greedy_branching(G) + # There are only two possible greedy branchings. The sorting is such + # that it should equal the second suboptimal branching: 1b. + B_ = build_branching(greedy_subopt_branching_1b) + assert_equal_branchings(B, B_) + + +def test_greedy_branching_kwarg_kind(): + G = G1() + with pytest.raises(nx.NetworkXException, match="Unknown value for `kind`."): + B = branchings.greedy_branching(G, kind="lol") + + +def test_greedy_branching_for_unsortable_nodes(): + G = nx.DiGraph() + G.add_weighted_edges_from([((2, 3), 5, 1), (3, "a", 1), (2, 4, 5)]) + edges = [(u, v, data.get("weight", 1)) for (u, v, data) in G.edges(data=True)] + with pytest.raises(TypeError): + edges.sort(key=itemgetter(2, 0, 1), reverse=True) + B = branchings.greedy_branching(G, kind="max").edges(data=True) + assert list(B) == [ + ((2, 3), 5, {"weight": 1}), + (3, "a", {"weight": 1}), + (2, 4, {"weight": 5}), + ] + + +def test_greedy_max2(): + # Different default weight. + # + G = G1() + del G[1][0][0]["weight"] + B = branchings.greedy_branching(G, default=6) + # Chosen so that edge (3,0,5) is not selected and (1,0,6) is instead. + + edges = [ + (1, 0, 6), + (1, 5, 13), + (7, 6, 15), + (2, 1, 17), + (3, 4, 17), + (8, 7, 18), + (2, 3, 21), + (6, 2, 21), + ] + B_ = build_branching(edges) + assert_equal_branchings(B, B_) + + +def test_greedy_max3(): + # All equal weights. + # + G = G1() + B = branchings.greedy_branching(G, attr=None) + + # This is mostly arbitrary...the output was generated by running the algo. + edges = [ + (2, 1, 1), + (3, 0, 1), + (3, 4, 1), + (5, 8, 1), + (6, 2, 1), + (7, 3, 1), + (7, 6, 1), + (8, 7, 1), + ] + B_ = build_branching(edges) + assert_equal_branchings(B, B_, default=1) + + +def test_greedy_min(): + G = G1() + B = branchings.greedy_branching(G, kind="min") + + edges = [ + (1, 0, 4), + (0, 2, 12), + (0, 4, 12), + (2, 5, 12), + (4, 7, 12), + (5, 8, 12), + (5, 6, 14), + (7, 3, 19), + ] + B_ = build_branching(edges) + assert_equal_branchings(B, B_) + + +def test_edmonds1_maxbranch(): + G = G1() + x = branchings.maximum_branching(G) + x_ = build_branching(optimal_arborescence_1) + assert_equal_branchings(x, x_) + + +def test_edmonds1_maxarbor(): + G = G1() + x = branchings.maximum_spanning_arborescence(G) + x_ = build_branching(optimal_arborescence_1) + assert_equal_branchings(x, x_) + + +def test_edmonds1_minimal_branching(): + # graph will have something like a minimum arborescence but no spanning one + G = nx.from_numpy_array(G_big_array, create_using=nx.DiGraph) + B = branchings.minimal_branching(G) + edges = [ + (3, 0, 5), + (0, 2, 12), + (0, 4, 12), + (2, 5, 12), + (4, 7, 12), + (5, 8, 12), + (5, 6, 14), + (2, 1, 17), + ] + B_ = build_branching(edges, double=True) + assert_equal_branchings(B, B_) + + +def test_edmonds2_maxbranch(): + G = G2() + x = branchings.maximum_branching(G) + x_ = build_branching(optimal_branching_2a) + assert_equal_branchings(x, x_) + + +def test_edmonds2_maxarbor(): + G = G2() + x = branchings.maximum_spanning_arborescence(G) + x_ = build_branching(optimal_arborescence_2) + assert_equal_branchings(x, x_) + + +def test_edmonds2_minarbor(): + G = G1() + x = branchings.minimum_spanning_arborescence(G) + # This was obtained from algorithm. Need to verify it independently. + # Branch weight is: 96 + edges = [ + (3, 0, 5), + (0, 2, 12), + (0, 4, 12), + (2, 5, 12), + (4, 7, 12), + (5, 8, 12), + (5, 6, 14), + (2, 1, 17), + ] + x_ = build_branching(edges) + assert_equal_branchings(x, x_) + + +def test_edmonds3_minbranch1(): + G = G1() + x = branchings.minimum_branching(G) + edges = [] + x_ = build_branching(edges) + assert_equal_branchings(x, x_) + + +def test_edmonds3_minbranch2(): + G = G1() + G.add_edge(8, 9, weight=-10) + x = branchings.minimum_branching(G) + edges = [(8, 9, -10)] + x_ = build_branching(edges) + assert_equal_branchings(x, x_) + + +# Need more tests + + +def test_mst(): + # Make sure we get the same results for undirected graphs. + # Example from: https://en.wikipedia.org/wiki/Kruskal's_algorithm + G = nx.Graph() + edgelist = [ + (0, 3, [("weight", 5)]), + (0, 1, [("weight", 7)]), + (1, 3, [("weight", 9)]), + (1, 2, [("weight", 8)]), + (1, 4, [("weight", 7)]), + (3, 4, [("weight", 15)]), + (3, 5, [("weight", 6)]), + (2, 4, [("weight", 5)]), + (4, 5, [("weight", 8)]), + (4, 6, [("weight", 9)]), + (5, 6, [("weight", 11)]), + ] + G.add_edges_from(edgelist) + G = G.to_directed() + x = branchings.minimum_spanning_arborescence(G) + + edges = [ + ({0, 1}, 7), + ({0, 3}, 5), + ({3, 5}, 6), + ({1, 4}, 7), + ({4, 2}, 5), + ({4, 6}, 9), + ] + + assert x.number_of_edges() == len(edges) + for u, v, d in x.edges(data=True): + assert ({u, v}, d["weight"]) in edges + + +def test_mixed_nodetypes(): + # Smoke test to make sure no TypeError is raised for mixed node types. + G = nx.Graph() + edgelist = [(0, 3, [("weight", 5)]), (0, "1", [("weight", 5)])] + G.add_edges_from(edgelist) + G = G.to_directed() + x = branchings.minimum_spanning_arborescence(G) + + +def test_edmonds1_minbranch(): + # Using -G_array and min should give the same as optimal_arborescence_1, + # but with all edges negative. + edges = [(u, v, -w) for (u, v, w) in optimal_arborescence_1] + + G = nx.from_numpy_array(-G_array, create_using=nx.DiGraph) + + # Quickly make sure max branching is empty. + x = branchings.maximum_branching(G) + x_ = build_branching([]) + assert_equal_branchings(x, x_) + + # Now test the min branching. + x = branchings.minimum_branching(G) + x_ = build_branching(edges) + assert_equal_branchings(x, x_) + + +def test_edge_attribute_preservation_normal_graph(): + # Test that edge attributes are preserved when finding an optimum graph + # using the Edmonds class for normal graphs. + G = nx.Graph() + + edgelist = [ + (0, 1, [("weight", 5), ("otherattr", 1), ("otherattr2", 3)]), + (0, 2, [("weight", 5), ("otherattr", 2), ("otherattr2", 2)]), + (1, 2, [("weight", 6), ("otherattr", 3), ("otherattr2", 1)]), + ] + G.add_edges_from(edgelist) + + B = branchings.maximum_branching(G, preserve_attrs=True) + + assert B[0][1]["otherattr"] == 1 + assert B[0][1]["otherattr2"] == 3 + + +def test_edge_attribute_preservation_multigraph(): + # Test that edge attributes are preserved when finding an optimum graph + # using the Edmonds class for multigraphs. + G = nx.MultiGraph() + + edgelist = [ + (0, 1, [("weight", 5), ("otherattr", 1), ("otherattr2", 3)]), + (0, 2, [("weight", 5), ("otherattr", 2), ("otherattr2", 2)]), + (1, 2, [("weight", 6), ("otherattr", 3), ("otherattr2", 1)]), + ] + G.add_edges_from(edgelist * 2) # Make sure we have duplicate edge paths + + B = branchings.maximum_branching(G, preserve_attrs=True) + + assert B[0][1][0]["otherattr"] == 1 + assert B[0][1][0]["otherattr2"] == 3 + + +def test_edge_attribute_discard(): + # Test that edge attributes are discarded if we do not specify to keep them + G = nx.Graph() + + edgelist = [ + (0, 1, [("weight", 5), ("otherattr", 1), ("otherattr2", 3)]), + (0, 2, [("weight", 5), ("otherattr", 2), ("otherattr2", 2)]), + (1, 2, [("weight", 6), ("otherattr", 3), ("otherattr2", 1)]), + ] + G.add_edges_from(edgelist) + + B = branchings.maximum_branching(G, preserve_attrs=False) + + edge_dict = B[0][1] + with pytest.raises(KeyError): + _ = edge_dict["otherattr"] + + +def test_partition_spanning_arborescence(): + """ + Test that we can generate minimum spanning arborescences which respect the + given partition. + """ + G = nx.from_numpy_array(G_array, create_using=nx.DiGraph) + G[3][0]["partition"] = nx.EdgePartition.EXCLUDED + G[2][3]["partition"] = nx.EdgePartition.INCLUDED + G[7][3]["partition"] = nx.EdgePartition.EXCLUDED + G[0][2]["partition"] = nx.EdgePartition.EXCLUDED + G[6][2]["partition"] = nx.EdgePartition.INCLUDED + + actual_edges = [ + (0, 4, 12), + (1, 0, 4), + (1, 5, 13), + (2, 3, 21), + (4, 7, 12), + (5, 6, 14), + (5, 8, 12), + (6, 2, 21), + ] + + B = branchings.minimum_spanning_arborescence(G, partition="partition") + assert_equal_branchings(build_branching(actual_edges), B) + + +def test_arborescence_iterator_min(): + """ + Tests the arborescence iterator. + + A brute force method found 680 arborescences in this graph. + This test will not verify all of them individually, but will check two + things + + * The iterator returns 680 arborescences + * The weight of the arborescences is non-strictly increasing + + for more information please visit + https://mjschwenne.github.io/2021/06/10/implementing-the-iterators.html + """ + G = nx.from_numpy_array(G_array, create_using=nx.DiGraph) + + arborescence_count = 0 + arborescence_weight = -math.inf + for B in branchings.ArborescenceIterator(G): + arborescence_count += 1 + new_arborescence_weight = B.size(weight="weight") + assert new_arborescence_weight >= arborescence_weight + arborescence_weight = new_arborescence_weight + + assert arborescence_count == 680 + + +def test_arborescence_iterator_max(): + """ + Tests the arborescence iterator. + + A brute force method found 680 arborescences in this graph. + This test will not verify all of them individually, but will check two + things + + * The iterator returns 680 arborescences + * The weight of the arborescences is non-strictly decreasing + + for more information please visit + https://mjschwenne.github.io/2021/06/10/implementing-the-iterators.html + """ + G = nx.from_numpy_array(G_array, create_using=nx.DiGraph) + + arborescence_count = 0 + arborescence_weight = math.inf + for B in branchings.ArborescenceIterator(G, minimum=False): + arborescence_count += 1 + new_arborescence_weight = B.size(weight="weight") + assert new_arborescence_weight <= arborescence_weight + arborescence_weight = new_arborescence_weight + + assert arborescence_count == 680 + + +def test_arborescence_iterator_initial_partition(): + """ + Tests the arborescence iterator with three included edges and three excluded + in the initial partition. + + A brute force method similar to the one used in the above tests found that + there are 16 arborescences which contain the included edges and not the + excluded edges. + """ + G = nx.from_numpy_array(G_array, create_using=nx.DiGraph) + included_edges = [(1, 0), (5, 6), (8, 7)] + excluded_edges = [(0, 2), (3, 6), (1, 5)] + + arborescence_count = 0 + arborescence_weight = -math.inf + for B in branchings.ArborescenceIterator( + G, init_partition=(included_edges, excluded_edges) + ): + arborescence_count += 1 + new_arborescence_weight = B.size(weight="weight") + assert new_arborescence_weight >= arborescence_weight + arborescence_weight = new_arborescence_weight + for e in included_edges: + assert e in B.edges + for e in excluded_edges: + assert e not in B.edges + assert arborescence_count == 16 + + +def test_branchings_with_default_weights(): + """ + Tests that various branching algorithms work on graphs without weights. + For more information, see issue #7279. + """ + graph = nx.erdos_renyi_graph(10, p=0.2, directed=True, seed=123) + + assert all( + "weight" not in d for (u, v, d) in graph.edges(data=True) + ), "test is for graphs without a weight attribute" + + # Calling these functions will modify graph inplace to add weights + # copy the graph to avoid this. + nx.minimum_spanning_arborescence(graph.copy()) + nx.maximum_spanning_arborescence(graph.copy()) + nx.minimum_branching(graph.copy()) + nx.maximum_branching(graph.copy()) + nx.algorithms.tree.minimal_branching(graph.copy()) + nx.algorithms.tree.branching_weight(graph.copy()) + nx.algorithms.tree.greedy_branching(graph.copy()) + + assert all( + "weight" not in d for (u, v, d) in graph.edges(data=True) + ), "The above calls should not modify the initial graph in-place" diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_coding.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_coding.py new file mode 100644 index 0000000000000000000000000000000000000000..26bd4083f52a0cc90b94c6de6d47b2c44e70a079 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_coding.py @@ -0,0 +1,114 @@ +"""Unit tests for the :mod:`~networkx.algorithms.tree.coding` module.""" + +from itertools import product + +import pytest + +import networkx as nx +from networkx.utils import edges_equal, nodes_equal + + +class TestPruferSequence: + """Unit tests for the Prüfer sequence encoding and decoding + functions. + + """ + + def test_nontree(self): + with pytest.raises(nx.NotATree): + G = nx.cycle_graph(3) + nx.to_prufer_sequence(G) + + def test_null_graph(self): + with pytest.raises(nx.NetworkXPointlessConcept): + nx.to_prufer_sequence(nx.null_graph()) + + def test_trivial_graph(self): + with pytest.raises(nx.NetworkXPointlessConcept): + nx.to_prufer_sequence(nx.trivial_graph()) + + def test_bad_integer_labels(self): + with pytest.raises(KeyError): + T = nx.Graph(nx.utils.pairwise("abc")) + nx.to_prufer_sequence(T) + + def test_encoding(self): + """Tests for encoding a tree as a Prüfer sequence using the + iterative strategy. + + """ + # Example from Wikipedia. + tree = nx.Graph([(0, 3), (1, 3), (2, 3), (3, 4), (4, 5)]) + sequence = nx.to_prufer_sequence(tree) + assert sequence == [3, 3, 3, 4] + + def test_decoding(self): + """Tests for decoding a tree from a Prüfer sequence.""" + # Example from Wikipedia. + sequence = [3, 3, 3, 4] + tree = nx.from_prufer_sequence(sequence) + assert nodes_equal(list(tree), list(range(6))) + edges = [(0, 3), (1, 3), (2, 3), (3, 4), (4, 5)] + assert edges_equal(list(tree.edges()), edges) + + def test_decoding2(self): + # Example from "An Optimal Algorithm for Prufer Codes". + sequence = [2, 4, 0, 1, 3, 3] + tree = nx.from_prufer_sequence(sequence) + assert nodes_equal(list(tree), list(range(8))) + edges = [(0, 1), (0, 4), (1, 3), (2, 4), (2, 5), (3, 6), (3, 7)] + assert edges_equal(list(tree.edges()), edges) + + def test_inverse(self): + """Tests that the encoding and decoding functions are inverses.""" + for T in nx.nonisomorphic_trees(4): + T2 = nx.from_prufer_sequence(nx.to_prufer_sequence(T)) + assert nodes_equal(list(T), list(T2)) + assert edges_equal(list(T.edges()), list(T2.edges())) + + for seq in product(range(4), repeat=2): + seq2 = nx.to_prufer_sequence(nx.from_prufer_sequence(seq)) + assert list(seq) == seq2 + + +class TestNestedTuple: + """Unit tests for the nested tuple encoding and decoding functions.""" + + def test_nontree(self): + with pytest.raises(nx.NotATree): + G = nx.cycle_graph(3) + nx.to_nested_tuple(G, 0) + + def test_unknown_root(self): + with pytest.raises(nx.NodeNotFound): + G = nx.path_graph(2) + nx.to_nested_tuple(G, "bogus") + + def test_encoding(self): + T = nx.full_rary_tree(2, 2**3 - 1) + expected = (((), ()), ((), ())) + actual = nx.to_nested_tuple(T, 0) + assert nodes_equal(expected, actual) + + def test_canonical_form(self): + T = nx.Graph() + T.add_edges_from([(0, 1), (0, 2), (0, 3)]) + T.add_edges_from([(1, 4), (1, 5)]) + T.add_edges_from([(3, 6), (3, 7)]) + root = 0 + actual = nx.to_nested_tuple(T, root, canonical_form=True) + expected = ((), ((), ()), ((), ())) + assert actual == expected + + def test_decoding(self): + balanced = (((), ()), ((), ())) + expected = nx.full_rary_tree(2, 2**3 - 1) + actual = nx.from_nested_tuple(balanced) + assert nx.is_isomorphic(expected, actual) + + def test_sensible_relabeling(self): + balanced = (((), ()), ((), ())) + T = nx.from_nested_tuple(balanced, sensible_relabeling=True) + edges = [(0, 1), (0, 2), (1, 3), (1, 4), (2, 5), (2, 6)] + assert nodes_equal(list(T), list(range(2**3 - 1))) + assert edges_equal(list(T.edges()), edges) diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_decomposition.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_decomposition.py new file mode 100644 index 0000000000000000000000000000000000000000..8c376053794537611f46c038ed074eb92b1ba676 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_decomposition.py @@ -0,0 +1,79 @@ +import networkx as nx +from networkx.algorithms.tree.decomposition import junction_tree + + +def test_junction_tree_directed_confounders(): + B = nx.DiGraph() + B.add_edges_from([("A", "C"), ("B", "C"), ("C", "D"), ("C", "E")]) + + G = junction_tree(B) + J = nx.Graph() + J.add_edges_from( + [ + (("C", "E"), ("C",)), + (("C",), ("A", "B", "C")), + (("A", "B", "C"), ("C",)), + (("C",), ("C", "D")), + ] + ) + + assert nx.is_isomorphic(G, J) + + +def test_junction_tree_directed_unconnected_nodes(): + B = nx.DiGraph() + B.add_nodes_from([("A", "B", "C", "D")]) + G = junction_tree(B) + + J = nx.Graph() + J.add_nodes_from([("A", "B", "C", "D")]) + + assert nx.is_isomorphic(G, J) + + +def test_junction_tree_directed_cascade(): + B = nx.DiGraph() + B.add_edges_from([("A", "B"), ("B", "C"), ("C", "D")]) + G = junction_tree(B) + + J = nx.Graph() + J.add_edges_from( + [ + (("A", "B"), ("B",)), + (("B",), ("B", "C")), + (("B", "C"), ("C",)), + (("C",), ("C", "D")), + ] + ) + assert nx.is_isomorphic(G, J) + + +def test_junction_tree_directed_unconnected_edges(): + B = nx.DiGraph() + B.add_edges_from([("A", "B"), ("C", "D"), ("E", "F")]) + G = junction_tree(B) + + J = nx.Graph() + J.add_nodes_from([("A", "B"), ("C", "D"), ("E", "F")]) + + assert nx.is_isomorphic(G, J) + + +def test_junction_tree_undirected(): + B = nx.Graph() + B.add_edges_from([("A", "C"), ("A", "D"), ("B", "C"), ("C", "E")]) + G = junction_tree(B) + + J = nx.Graph() + J.add_edges_from( + [ + (("A", "D"), ("A",)), + (("A",), ("A", "C")), + (("A", "C"), ("C",)), + (("C",), ("B", "C")), + (("B", "C"), ("C",)), + (("C",), ("C", "E")), + ] + ) + + assert nx.is_isomorphic(G, J) diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_mst.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_mst.py new file mode 100644 index 0000000000000000000000000000000000000000..f8945a71835dbfa35c0c45259c8c84b653b1f49b --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_mst.py @@ -0,0 +1,918 @@ +"""Unit tests for the :mod:`networkx.algorithms.tree.mst` module.""" + +import pytest + +import networkx as nx +from networkx.utils import edges_equal, nodes_equal + + +def test_unknown_algorithm(): + with pytest.raises(ValueError): + nx.minimum_spanning_tree(nx.Graph(), algorithm="random") + with pytest.raises( + ValueError, match="random is not a valid choice for an algorithm." + ): + nx.maximum_spanning_edges(nx.Graph(), algorithm="random") + + +class MinimumSpanningTreeTestBase: + """Base class for test classes for minimum spanning tree algorithms. + This class contains some common tests that will be inherited by + subclasses. Each subclass must have a class attribute + :data:`algorithm` that is a string representing the algorithm to + run, as described under the ``algorithm`` keyword argument for the + :func:`networkx.minimum_spanning_edges` function. Subclasses can + then implement any algorithm-specific tests. + """ + + def setup_method(self, method): + """Creates an example graph and stores the expected minimum and + maximum spanning tree edges. + """ + # This stores the class attribute `algorithm` in an instance attribute. + self.algo = self.algorithm + # This example graph comes from Wikipedia: + # https://en.wikipedia.org/wiki/Kruskal's_algorithm + edges = [ + (0, 1, 7), + (0, 3, 5), + (1, 2, 8), + (1, 3, 9), + (1, 4, 7), + (2, 4, 5), + (3, 4, 15), + (3, 5, 6), + (4, 5, 8), + (4, 6, 9), + (5, 6, 11), + ] + self.G = nx.Graph() + self.G.add_weighted_edges_from(edges) + self.minimum_spanning_edgelist = [ + (0, 1, {"weight": 7}), + (0, 3, {"weight": 5}), + (1, 4, {"weight": 7}), + (2, 4, {"weight": 5}), + (3, 5, {"weight": 6}), + (4, 6, {"weight": 9}), + ] + self.maximum_spanning_edgelist = [ + (0, 1, {"weight": 7}), + (1, 2, {"weight": 8}), + (1, 3, {"weight": 9}), + (3, 4, {"weight": 15}), + (4, 6, {"weight": 9}), + (5, 6, {"weight": 11}), + ] + + def test_minimum_edges(self): + edges = nx.minimum_spanning_edges(self.G, algorithm=self.algo) + # Edges from the spanning edges functions don't come in sorted + # orientation, so we need to sort each edge individually. + actual = sorted((min(u, v), max(u, v), d) for u, v, d in edges) + assert edges_equal(actual, self.minimum_spanning_edgelist) + + def test_maximum_edges(self): + edges = nx.maximum_spanning_edges(self.G, algorithm=self.algo) + # Edges from the spanning edges functions don't come in sorted + # orientation, so we need to sort each edge individually. + actual = sorted((min(u, v), max(u, v), d) for u, v, d in edges) + assert edges_equal(actual, self.maximum_spanning_edgelist) + + def test_without_data(self): + edges = nx.minimum_spanning_edges(self.G, algorithm=self.algo, data=False) + # Edges from the spanning edges functions don't come in sorted + # orientation, so we need to sort each edge individually. + actual = sorted((min(u, v), max(u, v)) for u, v in edges) + expected = [(u, v) for u, v, d in self.minimum_spanning_edgelist] + assert edges_equal(actual, expected) + + def test_nan_weights(self): + # Edge weights NaN never appear in the spanning tree. see #2164 + G = self.G + G.add_edge(0, 12, weight=float("nan")) + edges = nx.minimum_spanning_edges( + G, algorithm=self.algo, data=False, ignore_nan=True + ) + actual = sorted((min(u, v), max(u, v)) for u, v in edges) + expected = [(u, v) for u, v, d in self.minimum_spanning_edgelist] + assert edges_equal(actual, expected) + # Now test for raising exception + edges = nx.minimum_spanning_edges( + G, algorithm=self.algo, data=False, ignore_nan=False + ) + with pytest.raises(ValueError): + list(edges) + # test default for ignore_nan as False + edges = nx.minimum_spanning_edges(G, algorithm=self.algo, data=False) + with pytest.raises(ValueError): + list(edges) + + def test_nan_weights_MultiGraph(self): + G = nx.MultiGraph() + G.add_edge(0, 12, weight=float("nan")) + edges = nx.minimum_spanning_edges( + G, algorithm="prim", data=False, ignore_nan=False + ) + with pytest.raises(ValueError): + list(edges) + # test default for ignore_nan as False + edges = nx.minimum_spanning_edges(G, algorithm="prim", data=False) + with pytest.raises(ValueError): + list(edges) + + def test_nan_weights_order(self): + # now try again with a nan edge at the beginning of G.nodes + edges = [ + (0, 1, 7), + (0, 3, 5), + (1, 2, 8), + (1, 3, 9), + (1, 4, 7), + (2, 4, 5), + (3, 4, 15), + (3, 5, 6), + (4, 5, 8), + (4, 6, 9), + (5, 6, 11), + ] + G = nx.Graph() + G.add_weighted_edges_from([(u + 1, v + 1, wt) for u, v, wt in edges]) + G.add_edge(0, 7, weight=float("nan")) + edges = nx.minimum_spanning_edges( + G, algorithm=self.algo, data=False, ignore_nan=True + ) + actual = sorted((min(u, v), max(u, v)) for u, v in edges) + shift = [(u + 1, v + 1) for u, v, d in self.minimum_spanning_edgelist] + assert edges_equal(actual, shift) + + def test_isolated_node(self): + # now try again with an isolated node + edges = [ + (0, 1, 7), + (0, 3, 5), + (1, 2, 8), + (1, 3, 9), + (1, 4, 7), + (2, 4, 5), + (3, 4, 15), + (3, 5, 6), + (4, 5, 8), + (4, 6, 9), + (5, 6, 11), + ] + G = nx.Graph() + G.add_weighted_edges_from([(u + 1, v + 1, wt) for u, v, wt in edges]) + G.add_node(0) + edges = nx.minimum_spanning_edges( + G, algorithm=self.algo, data=False, ignore_nan=True + ) + actual = sorted((min(u, v), max(u, v)) for u, v in edges) + shift = [(u + 1, v + 1) for u, v, d in self.minimum_spanning_edgelist] + assert edges_equal(actual, shift) + + def test_minimum_tree(self): + T = nx.minimum_spanning_tree(self.G, algorithm=self.algo) + actual = sorted(T.edges(data=True)) + assert edges_equal(actual, self.minimum_spanning_edgelist) + + def test_maximum_tree(self): + T = nx.maximum_spanning_tree(self.G, algorithm=self.algo) + actual = sorted(T.edges(data=True)) + assert edges_equal(actual, self.maximum_spanning_edgelist) + + def test_disconnected(self): + G = nx.Graph([(0, 1, {"weight": 1}), (2, 3, {"weight": 2})]) + T = nx.minimum_spanning_tree(G, algorithm=self.algo) + assert nodes_equal(list(T), list(range(4))) + assert edges_equal(list(T.edges()), [(0, 1), (2, 3)]) + + def test_empty_graph(self): + G = nx.empty_graph(3) + T = nx.minimum_spanning_tree(G, algorithm=self.algo) + assert nodes_equal(sorted(T), list(range(3))) + assert T.number_of_edges() == 0 + + def test_attributes(self): + G = nx.Graph() + G.add_edge(1, 2, weight=1, color="red", distance=7) + G.add_edge(2, 3, weight=1, color="green", distance=2) + G.add_edge(1, 3, weight=10, color="blue", distance=1) + G.graph["foo"] = "bar" + T = nx.minimum_spanning_tree(G, algorithm=self.algo) + assert T.graph == G.graph + assert nodes_equal(T, G) + for u, v in T.edges(): + assert T.adj[u][v] == G.adj[u][v] + + def test_weight_attribute(self): + G = nx.Graph() + G.add_edge(0, 1, weight=1, distance=7) + G.add_edge(0, 2, weight=30, distance=1) + G.add_edge(1, 2, weight=1, distance=1) + G.add_node(3) + T = nx.minimum_spanning_tree(G, algorithm=self.algo, weight="distance") + assert nodes_equal(sorted(T), list(range(4))) + assert edges_equal(sorted(T.edges()), [(0, 2), (1, 2)]) + T = nx.maximum_spanning_tree(G, algorithm=self.algo, weight="distance") + assert nodes_equal(sorted(T), list(range(4))) + assert edges_equal(sorted(T.edges()), [(0, 1), (0, 2)]) + + +class TestBoruvka(MinimumSpanningTreeTestBase): + """Unit tests for computing a minimum (or maximum) spanning tree + using Borůvka's algorithm. + """ + + algorithm = "boruvka" + + def test_unicode_name(self): + """Tests that using a Unicode string can correctly indicate + Borůvka's algorithm. + """ + edges = nx.minimum_spanning_edges(self.G, algorithm="borůvka") + # Edges from the spanning edges functions don't come in sorted + # orientation, so we need to sort each edge individually. + actual = sorted((min(u, v), max(u, v), d) for u, v, d in edges) + assert edges_equal(actual, self.minimum_spanning_edgelist) + + +class MultigraphMSTTestBase(MinimumSpanningTreeTestBase): + # Abstract class + + def test_multigraph_keys_min(self): + """Tests that the minimum spanning edges of a multigraph + preserves edge keys. + """ + G = nx.MultiGraph() + G.add_edge(0, 1, key="a", weight=2) + G.add_edge(0, 1, key="b", weight=1) + min_edges = nx.minimum_spanning_edges + mst_edges = min_edges(G, algorithm=self.algo, data=False) + assert edges_equal([(0, 1, "b")], list(mst_edges)) + + def test_multigraph_keys_max(self): + """Tests that the maximum spanning edges of a multigraph + preserves edge keys. + """ + G = nx.MultiGraph() + G.add_edge(0, 1, key="a", weight=2) + G.add_edge(0, 1, key="b", weight=1) + max_edges = nx.maximum_spanning_edges + mst_edges = max_edges(G, algorithm=self.algo, data=False) + assert edges_equal([(0, 1, "a")], list(mst_edges)) + + +class TestKruskal(MultigraphMSTTestBase): + """Unit tests for computing a minimum (or maximum) spanning tree + using Kruskal's algorithm. + """ + + algorithm = "kruskal" + + def test_key_data_bool(self): + """Tests that the keys and data values are included in + MST edges based on whether keys and data parameters are + true or false""" + G = nx.MultiGraph() + G.add_edge(1, 2, key=1, weight=2) + G.add_edge(1, 2, key=2, weight=3) + G.add_edge(3, 2, key=1, weight=2) + G.add_edge(3, 1, key=1, weight=4) + + # keys are included and data is not included + mst_edges = nx.minimum_spanning_edges( + G, algorithm=self.algo, keys=True, data=False + ) + assert edges_equal([(1, 2, 1), (2, 3, 1)], list(mst_edges)) + + # keys are not included and data is included + mst_edges = nx.minimum_spanning_edges( + G, algorithm=self.algo, keys=False, data=True + ) + assert edges_equal( + [(1, 2, {"weight": 2}), (2, 3, {"weight": 2})], list(mst_edges) + ) + + # both keys and data are not included + mst_edges = nx.minimum_spanning_edges( + G, algorithm=self.algo, keys=False, data=False + ) + assert edges_equal([(1, 2), (2, 3)], list(mst_edges)) + + # both keys and data are included + mst_edges = nx.minimum_spanning_edges( + G, algorithm=self.algo, keys=True, data=True + ) + assert edges_equal( + [(1, 2, 1, {"weight": 2}), (2, 3, 1, {"weight": 2})], list(mst_edges) + ) + + +class TestPrim(MultigraphMSTTestBase): + """Unit tests for computing a minimum (or maximum) spanning tree + using Prim's algorithm. + """ + + algorithm = "prim" + + def test_prim_mst_edges_simple_graph(self): + H = nx.Graph() + H.add_edge(1, 2, key=2, weight=3) + H.add_edge(3, 2, key=1, weight=2) + H.add_edge(3, 1, key=1, weight=4) + + mst_edges = nx.minimum_spanning_edges(H, algorithm=self.algo, ignore_nan=True) + assert edges_equal( + [(1, 2, {"key": 2, "weight": 3}), (2, 3, {"key": 1, "weight": 2})], + list(mst_edges), + ) + + def test_ignore_nan(self): + """Tests that the edges with NaN weights are ignored or + raise an Error based on ignore_nan is true or false""" + H = nx.MultiGraph() + H.add_edge(1, 2, key=1, weight=float("nan")) + H.add_edge(1, 2, key=2, weight=3) + H.add_edge(3, 2, key=1, weight=2) + H.add_edge(3, 1, key=1, weight=4) + + # NaN weight edges are ignored when ignore_nan=True + mst_edges = nx.minimum_spanning_edges(H, algorithm=self.algo, ignore_nan=True) + assert edges_equal( + [(1, 2, 2, {"weight": 3}), (2, 3, 1, {"weight": 2})], list(mst_edges) + ) + + # NaN weight edges raise Error when ignore_nan=False + with pytest.raises(ValueError): + list(nx.minimum_spanning_edges(H, algorithm=self.algo, ignore_nan=False)) + + def test_multigraph_keys_tree(self): + G = nx.MultiGraph() + G.add_edge(0, 1, key="a", weight=2) + G.add_edge(0, 1, key="b", weight=1) + T = nx.minimum_spanning_tree(G, algorithm=self.algo) + assert edges_equal([(0, 1, 1)], list(T.edges(data="weight"))) + + def test_multigraph_keys_tree_max(self): + G = nx.MultiGraph() + G.add_edge(0, 1, key="a", weight=2) + G.add_edge(0, 1, key="b", weight=1) + T = nx.maximum_spanning_tree(G, algorithm=self.algo) + assert edges_equal([(0, 1, 2)], list(T.edges(data="weight"))) + + +class TestSpanningTreeIterator: + """ + Tests the spanning tree iterator on the example graph in the 2005 Sörensen + and Janssens paper An Algorithm to Generate all Spanning Trees of a Graph in + Order of Increasing Cost + """ + + def setup_method(self): + # Original Graph + edges = [(0, 1, 5), (1, 2, 4), (1, 4, 6), (2, 3, 5), (2, 4, 7), (3, 4, 3)] + self.G = nx.Graph() + self.G.add_weighted_edges_from(edges) + # List of lists of spanning trees in increasing order + self.spanning_trees = [ + # 1, MST, cost = 17 + [ + (0, 1, {"weight": 5}), + (1, 2, {"weight": 4}), + (2, 3, {"weight": 5}), + (3, 4, {"weight": 3}), + ], + # 2, cost = 18 + [ + (0, 1, {"weight": 5}), + (1, 2, {"weight": 4}), + (1, 4, {"weight": 6}), + (3, 4, {"weight": 3}), + ], + # 3, cost = 19 + [ + (0, 1, {"weight": 5}), + (1, 4, {"weight": 6}), + (2, 3, {"weight": 5}), + (3, 4, {"weight": 3}), + ], + # 4, cost = 19 + [ + (0, 1, {"weight": 5}), + (1, 2, {"weight": 4}), + (2, 4, {"weight": 7}), + (3, 4, {"weight": 3}), + ], + # 5, cost = 20 + [ + (0, 1, {"weight": 5}), + (1, 2, {"weight": 4}), + (1, 4, {"weight": 6}), + (2, 3, {"weight": 5}), + ], + # 6, cost = 21 + [ + (0, 1, {"weight": 5}), + (1, 4, {"weight": 6}), + (2, 4, {"weight": 7}), + (3, 4, {"weight": 3}), + ], + # 7, cost = 21 + [ + (0, 1, {"weight": 5}), + (1, 2, {"weight": 4}), + (2, 3, {"weight": 5}), + (2, 4, {"weight": 7}), + ], + # 8, cost = 23 + [ + (0, 1, {"weight": 5}), + (1, 4, {"weight": 6}), + (2, 3, {"weight": 5}), + (2, 4, {"weight": 7}), + ], + ] + + def test_minimum_spanning_tree_iterator(self): + """ + Tests that the spanning trees are correctly returned in increasing order + """ + tree_index = 0 + for tree in nx.SpanningTreeIterator(self.G): + actual = sorted(tree.edges(data=True)) + assert edges_equal(actual, self.spanning_trees[tree_index]) + tree_index += 1 + + def test_maximum_spanning_tree_iterator(self): + """ + Tests that the spanning trees are correctly returned in decreasing order + """ + tree_index = 7 + for tree in nx.SpanningTreeIterator(self.G, minimum=False): + actual = sorted(tree.edges(data=True)) + assert edges_equal(actual, self.spanning_trees[tree_index]) + tree_index -= 1 + + +class TestSpanningTreeMultiGraphIterator: + """ + Uses the same graph as the above class but with an added edge of twice the weight. + """ + + def setup_method(self): + # New graph + edges = [ + (0, 1, 5), + (0, 1, 10), + (1, 2, 4), + (1, 2, 8), + (1, 4, 6), + (1, 4, 12), + (2, 3, 5), + (2, 3, 10), + (2, 4, 7), + (2, 4, 14), + (3, 4, 3), + (3, 4, 6), + ] + self.G = nx.MultiGraph() + self.G.add_weighted_edges_from(edges) + + # There are 128 trees. I'd rather not list all 128 here, and computing them + # on such a small graph actually doesn't take that long. + from itertools import combinations + + self.spanning_trees = [] + for e in combinations(self.G.edges, 4): + tree = self.G.edge_subgraph(e) + if nx.is_tree(tree): + self.spanning_trees.append(sorted(tree.edges(keys=True, data=True))) + + def test_minimum_spanning_tree_iterator_multigraph(self): + """ + Tests that the spanning trees are correctly returned in increasing order + """ + tree_index = 0 + last_weight = 0 + for tree in nx.SpanningTreeIterator(self.G): + actual = sorted(tree.edges(keys=True, data=True)) + weight = sum([e[3]["weight"] for e in actual]) + assert actual in self.spanning_trees + assert weight >= last_weight + tree_index += 1 + + def test_maximum_spanning_tree_iterator_multigraph(self): + """ + Tests that the spanning trees are correctly returned in decreasing order + """ + tree_index = 127 + # Maximum weight tree is 46 + last_weight = 50 + for tree in nx.SpanningTreeIterator(self.G, minimum=False): + actual = sorted(tree.edges(keys=True, data=True)) + weight = sum([e[3]["weight"] for e in actual]) + assert actual in self.spanning_trees + assert weight <= last_weight + tree_index -= 1 + + +def test_random_spanning_tree_multiplicative_small(): + """ + Using a fixed seed, sample one tree for repeatability. + """ + from math import exp + + pytest.importorskip("scipy") + + gamma = { + (0, 1): -0.6383, + (0, 2): -0.6827, + (0, 5): 0, + (1, 2): -1.0781, + (1, 4): 0, + (2, 3): 0, + (5, 3): -0.2820, + (5, 4): -0.3327, + (4, 3): -0.9927, + } + + # The undirected support of gamma + G = nx.Graph() + for u, v in gamma: + G.add_edge(u, v, lambda_key=exp(gamma[(u, v)])) + + solution_edges = [(2, 3), (3, 4), (0, 5), (5, 4), (4, 1)] + solution = nx.Graph() + solution.add_edges_from(solution_edges) + + sampled_tree = nx.random_spanning_tree(G, "lambda_key", seed=42) + + assert nx.utils.edges_equal(solution.edges, sampled_tree.edges) + + +@pytest.mark.slow +def test_random_spanning_tree_multiplicative_large(): + """ + Sample many trees from the distribution created in the last test + """ + from math import exp + from random import Random + + pytest.importorskip("numpy") + stats = pytest.importorskip("scipy.stats") + + gamma = { + (0, 1): -0.6383, + (0, 2): -0.6827, + (0, 5): 0, + (1, 2): -1.0781, + (1, 4): 0, + (2, 3): 0, + (5, 3): -0.2820, + (5, 4): -0.3327, + (4, 3): -0.9927, + } + + # The undirected support of gamma + G = nx.Graph() + for u, v in gamma: + G.add_edge(u, v, lambda_key=exp(gamma[(u, v)])) + + # Find the multiplicative weight for each tree. + total_weight = 0 + tree_expected = {} + for t in nx.SpanningTreeIterator(G): + # Find the multiplicative weight of the spanning tree + weight = 1 + for u, v, d in t.edges(data="lambda_key"): + weight *= d + tree_expected[t] = weight + total_weight += weight + + # Assert that every tree has an entry in the expected distribution + assert len(tree_expected) == 75 + + # Set the sample size and then calculate the expected number of times we + # expect to see each tree. This test uses a near minimum sample size where + # the most unlikely tree has an expected frequency of 5.15. + # (Minimum required is 5) + # + # Here we also initialize the tree_actual dict so that we know the keys + # match between the two. We will later take advantage of the fact that since + # python 3.7 dict order is guaranteed so the expected and actual data will + # have the same order. + sample_size = 1200 + tree_actual = {} + for t in tree_expected: + tree_expected[t] = (tree_expected[t] / total_weight) * sample_size + tree_actual[t] = 0 + + # Sample the spanning trees + # + # Assert that they are actually trees and record which of the 75 trees we + # have sampled. + # + # For repeatability, we want to take advantage of the decorators in NetworkX + # to randomly sample the same sample each time. However, if we pass in a + # constant seed to sample_spanning_tree we will get the same tree each time. + # Instead, we can create our own random number generator with a fixed seed + # and pass those into sample_spanning_tree. + rng = Random(37) + for _ in range(sample_size): + sampled_tree = nx.random_spanning_tree(G, "lambda_key", seed=rng) + assert nx.is_tree(sampled_tree) + + for t in tree_expected: + if nx.utils.edges_equal(t.edges, sampled_tree.edges): + tree_actual[t] += 1 + break + + # Conduct a Chi squared test to see if the actual distribution matches the + # expected one at an alpha = 0.05 significance level. + # + # H_0: The distribution of trees in tree_actual matches the normalized product + # of the edge weights in the tree. + # + # H_a: The distribution of trees in tree_actual follows some other + # distribution of spanning trees. + _, p = stats.chisquare(list(tree_actual.values()), list(tree_expected.values())) + + # Assert that p is greater than the significance level so that we do not + # reject the null hypothesis + assert not p < 0.05 + + +def test_random_spanning_tree_additive_small(): + """ + Sample a single spanning tree from the additive method. + """ + pytest.importorskip("scipy") + + edges = { + (0, 1): 1, + (0, 2): 1, + (0, 5): 3, + (1, 2): 2, + (1, 4): 3, + (2, 3): 3, + (5, 3): 4, + (5, 4): 5, + (4, 3): 4, + } + + # Build the graph + G = nx.Graph() + for u, v in edges: + G.add_edge(u, v, weight=edges[(u, v)]) + + solution_edges = [(0, 2), (1, 2), (2, 3), (3, 4), (3, 5)] + solution = nx.Graph() + solution.add_edges_from(solution_edges) + + sampled_tree = nx.random_spanning_tree( + G, weight="weight", multiplicative=False, seed=37 + ) + + assert nx.utils.edges_equal(solution.edges, sampled_tree.edges) + + +@pytest.mark.slow +def test_random_spanning_tree_additive_large(): + """ + Sample many spanning trees from the additive method. + """ + from random import Random + + pytest.importorskip("numpy") + stats = pytest.importorskip("scipy.stats") + + edges = { + (0, 1): 1, + (0, 2): 1, + (0, 5): 3, + (1, 2): 2, + (1, 4): 3, + (2, 3): 3, + (5, 3): 4, + (5, 4): 5, + (4, 3): 4, + } + + # Build the graph + G = nx.Graph() + for u, v in edges: + G.add_edge(u, v, weight=edges[(u, v)]) + + # Find the additive weight for each tree. + total_weight = 0 + tree_expected = {} + for t in nx.SpanningTreeIterator(G): + # Find the multiplicative weight of the spanning tree + weight = 0 + for u, v, d in t.edges(data="weight"): + weight += d + tree_expected[t] = weight + total_weight += weight + + # Assert that every tree has an entry in the expected distribution + assert len(tree_expected) == 75 + + # Set the sample size and then calculate the expected number of times we + # expect to see each tree. This test uses a near minimum sample size where + # the most unlikely tree has an expected frequency of 5.07. + # (Minimum required is 5) + # + # Here we also initialize the tree_actual dict so that we know the keys + # match between the two. We will later take advantage of the fact that since + # python 3.7 dict order is guaranteed so the expected and actual data will + # have the same order. + sample_size = 500 + tree_actual = {} + for t in tree_expected: + tree_expected[t] = (tree_expected[t] / total_weight) * sample_size + tree_actual[t] = 0 + + # Sample the spanning trees + # + # Assert that they are actually trees and record which of the 75 trees we + # have sampled. + # + # For repeatability, we want to take advantage of the decorators in NetworkX + # to randomly sample the same sample each time. However, if we pass in a + # constant seed to sample_spanning_tree we will get the same tree each time. + # Instead, we can create our own random number generator with a fixed seed + # and pass those into sample_spanning_tree. + rng = Random(37) + for _ in range(sample_size): + sampled_tree = nx.random_spanning_tree( + G, "weight", multiplicative=False, seed=rng + ) + assert nx.is_tree(sampled_tree) + + for t in tree_expected: + if nx.utils.edges_equal(t.edges, sampled_tree.edges): + tree_actual[t] += 1 + break + + # Conduct a Chi squared test to see if the actual distribution matches the + # expected one at an alpha = 0.05 significance level. + # + # H_0: The distribution of trees in tree_actual matches the normalized product + # of the edge weights in the tree. + # + # H_a: The distribution of trees in tree_actual follows some other + # distribution of spanning trees. + _, p = stats.chisquare(list(tree_actual.values()), list(tree_expected.values())) + + # Assert that p is greater than the significance level so that we do not + # reject the null hypothesis + assert not p < 0.05 + + +def test_random_spanning_tree_empty_graph(): + G = nx.Graph() + rst = nx.tree.random_spanning_tree(G) + assert len(rst.nodes) == 0 + assert len(rst.edges) == 0 + + +def test_random_spanning_tree_single_node_graph(): + G = nx.Graph() + G.add_node(0) + rst = nx.tree.random_spanning_tree(G) + assert len(rst.nodes) == 1 + assert len(rst.edges) == 0 + + +def test_random_spanning_tree_single_node_loop(): + G = nx.Graph() + G.add_node(0) + G.add_edge(0, 0) + rst = nx.tree.random_spanning_tree(G) + assert len(rst.nodes) == 1 + assert len(rst.edges) == 0 + + +class TestNumberSpanningTrees: + @classmethod + def setup_class(cls): + global np + np = pytest.importorskip("numpy") + sp = pytest.importorskip("scipy") + + def test_nst_disconnected(self): + G = nx.empty_graph(2) + assert np.isclose(nx.number_of_spanning_trees(G), 0) + + def test_nst_no_nodes(self): + G = nx.Graph() + with pytest.raises(nx.NetworkXPointlessConcept): + nx.number_of_spanning_trees(G) + + def test_nst_weight(self): + G = nx.Graph() + G.add_edge(1, 2, weight=1) + G.add_edge(1, 3, weight=1) + G.add_edge(2, 3, weight=2) + # weights are ignored + assert np.isclose(nx.number_of_spanning_trees(G), 3) + # including weight + assert np.isclose(nx.number_of_spanning_trees(G, weight="weight"), 5) + + def test_nst_negative_weight(self): + G = nx.Graph() + G.add_edge(1, 2, weight=1) + G.add_edge(1, 3, weight=-1) + G.add_edge(2, 3, weight=-2) + # weights are ignored + assert np.isclose(nx.number_of_spanning_trees(G), 3) + # including weight + assert np.isclose(nx.number_of_spanning_trees(G, weight="weight"), -1) + + def test_nst_selfloop(self): + # self-loops are ignored + G = nx.complete_graph(3) + G.add_edge(1, 1) + assert np.isclose(nx.number_of_spanning_trees(G), 3) + + def test_nst_multigraph(self): + G = nx.MultiGraph() + G.add_edge(1, 2) + G.add_edge(1, 2) + G.add_edge(1, 3) + G.add_edge(2, 3) + assert np.isclose(nx.number_of_spanning_trees(G), 5) + + def test_nst_complete_graph(self): + # this is known as Cayley's formula + N = 5 + G = nx.complete_graph(N) + assert np.isclose(nx.number_of_spanning_trees(G), N ** (N - 2)) + + def test_nst_path_graph(self): + G = nx.path_graph(5) + assert np.isclose(nx.number_of_spanning_trees(G), 1) + + def test_nst_cycle_graph(self): + G = nx.cycle_graph(5) + assert np.isclose(nx.number_of_spanning_trees(G), 5) + + def test_nst_directed_noroot(self): + G = nx.empty_graph(3, create_using=nx.MultiDiGraph) + with pytest.raises(nx.NetworkXError): + nx.number_of_spanning_trees(G) + + def test_nst_directed_root_not_exist(self): + G = nx.empty_graph(3, create_using=nx.MultiDiGraph) + with pytest.raises(nx.NetworkXError): + nx.number_of_spanning_trees(G, root=42) + + def test_nst_directed_not_weak_connected(self): + G = nx.DiGraph() + G.add_edge(1, 2) + G.add_edge(3, 4) + assert np.isclose(nx.number_of_spanning_trees(G, root=1), 0) + + def test_nst_directed_cycle_graph(self): + G = nx.DiGraph() + G = nx.cycle_graph(7, G) + assert np.isclose(nx.number_of_spanning_trees(G, root=0), 1) + + def test_nst_directed_complete_graph(self): + G = nx.DiGraph() + G = nx.complete_graph(7, G) + assert np.isclose(nx.number_of_spanning_trees(G, root=0), 7**5) + + def test_nst_directed_multi(self): + G = nx.MultiDiGraph() + G = nx.cycle_graph(3, G) + G.add_edge(1, 2) + assert np.isclose(nx.number_of_spanning_trees(G, root=0), 2) + + def test_nst_directed_selfloop(self): + G = nx.MultiDiGraph() + G = nx.cycle_graph(3, G) + G.add_edge(1, 1) + assert np.isclose(nx.number_of_spanning_trees(G, root=0), 1) + + def test_nst_directed_weak_connected(self): + G = nx.MultiDiGraph() + G = nx.cycle_graph(3, G) + G.remove_edge(1, 2) + assert np.isclose(nx.number_of_spanning_trees(G, root=0), 0) + + def test_nst_directed_weighted(self): + # from root=1: + # arborescence 1: 1->2, 1->3, weight=2*1 + # arborescence 2: 1->2, 2->3, weight=2*3 + G = nx.DiGraph() + G.add_edge(1, 2, weight=2) + G.add_edge(1, 3, weight=1) + G.add_edge(2, 3, weight=3) + Nst = nx.number_of_spanning_trees(G, root=1, weight="weight") + assert np.isclose(Nst, 8) + Nst = nx.number_of_spanning_trees(G, root=2, weight="weight") + assert np.isclose(Nst, 0) + Nst = nx.number_of_spanning_trees(G, root=3, weight="weight") + assert np.isclose(Nst, 0) diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_operations.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_operations.py new file mode 100644 index 0000000000000000000000000000000000000000..284d94e2e5059de267b5ea47f6012a42c6ac4639 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_operations.py @@ -0,0 +1,53 @@ +from itertools import chain + +import networkx as nx +from networkx.utils import edges_equal, nodes_equal + + +def _check_custom_label_attribute(input_trees, res_tree, label_attribute): + res_attr_dict = nx.get_node_attributes(res_tree, label_attribute) + res_attr_set = set(res_attr_dict.values()) + input_label = (tree for tree, root in input_trees) + input_label_set = set(chain.from_iterable(input_label)) + return res_attr_set == input_label_set + + +def test_empty_sequence(): + """Joining the empty sequence results in the tree with one node.""" + T = nx.join_trees([]) + assert len(T) == 1 + assert T.number_of_edges() == 0 + + +def test_single(): + """Joining just one tree yields a tree with one more node.""" + T = nx.empty_graph(1) + trees = [(T, 0)] + actual_with_label = nx.join_trees(trees, label_attribute="custom_label") + expected = nx.path_graph(2) + assert nodes_equal(list(expected), list(actual_with_label)) + assert edges_equal(list(expected.edges()), list(actual_with_label.edges())) + + +def test_basic(): + """Joining multiple subtrees at a root node.""" + trees = [(nx.full_rary_tree(2, 2**2 - 1), 0) for i in range(2)] + expected = nx.full_rary_tree(2, 2**3 - 1) + actual = nx.join_trees(trees, label_attribute="old_labels") + assert nx.is_isomorphic(actual, expected) + assert _check_custom_label_attribute(trees, actual, "old_labels") + + actual_without_label = nx.join_trees(trees) + assert nx.is_isomorphic(actual_without_label, expected) + # check that no labels were stored + assert all(not data for _, data in actual_without_label.nodes(data=True)) + + +def test_first_label(): + """Test the functionality of the first_label argument.""" + T1 = nx.path_graph(3) + T2 = nx.path_graph(2) + actual = nx.join_trees([(T1, 0), (T2, 0)], first_label=10) + expected_nodes = set(range(10, 16)) + assert set(actual.nodes()) == expected_nodes + assert set(actual.neighbors(10)) == {11, 14} diff --git a/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_recognition.py b/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_recognition.py new file mode 100644 index 0000000000000000000000000000000000000000..105f5a89e9b10d37d1cc140880a66bc860d2e9f8 --- /dev/null +++ b/.venv/lib/python3.11/site-packages/networkx/algorithms/tree/tests/test_recognition.py @@ -0,0 +1,174 @@ +import pytest + +import networkx as nx + + +class TestTreeRecognition: + graph = nx.Graph + multigraph = nx.MultiGraph + + @classmethod + def setup_class(cls): + cls.T1 = cls.graph() + + cls.T2 = cls.graph() + cls.T2.add_node(1) + + cls.T3 = cls.graph() + cls.T3.add_nodes_from(range(5)) + edges = [(i, i + 1) for i in range(4)] + cls.T3.add_edges_from(edges) + + cls.T5 = cls.multigraph() + cls.T5.add_nodes_from(range(5)) + edges = [(i, i + 1) for i in range(4)] + cls.T5.add_edges_from(edges) + + cls.T6 = cls.graph() + cls.T6.add_nodes_from([6, 7]) + cls.T6.add_edge(6, 7) + + cls.F1 = nx.compose(cls.T6, cls.T3) + + cls.N4 = cls.graph() + cls.N4.add_node(1) + cls.N4.add_edge(1, 1) + + cls.N5 = cls.graph() + cls.N5.add_nodes_from(range(5)) + + cls.N6 = cls.graph() + cls.N6.add_nodes_from(range(3)) + cls.N6.add_edges_from([(0, 1), (1, 2), (2, 0)]) + + cls.NF1 = nx.compose(cls.T6, cls.N6) + + def test_null_tree(self): + with pytest.raises(nx.NetworkXPointlessConcept): + nx.is_tree(self.graph()) + + def test_null_tree2(self): + with pytest.raises(nx.NetworkXPointlessConcept): + nx.is_tree(self.multigraph()) + + def test_null_forest(self): + with pytest.raises(nx.NetworkXPointlessConcept): + nx.is_forest(self.graph()) + + def test_null_forest2(self): + with pytest.raises(nx.NetworkXPointlessConcept): + nx.is_forest(self.multigraph()) + + def test_is_tree(self): + assert nx.is_tree(self.T2) + assert nx.is_tree(self.T3) + assert nx.is_tree(self.T5) + + def test_is_not_tree(self): + assert not nx.is_tree(self.N4) + assert not nx.is_tree(self.N5) + assert not nx.is_tree(self.N6) + + def test_is_forest(self): + assert nx.is_forest(self.T2) + assert nx.is_forest(self.T3) + assert nx.is_forest(self.T5) + assert nx.is_forest(self.F1) + assert nx.is_forest(self.N5) + + def test_is_not_forest(self): + assert not nx.is_forest(self.N4) + assert not nx.is_forest(self.N6) + assert not nx.is_forest(self.NF1) + + +class TestDirectedTreeRecognition(TestTreeRecognition): + graph = nx.DiGraph + multigraph = nx.MultiDiGraph + + +def test_disconnected_graph(): + # https://github.com/networkx/networkx/issues/1144 + G = nx.Graph() + G.add_edges_from([(0, 1), (1, 2), (2, 0), (3, 4)]) + assert not nx.is_tree(G) + + G = nx.DiGraph() + G.add_edges_from([(0, 1), (1, 2), (2, 0), (3, 4)]) + assert not nx.is_tree(G) + + +def test_dag_nontree(): + G = nx.DiGraph() + G.add_edges_from([(0, 1), (0, 2), (1, 2)]) + assert not nx.is_tree(G) + assert nx.is_directed_acyclic_graph(G) + + +def test_multicycle(): + G = nx.MultiDiGraph() + G.add_edges_from([(0, 1), (0, 1)]) + assert not nx.is_tree(G) + assert nx.is_directed_acyclic_graph(G) + + +def test_emptybranch(): + G = nx.DiGraph() + G.add_nodes_from(range(10)) + assert nx.is_branching(G) + assert not nx.is_arborescence(G) + + +def test_is_branching_empty_graph_raises(): + G = nx.DiGraph() + with pytest.raises(nx.NetworkXPointlessConcept, match="G has no nodes."): + nx.is_branching(G) + + +def test_path(): + G = nx.DiGraph() + nx.add_path(G, range(5)) + assert nx.is_branching(G) + assert nx.is_arborescence(G) + + +def test_notbranching1(): + # Acyclic violation. + G = nx.MultiDiGraph() + G.add_nodes_from(range(10)) + G.add_edges_from([(0, 1), (1, 0)]) + assert not nx.is_branching(G) + assert not nx.is_arborescence(G) + + +def test_notbranching2(): + # In-degree violation. + G = nx.MultiDiGraph() + G.add_nodes_from(range(10)) + G.add_edges_from([(0, 1), (0, 2), (3, 2)]) + assert not nx.is_branching(G) + assert not nx.is_arborescence(G) + + +def test_notarborescence1(): + # Not an arborescence due to not spanning. + G = nx.MultiDiGraph() + G.add_nodes_from(range(10)) + G.add_edges_from([(0, 1), (0, 2), (1, 3), (5, 6)]) + assert nx.is_branching(G) + assert not nx.is_arborescence(G) + + +def test_notarborescence2(): + # Not an arborescence due to in-degree violation. + G = nx.MultiDiGraph() + nx.add_path(G, range(5)) + G.add_edge(6, 4) + assert not nx.is_branching(G) + assert not nx.is_arborescence(G) + + +def test_is_arborescense_empty_graph_raises(): + G = nx.DiGraph() + with pytest.raises(nx.NetworkXPointlessConcept, match="G has no nodes."): + nx.is_arborescence(G)