Add files using upload-large-folder tool

wemm/lib/python3.10/site-packages/botocore/data/m2/2021-04-28/endpoint-rule-set-1.json.gz

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:88c6e0a16a1567c4c2925bb8a62d4d85d50d8d666ab5d0a0341e0de61892b4a5
+size 1134

wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/__init__.py

@@ -0,0 +1,87 @@
+r"""This module provides functions and operations for bipartite
+graphs.  Bipartite graphs `B = (U, V, E)` have two node sets `U,V` and edges in
+`E` that only connect nodes from opposite sets. It is common in the literature
+to use an spatial analogy referring to the two node sets as top and bottom nodes.
+
+The bipartite algorithms are not imported into the networkx namespace
+at the top level so the easiest way to use them is with:
+
+>>> from networkx.algorithms import bipartite
+
+NetworkX does not have a custom bipartite graph class but the Graph()
+or DiGraph() classes can be used to represent bipartite graphs. However,
+you have to keep track of which set each node belongs to, and make
+sure that there is no edge between nodes of the same set. The convention used
+in NetworkX is to use a node attribute named `bipartite` with values 0 or 1 to
+identify the sets each node belongs to. This convention is not enforced in
+the source code of bipartite functions, it's only a recommendation.
+
+For example:
+
+>>> B = nx.Graph()
+>>> # Add nodes with the node attribute "bipartite"
+>>> B.add_nodes_from([1, 2, 3, 4], bipartite=0)
+>>> B.add_nodes_from(["a", "b", "c"], bipartite=1)
+>>> # Add edges only between nodes of opposite node sets
+>>> B.add_edges_from([(1, "a"), (1, "b"), (2, "b"), (2, "c"), (3, "c"), (4, "a")])
+
+Many algorithms of the bipartite module of NetworkX require, as an argument, a
+container with all the nodes that belong to one set, in addition to the bipartite
+graph `B`. The functions in the bipartite package do not check that the node set
+is actually correct nor that the input graph is actually bipartite.
+If `B` is connected, you can find the two node sets using a two-coloring
+algorithm:
+
+>>> nx.is_connected(B)
+True
+>>> bottom_nodes, top_nodes = bipartite.sets(B)
+
+However, if the input graph is not connected, there are more than one possible
+colorations. This is the reason why we require the user to pass a container
+with all nodes of one bipartite node set as an argument to most bipartite
+functions. In the face of ambiguity, we refuse the temptation to guess and
+raise an :exc:`AmbiguousSolution <networkx.AmbiguousSolution>`
+Exception if the input graph for
+:func:`bipartite.sets <networkx.algorithms.bipartite.basic.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 <networkx.algorithms.bipartite.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 *

wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/centrality.py

@@ -0,0 +1,290 @@
+import networkx as nx
+
+__all__ = ["degree_centrality", "betweenness_centrality", "closeness_centrality"]
+
+
+@nx._dispatchable(name="bipartite_degree_centrality")
+def degree_centrality(G, nodes):
+    r"""Compute the degree centrality for nodes in a bipartite network.
+
+    The degree centrality for a node `v` is the fraction of nodes
+    connected to it.
+
+    Parameters
+    ----------
+    G : graph
+       A bipartite network
+
+    nodes : list or container
+      Container with all nodes in one bipartite node set.
+
+    Returns
+    -------
+    centrality : dictionary
+       Dictionary keyed by node with bipartite degree centrality as the value.
+
+    Examples
+    --------
+    >>> G = nx.wheel_graph(5)
+    >>> top_nodes = {0, 1, 2}
+    >>> nx.bipartite.degree_centrality(G, nodes=top_nodes)
+    {0: 2.0, 1: 1.5, 2: 1.5, 3: 1.0, 4: 1.0}
+
+    See Also
+    --------
+    betweenness_centrality
+    closeness_centrality
+    :func:`~networkx.algorithms.bipartite.basic.sets`
+    :func:`~networkx.algorithms.bipartite.basic.is_bipartite`
+
+    Notes
+    -----
+    The nodes input parameter must contain all nodes in one bipartite node set,
+    but the dictionary returned contains all nodes from both bipartite node
+    sets. See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
+    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 <networkx.algorithms.bipartite>`
+    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 <networkx.algorithms.bipartite>`
+    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

wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/edgelist.py

@@ -0,0 +1,360 @@
+"""
+********************
+Bipartite Edge Lists
+********************
+Read and write NetworkX graphs as bipartite edge lists.
+
+Format
+------
+You can read or write three formats of edge lists with these functions.
+
+Node pairs with no data::
+
+ 1 2
+
+Python dictionary as data::
+
+ 1 2 {'weight':7, 'color':'green'}
+
+Arbitrary data::
+
+ 1 2 7 green
+
+For each edge (u, v) the node u is assigned to part 0 and the node v to part 1.
+"""
+
+__all__ = ["generate_edgelist", "write_edgelist", "parse_edgelist", "read_edgelist"]
+
+import networkx as nx
+from networkx.utils import not_implemented_for, open_file
+
+
+@open_file(1, mode="wb")
+def write_edgelist(G, path, comments="#", delimiter=" ", data=True, encoding="utf-8"):
+    """Write a bipartite graph as a list of edges.
+
+    Parameters
+    ----------
+    G : Graph
+       A NetworkX bipartite graph
+    path : file or string
+       File or filename to write. If a file is provided, it must be
+       opened in 'wb' mode. Filenames ending in .gz or .bz2 will be compressed.
+    comments : string, optional
+       The character used to indicate the start of a comment
+    delimiter : string, optional
+       The string used to separate values.  The default is whitespace.
+    data : bool or list, optional
+       If False write no edge data.
+       If True write a string representation of the edge data dictionary..
+       If a list (or other iterable) is provided, write the  keys specified
+       in the list.
+    encoding: string, optional
+       Specify which encoding to use when writing file.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> G.add_nodes_from([0, 2], bipartite=0)
+    >>> G.add_nodes_from([1, 3], bipartite=1)
+    >>> nx.write_edgelist(G, "test.edgelist")
+    >>> fh = open("test.edgelist", "wb")
+    >>> nx.write_edgelist(G, fh)
+    >>> nx.write_edgelist(G, "test.edgelist.gz")
+    >>> nx.write_edgelist(G, "test.edgelist.gz", data=False)
+
+    >>> G = nx.Graph()
+    >>> G.add_edge(1, 2, weight=7, color="red")
+    >>> nx.write_edgelist(G, "test.edgelist", data=False)
+    >>> nx.write_edgelist(G, "test.edgelist", data=["color"])
+    >>> nx.write_edgelist(G, "test.edgelist", data=["color", "weight"])
+
+    See Also
+    --------
+    write_edgelist
+    generate_edgelist
+    """
+    for line in generate_edgelist(G, delimiter, data):
+        line += "\n"
+        path.write(line.encode(encoding))
+
+
+@not_implemented_for("directed")
+def generate_edgelist(G, delimiter=" ", data=True):
+    """Generate a single line of the bipartite graph G in edge list format.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       The graph is assumed to have node attribute `part` set to 0,1 representing
+       the two graph parts
+
+    delimiter : string, optional
+       Separator for node labels
+
+    data : bool or list of keys
+       If False generate no edge data.  If True use a dictionary
+       representation of edge data.  If a list of keys use a list of data
+       values corresponding to the keys.
+
+    Returns
+    -------
+    lines : string
+        Lines of data in adjlist format.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)
+    >>> G.add_nodes_from([0, 2], bipartite=0)
+    >>> G.add_nodes_from([1, 3], bipartite=1)
+    >>> G[1][2]["weight"] = 3
+    >>> G[2][3]["capacity"] = 12
+    >>> for line in bipartite.generate_edgelist(G, data=False):
+    ...     print(line)
+    0 1
+    2 1
+    2 3
+
+    >>> for line in bipartite.generate_edgelist(G):
+    ...     print(line)
+    0 1 {}
+    2 1 {'weight': 3}
+    2 3 {'capacity': 12}
+
+    >>> for line in bipartite.generate_edgelist(G, data=["weight"]):
+    ...     print(line)
+    0 1
+    2 1 3
+    2 3
+    """
+    try:
+        part0 = [n for n, d in G.nodes.items() if d["bipartite"] == 0]
+    except BaseException as err:
+        raise AttributeError("Missing node attribute `bipartite`") from err
+    if data is True or data is False:
+        for n in part0:
+            for edge in G.edges(n, data=data):
+                yield delimiter.join(map(str, edge))
+    else:
+        for n in part0:
+            for u, v, d in G.edges(n, data=True):
+                edge = [u, v]
+                try:
+                    edge.extend(d[k] for k in data)
+                except KeyError:
+                    pass  # missing data for this edge, should warn?
+                yield delimiter.join(map(str, edge))
+
+
+@nx._dispatchable(name="bipartite_parse_edgelist", graphs=None, returns_graph=True)
+def parse_edgelist(
+    lines, comments="#", delimiter=None, create_using=None, nodetype=None, data=True
+):
+    """Parse lines of an edge list representation of a bipartite graph.
+
+    Parameters
+    ----------
+    lines : list or iterator of strings
+        Input data in edgelist format
+    comments : string, optional
+       Marker for comment lines
+    delimiter : string, optional
+       Separator for node labels
+    create_using: NetworkX graph container, optional
+       Use given NetworkX graph for holding nodes or edges.
+    nodetype : Python type, optional
+       Convert nodes to this type.
+    data : bool or list of (label,type) tuples
+       If False generate no edge data or if True use a dictionary
+       representation of edge data or a list tuples specifying dictionary
+       key names and types for edge data.
+
+    Returns
+    -------
+    G: NetworkX Graph
+        The bipartite graph corresponding to lines
+
+    Examples
+    --------
+    Edgelist with no data:
+
+    >>> from networkx.algorithms import bipartite
+    >>> lines = ["1 2", "2 3", "3 4"]
+    >>> G = bipartite.parse_edgelist(lines, nodetype=int)
+    >>> sorted(G.nodes())
+    [1, 2, 3, 4]
+    >>> sorted(G.nodes(data=True))
+    [(1, {'bipartite': 0}), (2, {'bipartite': 0}), (3, {'bipartite': 0}), (4, {'bipartite': 1})]
+    >>> sorted(G.edges())
+    [(1, 2), (2, 3), (3, 4)]
+
+    Edgelist with data in Python dictionary representation:
+
+    >>> lines = ["1 2 {'weight':3}", "2 3 {'weight':27}", "3 4 {'weight':3.0}"]
+    >>> G = bipartite.parse_edgelist(lines, nodetype=int)
+    >>> sorted(G.nodes())
+    [1, 2, 3, 4]
+    >>> sorted(G.edges(data=True))
+    [(1, 2, {'weight': 3}), (2, 3, {'weight': 27}), (3, 4, {'weight': 3.0})]
+
+    Edgelist with data in a list:
+
+    >>> lines = ["1 2 3", "2 3 27", "3 4 3.0"]
+    >>> G = bipartite.parse_edgelist(lines, nodetype=int, data=(("weight", float),))
+    >>> sorted(G.nodes())
+    [1, 2, 3, 4]
+    >>> sorted(G.edges(data=True))
+    [(1, 2, {'weight': 3.0}), (2, 3, {'weight': 27.0}), (3, 4, {'weight': 3.0})]
+
+    See Also
+    --------
+    """
+    from ast import literal_eval
+
+    G = nx.empty_graph(0, create_using)
+    for line in lines:
+        p = line.find(comments)
+        if p >= 0:
+            line = line[:p]
+        if not len(line):
+            continue
+        # split line, should have 2 or more
+        s = line.rstrip("\n").split(delimiter)
+        if len(s) < 2:
+            continue
+        u = s.pop(0)
+        v = s.pop(0)
+        d = s
+        if nodetype is not None:
+            try:
+                u = nodetype(u)
+                v = nodetype(v)
+            except BaseException as err:
+                raise TypeError(
+                    f"Failed to convert nodes {u},{v} to type {nodetype}."
+                ) from err
+
+        if len(d) == 0 or data is False:
+            # no data or data type specified
+            edgedata = {}
+        elif data is True:
+            # no edge types specified
+            try:  # try to evaluate as dictionary
+                edgedata = dict(literal_eval(" ".join(d)))
+            except BaseException as err:
+                raise TypeError(
+                    f"Failed to convert edge data ({d}) to dictionary."
+                ) from err
+        else:
+            # convert edge data to dictionary with specified keys and type
+            if len(d) != len(data):
+                raise IndexError(
+                    f"Edge data {d} and data_keys {data} are not the same length"
+                )
+            edgedata = {}
+            for (edge_key, edge_type), edge_value in zip(data, d):
+                try:
+                    edge_value = edge_type(edge_value)
+                except BaseException as err:
+                    raise TypeError(
+                        f"Failed to convert {edge_key} data "
+                        f"{edge_value} to type {edge_type}."
+                    ) from err
+                edgedata.update({edge_key: edge_value})
+        G.add_node(u, bipartite=0)
+        G.add_node(v, bipartite=1)
+        G.add_edge(u, v, **edgedata)
+    return G
+
+
+@open_file(0, mode="rb")
+@nx._dispatchable(name="bipartite_read_edgelist", graphs=None, returns_graph=True)
+def read_edgelist(
+    path,
+    comments="#",
+    delimiter=None,
+    create_using=None,
+    nodetype=None,
+    data=True,
+    edgetype=None,
+    encoding="utf-8",
+):
+    """Read a bipartite graph from a list of edges.
+
+    Parameters
+    ----------
+    path : file or string
+       File or filename to read. If a file is provided, it must be
+       opened in 'rb' mode.
+       Filenames ending in .gz or .bz2 will be uncompressed.
+    comments : string, optional
+       The character used to indicate the start of a comment.
+    delimiter : string, optional
+       The string used to separate values.  The default is whitespace.
+    create_using : Graph container, optional,
+       Use specified container to build graph.  The default is networkx.Graph,
+       an undirected graph.
+    nodetype : int, float, str, Python type, optional
+       Convert node data from strings to specified type
+    data : bool or list of (label,type) tuples
+       Tuples specifying dictionary key names and types for edge data
+    edgetype : int, float, str, Python type, optional OBSOLETE
+       Convert edge data from strings to specified type and use as 'weight'
+    encoding: string, optional
+       Specify which encoding to use when reading file.
+
+    Returns
+    -------
+    G : graph
+       A networkx Graph or other type specified with create_using
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)
+    >>> G.add_nodes_from([0, 2], bipartite=0)
+    >>> G.add_nodes_from([1, 3], bipartite=1)
+    >>> bipartite.write_edgelist(G, "test.edgelist")
+    >>> G = bipartite.read_edgelist("test.edgelist")
+
+    >>> fh = open("test.edgelist", "rb")
+    >>> G = bipartite.read_edgelist(fh)
+    >>> fh.close()
+
+    >>> G = bipartite.read_edgelist("test.edgelist", nodetype=int)
+
+    Edgelist with data in a list:
+
+    >>> textline = "1 2 3"
+    >>> fh = open("test.edgelist", "w")
+    >>> d = fh.write(textline)
+    >>> fh.close()
+    >>> G = bipartite.read_edgelist(
+    ...     "test.edgelist", nodetype=int, data=(("weight", float),)
+    ... )
+    >>> list(G)
+    [1, 2]
+    >>> list(G.edges(data=True))
+    [(1, 2, {'weight': 3.0})]
+
+    See parse_edgelist() for more examples of formatting.
+
+    See Also
+    --------
+    parse_edgelist
+
+    Notes
+    -----
+    Since nodes must be hashable, the function nodetype must return hashable
+    types (e.g. int, float, str, frozenset - or tuples of those, etc.)
+    """
+    lines = (line.decode(encoding) for line in path)
+    return parse_edgelist(
+        lines,
+        comments=comments,
+        delimiter=delimiter,
+        create_using=create_using,
+        nodetype=nodetype,
+        data=data,
+    )

wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/projection.py

@@ -0,0 +1,526 @@
+"""One-mode (unipartite) projections of bipartite graphs."""
+
+import networkx as nx
+from networkx.exception import NetworkXAlgorithmError
+from networkx.utils import not_implemented_for
+
+__all__ = [
+    "projected_graph",
+    "weighted_projected_graph",
+    "collaboration_weighted_projected_graph",
+    "overlap_weighted_projected_graph",
+    "generic_weighted_projected_graph",
+]
+
+
+@nx._dispatchable(
+    graphs="B", preserve_node_attrs=True, preserve_graph_attrs=True, returns_graph=True
+)
+def projected_graph(B, nodes, multigraph=False):
+    r"""Returns the projection of B onto one of its node sets.
+
+    Returns the graph G that is the projection of the bipartite graph B
+    onto the specified nodes. They retain their attributes and are connected
+    in G if they have a common neighbor in B.
+
+    Parameters
+    ----------
+    B : NetworkX graph
+      The input graph should be bipartite.
+
+    nodes : list or iterable
+      Nodes to project onto (the "bottom" nodes).
+
+    multigraph: bool (default=False)
+       If True return a multigraph where the multiple edges represent multiple
+       shared neighbors.  They edge key in the multigraph is assigned to the
+       label of the neighbor.
+
+    Returns
+    -------
+    Graph : NetworkX graph or multigraph
+       A graph that is the projection onto the given nodes.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> B = nx.path_graph(4)
+    >>> G = bipartite.projected_graph(B, [1, 3])
+    >>> list(G)
+    [1, 3]
+    >>> list(G.edges())
+    [(1, 3)]
+
+    If nodes `a`, and `b` are connected through both nodes 1 and 2 then
+    building a multigraph results in two edges in the projection onto
+    [`a`, `b`]:
+
+    >>> B = nx.Graph()
+    >>> B.add_edges_from([("a", 1), ("b", 1), ("a", 2), ("b", 2)])
+    >>> G = bipartite.projected_graph(B, ["a", "b"], multigraph=True)
+    >>> print([sorted((u, v)) for u, v in G.edges()])
+    [['a', 'b'], ['a', 'b']]
+
+    Notes
+    -----
+    No attempt is made to verify that the input graph B is bipartite.
+    Returns a simple graph that is the projection of the bipartite graph B
+    onto the set of nodes given in list nodes.  If multigraph=True then
+    a multigraph is returned with an edge for every shared neighbor.
+
+    Directed graphs are allowed as input.  The output will also then
+    be a directed graph with edges if there is a directed path between
+    the nodes.
+
+    The graph and node properties are (shallow) copied to the projected graph.
+
+    See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
+    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 <networkx.algorithms.bipartite>`
+    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 <networkx.algorithms.bipartite>`
+    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 <networkx.algorithms.bipartite>`
+    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 <networkx.algorithms.bipartite>`
+    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

wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/redundancy.py

@@ -0,0 +1,112 @@
+"""Node redundancy for bipartite graphs."""
+
+from itertools import combinations
+
+import networkx as nx
+from networkx import NetworkXError
+
+__all__ = ["node_redundancy"]
+
+
+@nx._dispatchable
+def node_redundancy(G, nodes=None):
+    r"""Computes the node redundancy coefficients for the nodes in the bipartite
+    graph `G`.
+
+    The redundancy coefficient of a node `v` is the fraction of pairs of
+    neighbors of `v` that are both linked to other nodes. In a one-mode
+    projection these nodes would be linked together even if `v` were
+    not there.
+
+    More formally, for any vertex `v`, the *redundancy coefficient of `v`* is
+    defined by
+
+    .. math::
+
+        rc(v) = \frac{|\{\{u, w\} \subseteq N(v),
+        \: \exists v' \neq  v,\: (v',u) \in E\:
+        \mathrm{and}\: (v',w) \in E\}|}{ \frac{|N(v)|(|N(v)|-1)}{2}},
+
+    where `N(v)` is the set of neighbors of `v` in `G`.
+
+    Parameters
+    ----------
+    G : graph
+        A bipartite graph
+
+    nodes : list or iterable (optional)
+        Compute redundancy for these nodes. The default is all nodes in G.
+
+    Returns
+    -------
+    redundancy : dictionary
+        A dictionary keyed by node with the node redundancy value.
+
+    Examples
+    --------
+    Compute the redundancy coefficient of each node in a graph::
+
+        >>> from networkx.algorithms import bipartite
+        >>> G = nx.cycle_graph(4)
+        >>> rc = bipartite.node_redundancy(G)
+        >>> rc[0]
+        1.0
+
+    Compute the average redundancy for the graph::
+
+        >>> from networkx.algorithms import bipartite
+        >>> G = nx.cycle_graph(4)
+        >>> rc = bipartite.node_redundancy(G)
+        >>> sum(rc.values()) / len(G)
+        1.0
+
+    Compute the average redundancy for a set of nodes::
+
+        >>> from networkx.algorithms import bipartite
+        >>> G = nx.cycle_graph(4)
+        >>> rc = bipartite.node_redundancy(G)
+        >>> nodes = [0, 2]
+        >>> sum(rc[n] for n in nodes) / len(nodes)
+        1.0
+
+    Raises
+    ------
+    NetworkXError
+        If any of the nodes in the graph (or in `nodes`, if specified) has
+        (out-)degree less than two (which would result in division by zero,
+        according to the definition of the redundancy coefficient).
+
+    References
+    ----------
+    .. [1] Latapy, Matthieu, Clémence Magnien, and Nathalie Del Vecchio (2008).
+       Basic notions for the analysis of large two-mode networks.
+       Social Networks 30(1), 31--48.
+
+    """
+    if nodes is None:
+        nodes = G
+    if any(len(G[v]) < 2 for v in nodes):
+        raise NetworkXError(
+            "Cannot compute redundancy coefficient for a node"
+            " that has fewer than two neighbors."
+        )
+    # TODO This can be trivially parallelized.
+    return {v: _node_redundancy(G, v) for v in nodes}
+
+
+def _node_redundancy(G, v):
+    """Returns the redundancy of the node `v` in the bipartite graph `G`.
+
+    If `G` is a graph with `n` nodes, the redundancy of a node is the ratio
+    of the "overlap" of `v` to the maximum possible overlap of `v`
+    according to its degree. The overlap of `v` is the number of pairs of
+    neighbors that have mutual neighbors themselves, other than `v`.
+
+    `v` must have at least two neighbors in `G`.
+
+    """
+    n = len(G[v])
+    overlap = sum(
+        1 for (u, w) in combinations(G[v], 2) if (set(G[u]) & set(G[w])) - {v}
+    )
+    return (2 * overlap) / (n * (n - 1))

wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/spectral.py

@@ -0,0 +1,69 @@
+"""
+Spectral bipartivity measure.
+"""
+
+import networkx as nx
+
+__all__ = ["spectral_bipartivity"]
+
+
+@nx._dispatchable(edge_attrs="weight")
+def spectral_bipartivity(G, nodes=None, weight="weight"):
+    """Returns the spectral bipartivity.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    nodes : list or container  optional(default is all nodes)
+      Nodes to return value of spectral bipartivity contribution.
+
+    weight : string or None  optional (default = 'weight')
+      Edge data key to use for edge weights. If None, weights set to 1.
+
+    Returns
+    -------
+    sb : float or dict
+       A single number if the keyword nodes is not specified, or
+       a dictionary keyed by node with the spectral bipartivity contribution
+       of that node as the value.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)
+    >>> bipartite.spectral_bipartivity(G)
+    1.0
+
+    Notes
+    -----
+    This implementation uses Numpy (dense) matrices which are not efficient
+    for storing large sparse graphs.
+
+    See Also
+    --------
+    color
+
+    References
+    ----------
+    .. [1] E. Estrada and J. A. Rodríguez-Velázquez, "Spectral measures of
+       bipartivity in complex networks", PhysRev E 72, 046105 (2005)
+    """
+    import scipy as sp
+
+    nodelist = list(G)  # ordering of nodes in matrix
+    A = nx.to_numpy_array(G, nodelist, weight=weight)
+    expA = sp.linalg.expm(A)
+    expmA = sp.linalg.expm(-A)
+    coshA = 0.5 * (expA + expmA)
+    if nodes is None:
+        # return single number for entire graph
+        return float(coshA.diagonal().sum() / expA.diagonal().sum())
+    else:
+        # contribution for individual nodes
+        index = dict(zip(nodelist, range(len(nodelist))))
+        sb = {}
+        for n in nodes:
+            i = index[n]
+            sb[n] = coshA.item(i, i) / expA.item(i, i)
+        return sb

wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/test_basic.py

@@ -0,0 +1,125 @@
+import pytest
+
+import networkx as nx
+from networkx.algorithms import bipartite
+
+
+class TestBipartiteBasic:
+    def test_is_bipartite(self):
+        assert bipartite.is_bipartite(nx.path_graph(4))
+        assert bipartite.is_bipartite(nx.DiGraph([(1, 0)]))
+        assert not bipartite.is_bipartite(nx.complete_graph(3))
+
+    def test_bipartite_color(self):
+        G = nx.path_graph(4)
+        c = bipartite.color(G)
+        assert c == {0: 1, 1: 0, 2: 1, 3: 0}
+
+    def test_not_bipartite_color(self):
+        with pytest.raises(nx.NetworkXError):
+            c = bipartite.color(nx.complete_graph(4))
+
+    def test_bipartite_directed(self):
+        G = bipartite.random_graph(10, 10, 0.1, directed=True)
+        assert bipartite.is_bipartite(G)
+
+    def test_bipartite_sets(self):
+        G = nx.path_graph(4)
+        X, Y = bipartite.sets(G)
+        assert X == {0, 2}
+        assert Y == {1, 3}
+
+    def test_bipartite_sets_directed(self):
+        G = nx.path_graph(4)
+        D = G.to_directed()
+        X, Y = bipartite.sets(D)
+        assert X == {0, 2}
+        assert Y == {1, 3}
+
+    def test_bipartite_sets_given_top_nodes(self):
+        G = nx.path_graph(4)
+        top_nodes = [0, 2]
+        X, Y = bipartite.sets(G, top_nodes)
+        assert X == {0, 2}
+        assert Y == {1, 3}
+
+    def test_bipartite_sets_disconnected(self):
+        with pytest.raises(nx.AmbiguousSolution):
+            G = nx.path_graph(4)
+            G.add_edges_from([(5, 6), (6, 7)])
+            X, Y = bipartite.sets(G)
+
+    def test_is_bipartite_node_set(self):
+        G = nx.path_graph(4)
+
+        with pytest.raises(nx.AmbiguousSolution):
+            bipartite.is_bipartite_node_set(G, [1, 1, 2, 3])
+
+        assert bipartite.is_bipartite_node_set(G, [0, 2])
+        assert bipartite.is_bipartite_node_set(G, [1, 3])
+        assert not bipartite.is_bipartite_node_set(G, [1, 2])
+        G.add_edge(10, 20)
+        assert bipartite.is_bipartite_node_set(G, [0, 2, 10])
+        assert bipartite.is_bipartite_node_set(G, [0, 2, 20])
+        assert bipartite.is_bipartite_node_set(G, [1, 3, 10])
+        assert bipartite.is_bipartite_node_set(G, [1, 3, 20])
+
+    def test_bipartite_density(self):
+        G = nx.path_graph(5)
+        X, Y = bipartite.sets(G)
+        density = len(list(G.edges())) / (len(X) * len(Y))
+        assert bipartite.density(G, X) == density
+        D = nx.DiGraph(G.edges())
+        assert bipartite.density(D, X) == density / 2.0
+        assert bipartite.density(nx.Graph(), {}) == 0.0
+
+    def test_bipartite_degrees(self):
+        G = nx.path_graph(5)
+        X = {1, 3}
+        Y = {0, 2, 4}
+        u, d = bipartite.degrees(G, Y)
+        assert dict(u) == {1: 2, 3: 2}
+        assert dict(d) == {0: 1, 2: 2, 4: 1}
+
+    def test_bipartite_weighted_degrees(self):
+        G = nx.path_graph(5)
+        G.add_edge(0, 1, weight=0.1, other=0.2)
+        X = {1, 3}
+        Y = {0, 2, 4}
+        u, d = bipartite.degrees(G, Y, weight="weight")
+        assert dict(u) == {1: 1.1, 3: 2}
+        assert dict(d) == {0: 0.1, 2: 2, 4: 1}
+        u, d = bipartite.degrees(G, Y, weight="other")
+        assert dict(u) == {1: 1.2, 3: 2}
+        assert dict(d) == {0: 0.2, 2: 2, 4: 1}
+
+    def test_biadjacency_matrix_weight(self):
+        pytest.importorskip("scipy")
+        G = nx.path_graph(5)
+        G.add_edge(0, 1, weight=2, other=4)
+        X = [1, 3]
+        Y = [0, 2, 4]
+        M = bipartite.biadjacency_matrix(G, X, weight="weight")
+        assert M[0, 0] == 2
+        M = bipartite.biadjacency_matrix(G, X, weight="other")
+        assert M[0, 0] == 4
+
+    def test_biadjacency_matrix(self):
+        pytest.importorskip("scipy")
+        tops = [2, 5, 10]
+        bots = [5, 10, 15]
+        for i in range(len(tops)):
+            G = bipartite.random_graph(tops[i], bots[i], 0.2)
+            top = [n for n, d in G.nodes(data=True) if d["bipartite"] == 0]
+            M = bipartite.biadjacency_matrix(G, top)
+            assert M.shape[0] == tops[i]
+            assert M.shape[1] == bots[i]
+
+    def test_biadjacency_matrix_order(self):
+        pytest.importorskip("scipy")
+        G = nx.path_graph(5)
+        G.add_edge(0, 1, weight=2)
+        X = [3, 1]
+        Y = [4, 2, 0]
+        M = bipartite.biadjacency_matrix(G, X, Y, weight="weight")
+        assert M[1, 2] == 2

wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/test_edgelist.py

@@ -0,0 +1,240 @@
+"""
+Unit tests for bipartite edgelists.
+"""
+
+import io
+
+import pytest
+
+import networkx as nx
+from networkx.algorithms import bipartite
+from networkx.utils import edges_equal, graphs_equal, nodes_equal
+
+
+class TestEdgelist:
+    @classmethod
+    def setup_class(cls):
+        cls.G = nx.Graph(name="test")
+        e = [("a", "b"), ("b", "c"), ("c", "d"), ("d", "e"), ("e", "f"), ("a", "f")]
+        cls.G.add_edges_from(e)
+        cls.G.add_nodes_from(["a", "c", "e"], bipartite=0)
+        cls.G.add_nodes_from(["b", "d", "f"], bipartite=1)
+        cls.G.add_node("g", bipartite=0)
+        cls.DG = nx.DiGraph(cls.G)
+        cls.MG = nx.MultiGraph()
+        cls.MG.add_edges_from([(1, 2), (1, 2), (1, 2)])
+        cls.MG.add_node(1, bipartite=0)
+        cls.MG.add_node(2, bipartite=1)
+
+    def test_read_edgelist_1(self):
+        s = b"""\
+# comment line
+1 2
+# comment line
+2 3
+"""
+        bytesIO = io.BytesIO(s)
+        G = bipartite.read_edgelist(bytesIO, nodetype=int)
+        assert edges_equal(G.edges(), [(1, 2), (2, 3)])
+
+    def test_read_edgelist_3(self):
+        s = b"""\
+# comment line
+1 2 {'weight':2.0}
+# comment line
+2 3 {'weight':3.0}
+"""
+        bytesIO = io.BytesIO(s)
+        G = bipartite.read_edgelist(bytesIO, nodetype=int, data=False)
+        assert edges_equal(G.edges(), [(1, 2), (2, 3)])
+
+        bytesIO = io.BytesIO(s)
+        G = bipartite.read_edgelist(bytesIO, nodetype=int, data=True)
+        assert edges_equal(
+            G.edges(data=True), [(1, 2, {"weight": 2.0}), (2, 3, {"weight": 3.0})]
+        )
+
+    def test_write_edgelist_1(self):
+        fh = io.BytesIO()
+        G = nx.Graph()
+        G.add_edges_from([(1, 2), (2, 3)])
+        G.add_node(1, bipartite=0)
+        G.add_node(2, bipartite=1)
+        G.add_node(3, bipartite=0)
+        bipartite.write_edgelist(G, fh, data=False)
+        fh.seek(0)
+        assert fh.read() == b"1 2\n3 2\n"
+
+    def test_write_edgelist_2(self):
+        fh = io.BytesIO()
+        G = nx.Graph()
+        G.add_edges_from([(1, 2), (2, 3)])
+        G.add_node(1, bipartite=0)
+        G.add_node(2, bipartite=1)
+        G.add_node(3, bipartite=0)
+        bipartite.write_edgelist(G, fh, data=True)
+        fh.seek(0)
+        assert fh.read() == b"1 2 {}\n3 2 {}\n"
+
+    def test_write_edgelist_3(self):
+        fh = io.BytesIO()
+        G = nx.Graph()
+        G.add_edge(1, 2, weight=2.0)
+        G.add_edge(2, 3, weight=3.0)
+        G.add_node(1, bipartite=0)
+        G.add_node(2, bipartite=1)
+        G.add_node(3, bipartite=0)
+        bipartite.write_edgelist(G, fh, data=True)
+        fh.seek(0)
+        assert fh.read() == b"1 2 {'weight': 2.0}\n3 2 {'weight': 3.0}\n"
+
+    def test_write_edgelist_4(self):
+        fh = io.BytesIO()
+        G = nx.Graph()
+        G.add_edge(1, 2, weight=2.0)
+        G.add_edge(2, 3, weight=3.0)
+        G.add_node(1, bipartite=0)
+        G.add_node(2, bipartite=1)
+        G.add_node(3, bipartite=0)
+        bipartite.write_edgelist(G, fh, data=[("weight")])
+        fh.seek(0)
+        assert fh.read() == b"1 2 2.0\n3 2 3.0\n"
+
+    def test_unicode(self, tmp_path):
+        G = nx.Graph()
+        name1 = chr(2344) + chr(123) + chr(6543)
+        name2 = chr(5543) + chr(1543) + chr(324)
+        G.add_edge(name1, "Radiohead", **{name2: 3})
+        G.add_node(name1, bipartite=0)
+        G.add_node("Radiohead", bipartite=1)
+
+        fname = tmp_path / "edgelist.txt"
+        bipartite.write_edgelist(G, fname)
+        H = bipartite.read_edgelist(fname)
+        assert graphs_equal(G, H)
+
+    def test_latin1_issue(self, tmp_path):
+        G = nx.Graph()
+        name1 = chr(2344) + chr(123) + chr(6543)
+        name2 = chr(5543) + chr(1543) + chr(324)
+        G.add_edge(name1, "Radiohead", **{name2: 3})
+        G.add_node(name1, bipartite=0)
+        G.add_node("Radiohead", bipartite=1)
+
+        fname = tmp_path / "edgelist.txt"
+        with pytest.raises(UnicodeEncodeError):
+            bipartite.write_edgelist(G, fname, encoding="latin-1")
+
+    def test_latin1(self, tmp_path):
+        G = nx.Graph()
+        name1 = "Bj" + chr(246) + "rk"
+        name2 = chr(220) + "ber"
+        G.add_edge(name1, "Radiohead", **{name2: 3})
+        G.add_node(name1, bipartite=0)
+        G.add_node("Radiohead", bipartite=1)
+
+        fname = tmp_path / "edgelist.txt"
+        bipartite.write_edgelist(G, fname, encoding="latin-1")
+        H = bipartite.read_edgelist(fname, encoding="latin-1")
+        assert graphs_equal(G, H)
+
+    def test_edgelist_graph(self, tmp_path):
+        G = self.G
+        fname = tmp_path / "edgelist.txt"
+        bipartite.write_edgelist(G, fname)
+        H = bipartite.read_edgelist(fname)
+        H2 = bipartite.read_edgelist(fname)
+        assert H is not H2  # they should be different graphs
+        G.remove_node("g")  # isolated nodes are not written in edgelist
+        assert nodes_equal(list(H), list(G))
+        assert edges_equal(list(H.edges()), list(G.edges()))
+
+    def test_edgelist_integers(self, tmp_path):
+        G = nx.convert_node_labels_to_integers(self.G)
+        fname = tmp_path / "edgelist.txt"
+        bipartite.write_edgelist(G, fname)
+        H = bipartite.read_edgelist(fname, nodetype=int)
+        # isolated nodes are not written in edgelist
+        G.remove_nodes_from(list(nx.isolates(G)))
+        assert nodes_equal(list(H), list(G))
+        assert edges_equal(list(H.edges()), list(G.edges()))
+
+    def test_edgelist_multigraph(self, tmp_path):
+        G = self.MG
+        fname = tmp_path / "edgelist.txt"
+        bipartite.write_edgelist(G, fname)
+        H = bipartite.read_edgelist(fname, nodetype=int, create_using=nx.MultiGraph())
+        H2 = bipartite.read_edgelist(fname, nodetype=int, create_using=nx.MultiGraph())
+        assert H is not H2  # they should be different graphs
+        assert nodes_equal(list(H), list(G))
+        assert edges_equal(list(H.edges()), list(G.edges()))
+
+    def test_empty_digraph(self):
+        with pytest.raises(nx.NetworkXNotImplemented):
+            bytesIO = io.BytesIO()
+            bipartite.write_edgelist(nx.DiGraph(), bytesIO)
+
+    def test_raise_attribute(self):
+        with pytest.raises(AttributeError):
+            G = nx.path_graph(4)
+            bytesIO = io.BytesIO()
+            bipartite.write_edgelist(G, bytesIO)
+
+    def test_parse_edgelist(self):
+        """Tests for conditions specific to
+        parse_edge_list method"""
+
+        # ignore strings of length less than 2
+        lines = ["1 2", "2 3", "3 1", "4", " "]
+        G = bipartite.parse_edgelist(lines, nodetype=int)
+        assert list(G.nodes) == [1, 2, 3]
+
+        # Exception raised when node is not convertible
+        # to specified data type
+        with pytest.raises(TypeError, match=".*Failed to convert nodes"):
+            lines = ["a b", "b c", "c a"]
+            G = bipartite.parse_edgelist(lines, nodetype=int)
+
+        # Exception raised when format of data is not
+        # convertible to dictionary object
+        with pytest.raises(TypeError, match=".*Failed to convert edge data"):
+            lines = ["1 2 3", "2 3 4", "3 1 2"]
+            G = bipartite.parse_edgelist(lines, nodetype=int)
+
+        # Exception raised when edge data and data
+        # keys are not of same length
+        with pytest.raises(IndexError):
+            lines = ["1 2 3 4", "2 3 4"]
+            G = bipartite.parse_edgelist(
+                lines, nodetype=int, data=[("weight", int), ("key", int)]
+            )
+
+        # Exception raised when edge data is not
+        # convertible to specified data type
+        with pytest.raises(TypeError, match=".*Failed to convert key data"):
+            lines = ["1 2 3 a", "2 3 4 b"]
+            G = bipartite.parse_edgelist(
+                lines, nodetype=int, data=[("weight", int), ("key", int)]
+            )
+
+
+def test_bipartite_edgelist_consistent_strip_handling():
+    """See gh-7462
+
+    Input when printed looks like:
+
+        A       B       interaction     2
+        B       C       interaction     4
+        C       A       interaction
+
+    Note the trailing \\t in the last line, which indicates the existence of
+    an empty data field.
+    """
+    lines = io.StringIO(
+        "A\tB\tinteraction\t2\nB\tC\tinteraction\t4\nC\tA\tinteraction\t"
+    )
+    descr = [("type", str), ("weight", str)]
+    # Should not raise
+    G = nx.bipartite.parse_edgelist(lines, delimiter="\t", data=descr)
+    expected = [("A", "B", "2"), ("A", "C", ""), ("B", "C", "4")]
+    assert sorted(G.edges(data="weight")) == expected

wemm/lib/python3.10/site-packages/networkx/algorithms/bipartite/tests/test_matching.py

@@ -0,0 +1,327 @@
+"""Unit tests for the :mod:`networkx.algorithms.bipartite.matching` module."""
+
+import itertools
+
+import pytest
+
+import networkx as nx
+from networkx.algorithms.bipartite.matching import (
+    eppstein_matching,
+    hopcroft_karp_matching,
+    maximum_matching,
+    minimum_weight_full_matching,
+    to_vertex_cover,
+)
+
+
+class TestMatching:
+    """Tests for bipartite matching algorithms."""
+
+    def setup_method(self):
+        """Creates a bipartite graph for use in testing matching algorithms.
+
+        The bipartite graph has a maximum cardinality matching that leaves
+        vertex 1 and vertex 10 unmatched. The first six numbers are the left
+        vertices and the next six numbers are the right vertices.
+
+        """
+        self.simple_graph = nx.complete_bipartite_graph(2, 3)
+        self.simple_solution = {0: 2, 1: 3, 2: 0, 3: 1}
+
+        edges = [(0, 7), (0, 8), (2, 6), (2, 9), (3, 8), (4, 8), (4, 9), (5, 11)]
+        self.top_nodes = set(range(6))
+        self.graph = nx.Graph()
+        self.graph.add_nodes_from(range(12))
+        self.graph.add_edges_from(edges)
+
+        # Example bipartite graph from issue 2127
+        G = nx.Graph()
+        G.add_nodes_from(
+            [
+                (1, "C"),
+                (1, "B"),
+                (0, "G"),
+                (1, "F"),
+                (1, "E"),
+                (0, "C"),
+                (1, "D"),
+                (1, "I"),
+                (0, "A"),
+                (0, "D"),
+                (0, "F"),
+                (0, "E"),
+                (0, "H"),
+                (1, "G"),
+                (1, "A"),
+                (0, "I"),
+                (0, "B"),
+                (1, "H"),
+            ]
+        )
+        G.add_edge((1, "C"), (0, "A"))
+        G.add_edge((1, "B"), (0, "A"))
+        G.add_edge((0, "G"), (1, "I"))
+        G.add_edge((0, "G"), (1, "H"))
+        G.add_edge((1, "F"), (0, "A"))
+        G.add_edge((1, "F"), (0, "C"))
+        G.add_edge((1, "F"), (0, "E"))
+        G.add_edge((1, "E"), (0, "A"))
+        G.add_edge((1, "E"), (0, "C"))
+        G.add_edge((0, "C"), (1, "D"))
+        G.add_edge((0, "C"), (1, "I"))
+        G.add_edge((0, "C"), (1, "G"))
+        G.add_edge((0, "C"), (1, "H"))
+        G.add_edge((1, "D"), (0, "A"))
+        G.add_edge((1, "I"), (0, "A"))
+        G.add_edge((1, "I"), (0, "E"))
+        G.add_edge((0, "A"), (1, "G"))
+        G.add_edge((0, "A"), (1, "H"))
+        G.add_edge((0, "E"), (1, "G"))
+        G.add_edge((0, "E"), (1, "H"))
+        self.disconnected_graph = G
+
+    def check_match(self, matching):
+        """Asserts that the matching is what we expect from the bipartite graph
+        constructed in the :meth:`setup` fixture.
+
+        """
+        # For the sake of brevity, rename `matching` to `M`.
+        M = matching
+        matched_vertices = frozenset(itertools.chain(*M.items()))
+        # Assert that the maximum number of vertices (10) is matched.
+        assert matched_vertices == frozenset(range(12)) - {1, 10}
+        # Assert that no vertex appears in two edges, or in other words, that
+        # the matching (u, v) and (v, u) both appear in the matching
+        # dictionary.
+        assert all(u == M[M[u]] for u in range(12) if u in M)
+
+    def check_vertex_cover(self, vertices):
+        """Asserts that the given set of vertices is the vertex cover we
+        expected from the bipartite graph constructed in the :meth:`setup`
+        fixture.
+
+        """
+        # By Konig's theorem, the number of edges in a maximum matching equals
+        # the number of vertices in a minimum vertex cover.
+        assert len(vertices) == 5
+        # Assert that the set is truly a vertex cover.
+        for u, v in self.graph.edges():
+            assert u in vertices or v in vertices
+        # TODO Assert that the vertices are the correct ones.
+
+    def test_eppstein_matching(self):
+        """Tests that David Eppstein's implementation of the Hopcroft--Karp
+        algorithm produces a maximum cardinality matching.
+
+        """
+        self.check_match(eppstein_matching(self.graph, self.top_nodes))
+
+    def test_hopcroft_karp_matching(self):
+        """Tests that the Hopcroft--Karp algorithm produces a maximum
+        cardinality matching in a bipartite graph.
+
+        """
+        self.check_match(hopcroft_karp_matching(self.graph, self.top_nodes))
+
+    def test_to_vertex_cover(self):
+        """Test for converting a maximum matching to a minimum vertex cover."""
+        matching = maximum_matching(self.graph, self.top_nodes)
+        vertex_cover = to_vertex_cover(self.graph, matching, self.top_nodes)
+        self.check_vertex_cover(vertex_cover)
+
+    def test_eppstein_matching_simple(self):
+        match = eppstein_matching(self.simple_graph)
+        assert match == self.simple_solution
+
+    def test_hopcroft_karp_matching_simple(self):
+        match = hopcroft_karp_matching(self.simple_graph)
+        assert match == self.simple_solution
+
+    def test_eppstein_matching_disconnected(self):
+        with pytest.raises(nx.AmbiguousSolution):
+            match = eppstein_matching(self.disconnected_graph)
+
+    def test_hopcroft_karp_matching_disconnected(self):
+        with pytest.raises(nx.AmbiguousSolution):
+            match = hopcroft_karp_matching(self.disconnected_graph)
+
+    def test_issue_2127(self):
+        """Test from issue 2127"""
+        # Build the example DAG
+        G = nx.DiGraph()
+        G.add_edge("A", "C")
+        G.add_edge("A", "B")
+        G.add_edge("C", "E")
+        G.add_edge("C", "D")
+        G.add_edge("E", "G")
+        G.add_edge("E", "F")
+        G.add_edge("G", "I")
+        G.add_edge("G", "H")
+
+        tc = nx.transitive_closure(G)
+        btc = nx.Graph()
+
+        # Create a bipartite graph based on the transitive closure of G
+        for v in tc.nodes():
+            btc.add_node((0, v))
+            btc.add_node((1, v))
+
+        for u, v in tc.edges():
+            btc.add_edge((0, u), (1, v))
+
+        top_nodes = {n for n in btc if n[0] == 0}
+        matching = hopcroft_karp_matching(btc, top_nodes)
+        vertex_cover = to_vertex_cover(btc, matching, top_nodes)
+        independent_set = set(G) - {v for _, v in vertex_cover}
+        assert {"B", "D", "F", "I", "H"} == independent_set
+
+    def test_vertex_cover_issue_2384(self):
+        G = nx.Graph([(0, 3), (1, 3), (1, 4), (2, 3)])
+        matching = maximum_matching(G)
+        vertex_cover = to_vertex_cover(G, matching)
+        for u, v in G.edges():
+            assert u in vertex_cover or v in vertex_cover
+
+    def test_vertex_cover_issue_3306(self):
+        G = nx.Graph()
+        edges = [(0, 2), (1, 0), (1, 1), (1, 2), (2, 2)]
+        G.add_edges_from([((i, "L"), (j, "R")) for i, j in edges])
+
+        matching = maximum_matching(G)
+        vertex_cover = to_vertex_cover(G, matching)
+        for u, v in G.edges():
+            assert u in vertex_cover or v in vertex_cover
+
+    def test_unorderable_nodes(self):
+        a = object()
+        b = object()
+        c = object()
+        d = object()
+        e = object()
+        G = nx.Graph([(a, d), (b, d), (b, e), (c, d)])
+        matching = maximum_matching(G)
+        vertex_cover = to_vertex_cover(G, matching)
+        for u, v in G.edges():
+            assert u in vertex_cover or v in vertex_cover
+
+
+def test_eppstein_matching():
+    """Test in accordance to issue #1927"""
+    G = nx.Graph()
+    G.add_nodes_from(["a", 2, 3, 4], bipartite=0)
+    G.add_nodes_from([1, "b", "c"], bipartite=1)
+    G.add_edges_from([("a", 1), ("a", "b"), (2, "b"), (2, "c"), (3, "c"), (4, 1)])
+    matching = eppstein_matching(G)
+    assert len(matching) == len(maximum_matching(G))
+    assert all(x in set(matching.keys()) for x in set(matching.values()))
+
+
+class TestMinimumWeightFullMatching:
+    @classmethod
+    def setup_class(cls):
+        pytest.importorskip("scipy")
+
+    def test_minimum_weight_full_matching_incomplete_graph(self):
+        B = nx.Graph()
+        B.add_nodes_from([1, 2], bipartite=0)
+        B.add_nodes_from([3, 4], bipartite=1)
+        B.add_edge(1, 4, weight=100)
+        B.add_edge(2, 3, weight=100)
+        B.add_edge(2, 4, weight=50)
+        matching = minimum_weight_full_matching(B)
+        assert matching == {1: 4, 2: 3, 4: 1, 3: 2}
+
+    def test_minimum_weight_full_matching_with_no_full_matching(self):
+        B = nx.Graph()
+        B.add_nodes_from([1, 2, 3], bipartite=0)
+        B.add_nodes_from([4, 5, 6], bipartite=1)
+        B.add_edge(1, 4, weight=100)
+        B.add_edge(2, 4, weight=100)
+        B.add_edge(3, 4, weight=50)
+        B.add_edge(3, 5, weight=50)
+        B.add_edge(3, 6, weight=50)
+        with pytest.raises(ValueError):
+            minimum_weight_full_matching(B)
+
+    def test_minimum_weight_full_matching_square(self):
+        G = nx.complete_bipartite_graph(3, 3)
+        G.add_edge(0, 3, weight=400)
+        G.add_edge(0, 4, weight=150)
+        G.add_edge(0, 5, weight=400)
+        G.add_edge(1, 3, weight=400)
+        G.add_edge(1, 4, weight=450)
+        G.add_edge(1, 5, weight=600)
+        G.add_edge(2, 3, weight=300)
+        G.add_edge(2, 4, weight=225)
+        G.add_edge(2, 5, weight=300)
+        matching = minimum_weight_full_matching(G)
+        assert matching == {0: 4, 1: 3, 2: 5, 4: 0, 3: 1, 5: 2}
+
+    def test_minimum_weight_full_matching_smaller_left(self):
+        G = nx.complete_bipartite_graph(3, 4)
+        G.add_edge(0, 3, weight=400)
+        G.add_edge(0, 4, weight=150)
+        G.add_edge(0, 5, weight=400)
+        G.add_edge(0, 6, weight=1)
+        G.add_edge(1, 3, weight=400)
+        G.add_edge(1, 4, weight=450)
+        G.add_edge(1, 5, weight=600)
+        G.add_edge(1, 6, weight=2)
+        G.add_edge(2, 3, weight=300)
+        G.add_edge(2, 4, weight=225)
+        G.add_edge(2, 5, weight=290)
+        G.add_edge(2, 6, weight=3)
+        matching = minimum_weight_full_matching(G)
+        assert matching == {0: 4, 1: 6, 2: 5, 4: 0, 5: 2, 6: 1}
+
+    def test_minimum_weight_full_matching_smaller_top_nodes_right(self):
+        G = nx.complete_bipartite_graph(3, 4)
+        G.add_edge(0, 3, weight=400)
+        G.add_edge(0, 4, weight=150)
+        G.add_edge(0, 5, weight=400)
+        G.add_edge(0, 6, weight=1)
+        G.add_edge(1, 3, weight=400)
+        G.add_edge(1, 4, weight=450)
+        G.add_edge(1, 5, weight=600)
+        G.add_edge(1, 6, weight=2)
+        G.add_edge(2, 3, weight=300)
+        G.add_edge(2, 4, weight=225)
+        G.add_edge(2, 5, weight=290)
+        G.add_edge(2, 6, weight=3)
+        matching = minimum_weight_full_matching(G, top_nodes=[3, 4, 5, 6])
+        assert matching == {0: 4, 1: 6, 2: 5, 4: 0, 5: 2, 6: 1}
+
+    def test_minimum_weight_full_matching_smaller_right(self):
+        G = nx.complete_bipartite_graph(4, 3)
+        G.add_edge(0, 4, weight=400)
+        G.add_edge(0, 5, weight=400)
+        G.add_edge(0, 6, weight=300)
+        G.add_edge(1, 4, weight=150)
+        G.add_edge(1, 5, weight=450)
+        G.add_edge(1, 6, weight=225)
+        G.add_edge(2, 4, weight=400)
+        G.add_edge(2, 5, weight=600)
+        G.add_edge(2, 6, weight=290)
+        G.add_edge(3, 4, weight=1)
+        G.add_edge(3, 5, weight=2)
+        G.add_edge(3, 6, weight=3)
+        matching = minimum_weight_full_matching(G)
+        assert matching == {1: 4, 2: 6, 3: 5, 4: 1, 5: 3, 6: 2}
+
+    def test_minimum_weight_full_matching_negative_weights(self):
+        G = nx.complete_bipartite_graph(2, 2)
+        G.add_edge(0, 2, weight=-2)
+        G.add_edge(0, 3, weight=0.2)
+        G.add_edge(1, 2, weight=-2)
+        G.add_edge(1, 3, weight=0.3)
+        matching = minimum_weight_full_matching(G)
+        assert matching == {0: 3, 1: 2, 2: 1, 3: 0}
+
+    def test_minimum_weight_full_matching_different_weight_key(self):
+        G = nx.complete_bipartite_graph(2, 2)
+        G.add_edge(0, 2, mass=2)
+        G.add_edge(0, 3, mass=0.2)
+        G.add_edge(1, 2, mass=1)
+        G.add_edge(1, 3, mass=2)
+        matching = minimum_weight_full_matching(G, weight="mass")
+        assert matching == {0: 3, 1: 2, 2: 1, 3: 0}

wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/dispersion.py

@@ -0,0 +1,107 @@
+from itertools import combinations
+
+import networkx as nx
+
+__all__ = ["dispersion"]
+
+
+@nx._dispatchable
+def dispersion(G, u=None, v=None, normalized=True, alpha=1.0, b=0.0, c=0.0):
+    r"""Calculate dispersion between `u` and `v` in `G`.
+
+    A link between two actors (`u` and `v`) has a high dispersion when their
+    mutual ties (`s` and `t`) are not well connected with each other.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph.
+    u : node, optional
+        The source for the dispersion score (e.g. ego node of the network).
+    v : node, optional
+        The target of the dispersion score if specified.
+    normalized : bool
+        If True (default) normalize by the embeddedness of the nodes (u and v).
+    alpha, b, c : float
+        Parameters for the normalization procedure. When `normalized` is True,
+        the dispersion value is normalized by::
+
+            result = ((dispersion + b) ** alpha) / (embeddedness + c)
+
+        as long as the denominator is nonzero.
+
+    Returns
+    -------
+    nodes : dictionary
+        If u (v) is specified, returns a dictionary of nodes with dispersion
+        score for all "target" ("source") nodes. If neither u nor v is
+        specified, returns a dictionary of dictionaries for all nodes 'u' in the
+        graph with a dispersion score for each node 'v'.
+
+    Notes
+    -----
+    This implementation follows Lars Backstrom and Jon Kleinberg [1]_. Typical
+    usage would be to run dispersion on the ego network $G_u$ if $u$ were
+    specified.  Running :func:`dispersion` with neither $u$ nor $v$ specified
+    can take some time to complete.
+
+    References
+    ----------
+    .. [1] Romantic Partnerships and the Dispersion of Social Ties:
+        A Network Analysis of Relationship Status on Facebook.
+        Lars Backstrom, Jon Kleinberg.
+        https://arxiv.org/pdf/1310.6753v1.pdf
+
+    """
+
+    def _dispersion(G_u, u, v):
+        """dispersion for all nodes 'v' in a ego network G_u of node 'u'"""
+        u_nbrs = set(G_u[u])
+        ST = {n for n in G_u[v] if n in u_nbrs}
+        set_uv = {u, v}
+        # all possible ties of connections that u and b share
+        possib = combinations(ST, 2)
+        total = 0
+        for s, t in possib:
+            # neighbors of s that are in G_u, not including u and v
+            nbrs_s = u_nbrs.intersection(G_u[s]) - set_uv
+            # s and t are not directly connected
+            if t not in nbrs_s:
+                # s and t do not share a connection
+                if nbrs_s.isdisjoint(G_u[t]):
+                    # tick for disp(u, v)
+                    total += 1
+        # neighbors that u and v share
+        embeddedness = len(ST)
+
+        dispersion_val = total
+        if normalized:
+            dispersion_val = (total + b) ** alpha
+            if embeddedness + c != 0:
+                dispersion_val /= embeddedness + c
+
+        return dispersion_val
+
+    if u is None:
+        # v and u are not specified
+        if v is None:
+            results = {n: {} for n in G}
+            for u in G:
+                for v in G[u]:
+                    results[u][v] = _dispersion(G, u, v)
+        # u is not specified, but v is
+        else:
+            results = dict.fromkeys(G[v], {})
+            for u in G[v]:
+                results[u] = _dispersion(G, v, u)
+    else:
+        # u is specified with no target v
+        if v is None:
+            results = dict.fromkeys(G[u], {})
+            for v in G[u]:
+                results[v] = _dispersion(G, u, v)
+        # both u and v are specified
+        else:
+            results = _dispersion(G, u, v)
+
+    return results

wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/flow_matrix.py

@@ -0,0 +1,130 @@
+# Helpers for current-flow betweenness and current-flow closeness
+# Lazy computations for inverse Laplacian and flow-matrix rows.
+import networkx as nx
+
+
+@nx._dispatchable(edge_attrs="weight")
+def flow_matrix_row(G, weight=None, dtype=float, solver="lu"):
+    # Generate a row of the current-flow matrix
+    import numpy as np
+
+    solvername = {
+        "full": FullInverseLaplacian,
+        "lu": SuperLUInverseLaplacian,
+        "cg": CGInverseLaplacian,
+    }
+    n = G.number_of_nodes()
+    L = nx.laplacian_matrix(G, nodelist=range(n), weight=weight).asformat("csc")
+    L = L.astype(dtype)
+    C = solvername[solver](L, dtype=dtype)  # initialize solver
+    w = C.w  # w is the Laplacian matrix width
+    # row-by-row flow matrix
+    for u, v in sorted(sorted((u, v)) for u, v in G.edges()):
+        B = np.zeros(w, dtype=dtype)
+        c = G[u][v].get(weight, 1.0)
+        B[u % w] = c
+        B[v % w] = -c
+        # get only the rows needed in the inverse laplacian
+        # and multiply to get the flow matrix row
+        row = B @ C.get_rows(u, v)
+        yield row, (u, v)
+
+
+# Class to compute the inverse laplacian only for specified rows
+# Allows computation of the current-flow matrix without storing entire
+# inverse laplacian matrix
+class InverseLaplacian:
+    def __init__(self, L, width=None, dtype=None):
+        global np
+        import numpy as np
+
+        (n, n) = L.shape
+        self.dtype = dtype
+        self.n = n
+        if width is None:
+            self.w = self.width(L)
+        else:
+            self.w = width
+        self.C = np.zeros((self.w, n), dtype=dtype)
+        self.L1 = L[1:, 1:]
+        self.init_solver(L)
+
+    def init_solver(self, L):
+        pass
+
+    def solve(self, r):
+        raise nx.NetworkXError("Implement solver")
+
+    def solve_inverse(self, r):
+        raise nx.NetworkXError("Implement solver")
+
+    def get_rows(self, r1, r2):
+        for r in range(r1, r2 + 1):
+            self.C[r % self.w, 1:] = self.solve_inverse(r)
+        return self.C
+
+    def get_row(self, r):
+        self.C[r % self.w, 1:] = self.solve_inverse(r)
+        return self.C[r % self.w]
+
+    def width(self, L):
+        m = 0
+        for i, row in enumerate(L):
+            w = 0
+            y = np.nonzero(row)[-1]
+            if len(y) > 0:
+                v = y - i
+                w = v.max() - v.min() + 1
+                m = max(w, m)
+        return m
+
+
+class FullInverseLaplacian(InverseLaplacian):
+    def init_solver(self, L):
+        self.IL = np.zeros(L.shape, dtype=self.dtype)
+        self.IL[1:, 1:] = np.linalg.inv(self.L1.todense())
+
+    def solve(self, rhs):
+        s = np.zeros(rhs.shape, dtype=self.dtype)
+        s = self.IL @ rhs
+        return s
+
+    def solve_inverse(self, r):
+        return self.IL[r, 1:]
+
+
+class SuperLUInverseLaplacian(InverseLaplacian):
+    def init_solver(self, L):
+        import scipy as sp
+
+        self.lusolve = sp.sparse.linalg.factorized(self.L1.tocsc())
+
+    def solve_inverse(self, r):
+        rhs = np.zeros(self.n, dtype=self.dtype)
+        rhs[r] = 1
+        return self.lusolve(rhs[1:])
+
+    def solve(self, rhs):
+        s = np.zeros(rhs.shape, dtype=self.dtype)
+        s[1:] = self.lusolve(rhs[1:])
+        return s
+
+
+class CGInverseLaplacian(InverseLaplacian):
+    def init_solver(self, L):
+        global sp
+        import scipy as sp
+
+        ilu = sp.sparse.linalg.spilu(self.L1.tocsc())
+        n = self.n - 1
+        self.M = sp.sparse.linalg.LinearOperator(shape=(n, n), matvec=ilu.solve)
+
+    def solve(self, rhs):
+        s = np.zeros(rhs.shape, dtype=self.dtype)
+        s[1:] = sp.sparse.linalg.cg(self.L1, rhs[1:], M=self.M, atol=0)[0]
+        return s
+
+    def solve_inverse(self, r):
+        rhs = np.zeros(self.n, self.dtype)
+        rhs[r] = 1
+        return sp.sparse.linalg.cg(self.L1, rhs[1:], M=self.M, atol=0)[0]

wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/laplacian.py

@@ -0,0 +1,150 @@
+"""
+Laplacian centrality measures.
+"""
+
+import networkx as nx
+
+__all__ = ["laplacian_centrality"]
+
+
+@nx._dispatchable(edge_attrs="weight")
+def laplacian_centrality(
+    G, normalized=True, nodelist=None, weight="weight", walk_type=None, alpha=0.95
+):
+    r"""Compute the Laplacian centrality for nodes in the graph `G`.
+
+    The Laplacian Centrality of a node ``i`` is measured by the drop in the
+    Laplacian Energy after deleting node ``i`` from the graph. The Laplacian Energy
+    is the sum of the squared eigenvalues of a graph's Laplacian matrix.
+
+    .. math::
+
+        C_L(u_i,G) = \frac{(\Delta E)_i}{E_L (G)} = \frac{E_L (G)-E_L (G_i)}{E_L (G)}
+
+        E_L (G) = \sum_{i=0}^n \lambda_i^2
+
+    Where $E_L (G)$ is the Laplacian energy of graph `G`,
+    E_L (G_i) is the Laplacian energy of graph `G` after deleting node ``i``
+    and $\lambda_i$ are the eigenvalues of `G`'s Laplacian matrix.
+    This formula shows the normalized value. Without normalization,
+    the numerator on the right side is returned.
+
+    Parameters
+    ----------
+    G : graph
+        A networkx graph
+
+    normalized : bool (default = True)
+        If True the centrality score is scaled so the sum over all nodes is 1.
+        If False the centrality score for each node is the drop in Laplacian
+        energy when that node is removed.
+
+    nodelist : list, optional (default = None)
+        The rows and columns are ordered according to the nodes in nodelist.
+        If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight: string or None, optional (default=`weight`)
+        Optional parameter `weight` to compute the Laplacian matrix.
+        The edge data key used to compute each value in the matrix.
+        If None, then each edge has weight 1.
+
+    walk_type : string or None, optional (default=None)
+        Optional parameter `walk_type` used when calling
+        :func:`directed_laplacian_matrix <networkx.directed_laplacian_matrix>`.
+        One of ``"random"``, ``"lazy"``, or ``"pagerank"``. If ``walk_type=None``
+        (the default), then a value is selected according to the properties of `G`:
+        - ``walk_type="random"`` if `G` is strongly connected and aperiodic
+        - ``walk_type="lazy"`` if `G` is strongly connected but not aperiodic
+        - ``walk_type="pagerank"`` for all other cases.
+
+    alpha : real (default = 0.95)
+        Optional parameter `alpha` used when calling
+        :func:`directed_laplacian_matrix <networkx.directed_laplacian_matrix>`.
+        (1 - alpha) is the teleportation probability used with pagerank.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with Laplacian centrality as the value.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> edges = [(0, 1, 4), (0, 2, 2), (2, 1, 1), (1, 3, 2), (1, 4, 2), (4, 5, 1)]
+    >>> G.add_weighted_edges_from(edges)
+    >>> sorted((v, f"{c:0.2f}") for v, c in laplacian_centrality(G).items())
+    [(0, '0.70'), (1, '0.90'), (2, '0.28'), (3, '0.22'), (4, '0.26'), (5, '0.04')]
+
+    Notes
+    -----
+    The algorithm is implemented based on [1]_ with an extension to directed graphs
+    using the ``directed_laplacian_matrix`` function.
+
+    Raises
+    ------
+    NetworkXPointlessConcept
+        If the graph `G` is the null graph.
+    ZeroDivisionError
+        If the graph `G` has no edges (is empty) and normalization is requested.
+
+    References
+    ----------
+    .. [1] Qi, X., Fuller, E., Wu, Q., Wu, Y., and Zhang, C.-Q. (2012).
+       Laplacian centrality: A new centrality measure for weighted networks.
+       Information Sciences, 194:240-253.
+       https://math.wvu.edu/~cqzhang/Publication-files/my-paper/INS-2012-Laplacian-W.pdf
+
+    See Also
+    --------
+    :func:`~networkx.linalg.laplacianmatrix.directed_laplacian_matrix`
+    :func:`~networkx.linalg.laplacianmatrix.laplacian_matrix`
+    """
+    import numpy as np
+    import scipy as sp
+
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept("null graph has no centrality defined")
+    if G.size(weight=weight) == 0:
+        if normalized:
+            raise ZeroDivisionError("graph with no edges has zero full energy")
+        return {n: 0 for n in G}
+
+    if nodelist is not None:
+        nodeset = set(G.nbunch_iter(nodelist))
+        if len(nodeset) != len(nodelist):
+            raise nx.NetworkXError("nodelist has duplicate nodes or nodes not in G")
+        nodes = nodelist + [n for n in G if n not in nodeset]
+    else:
+        nodelist = nodes = list(G)
+
+    if G.is_directed():
+        lap_matrix = nx.directed_laplacian_matrix(G, nodes, weight, walk_type, alpha)
+    else:
+        lap_matrix = nx.laplacian_matrix(G, nodes, weight).toarray()
+
+    full_energy = np.power(sp.linalg.eigh(lap_matrix, eigvals_only=True), 2).sum()
+
+    # calculate laplacian centrality
+    laplace_centralities_dict = {}
+    for i, node in enumerate(nodelist):
+        # remove row and col i from lap_matrix
+        all_but_i = list(np.arange(lap_matrix.shape[0]))
+        all_but_i.remove(i)
+        A_2 = lap_matrix[all_but_i, :][:, all_but_i]
+
+        # Adjust diagonal for removed row
+        new_diag = lap_matrix.diagonal() - abs(lap_matrix[:, i])
+        np.fill_diagonal(A_2, new_diag[all_but_i])
+
+        if len(all_but_i) > 0:  # catches degenerate case of single node
+            new_energy = np.power(sp.linalg.eigh(A_2, eigvals_only=True), 2).sum()
+        else:
+            new_energy = 0.0
+
+        lapl_cent = full_energy - new_energy
+        if normalized:
+            lapl_cent = lapl_cent / full_energy
+
+        laplace_centralities_dict[node] = float(lapl_cent)
+
+    return laplace_centralities_dict

wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/tests/test_closeness_centrality.py

@@ -0,0 +1,307 @@
+"""
+Tests for closeness centrality.
+"""
+
+import pytest
+
+import networkx as nx
+
+
+class TestClosenessCentrality:
+    @classmethod
+    def setup_class(cls):
+        cls.K = nx.krackhardt_kite_graph()
+        cls.P3 = nx.path_graph(3)
+        cls.P4 = nx.path_graph(4)
+        cls.K5 = nx.complete_graph(5)
+
+        cls.C4 = nx.cycle_graph(4)
+        cls.T = nx.balanced_tree(r=2, h=2)
+        cls.Gb = nx.Graph()
+        cls.Gb.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (4, 5), (3, 5)])
+
+        F = nx.florentine_families_graph()
+        cls.F = F
+
+        cls.LM = nx.les_miserables_graph()
+
+        # Create random undirected, unweighted graph for testing incremental version
+        cls.undirected_G = nx.fast_gnp_random_graph(n=100, p=0.6, seed=123)
+        cls.undirected_G_cc = nx.closeness_centrality(cls.undirected_G)
+
+    def test_wf_improved(self):
+        G = nx.union(self.P4, nx.path_graph([4, 5, 6]))
+        c = nx.closeness_centrality(G)
+        cwf = nx.closeness_centrality(G, wf_improved=False)
+        res = {0: 0.25, 1: 0.375, 2: 0.375, 3: 0.25, 4: 0.222, 5: 0.333, 6: 0.222}
+        wf_res = {0: 0.5, 1: 0.75, 2: 0.75, 3: 0.5, 4: 0.667, 5: 1.0, 6: 0.667}
+        for n in G:
+            assert c[n] == pytest.approx(res[n], abs=1e-3)
+            assert cwf[n] == pytest.approx(wf_res[n], abs=1e-3)
+
+    def test_digraph(self):
+        G = nx.path_graph(3, create_using=nx.DiGraph())
+        c = nx.closeness_centrality(G)
+        cr = nx.closeness_centrality(G.reverse())
+        d = {0: 0.0, 1: 0.500, 2: 0.667}
+        dr = {0: 0.667, 1: 0.500, 2: 0.0}
+        for n in sorted(self.P3):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+            assert cr[n] == pytest.approx(dr[n], abs=1e-3)
+
+    def test_k5_closeness(self):
+        c = nx.closeness_centrality(self.K5)
+        d = {0: 1.000, 1: 1.000, 2: 1.000, 3: 1.000, 4: 1.000}
+        for n in sorted(self.K5):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_p3_closeness(self):
+        c = nx.closeness_centrality(self.P3)
+        d = {0: 0.667, 1: 1.000, 2: 0.667}
+        for n in sorted(self.P3):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_krackhardt_closeness(self):
+        c = nx.closeness_centrality(self.K)
+        d = {
+            0: 0.529,
+            1: 0.529,
+            2: 0.500,
+            3: 0.600,
+            4: 0.500,
+            5: 0.643,
+            6: 0.643,
+            7: 0.600,
+            8: 0.429,
+            9: 0.310,
+        }
+        for n in sorted(self.K):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_florentine_families_closeness(self):
+        c = nx.closeness_centrality(self.F)
+        d = {
+            "Acciaiuoli": 0.368,
+            "Albizzi": 0.483,
+            "Barbadori": 0.4375,
+            "Bischeri": 0.400,
+            "Castellani": 0.389,
+            "Ginori": 0.333,
+            "Guadagni": 0.467,
+            "Lamberteschi": 0.326,
+            "Medici": 0.560,
+            "Pazzi": 0.286,
+            "Peruzzi": 0.368,
+            "Ridolfi": 0.500,
+            "Salviati": 0.389,
+            "Strozzi": 0.4375,
+            "Tornabuoni": 0.483,
+        }
+        for n in sorted(self.F):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_les_miserables_closeness(self):
+        c = nx.closeness_centrality(self.LM)
+        d = {
+            "Napoleon": 0.302,
+            "Myriel": 0.429,
+            "MlleBaptistine": 0.413,
+            "MmeMagloire": 0.413,
+            "CountessDeLo": 0.302,
+            "Geborand": 0.302,
+            "Champtercier": 0.302,
+            "Cravatte": 0.302,
+            "Count": 0.302,
+            "OldMan": 0.302,
+            "Valjean": 0.644,
+            "Labarre": 0.394,
+            "Marguerite": 0.413,
+            "MmeDeR": 0.394,
+            "Isabeau": 0.394,
+            "Gervais": 0.394,
+            "Listolier": 0.341,
+            "Tholomyes": 0.392,
+            "Fameuil": 0.341,
+            "Blacheville": 0.341,
+            "Favourite": 0.341,
+            "Dahlia": 0.341,
+            "Zephine": 0.341,
+            "Fantine": 0.461,
+            "MmeThenardier": 0.461,
+            "Thenardier": 0.517,
+            "Cosette": 0.478,
+            "Javert": 0.517,
+            "Fauchelevent": 0.402,
+            "Bamatabois": 0.427,
+            "Perpetue": 0.318,
+            "Simplice": 0.418,
+            "Scaufflaire": 0.394,
+            "Woman1": 0.396,
+            "Judge": 0.404,
+            "Champmathieu": 0.404,
+            "Brevet": 0.404,
+            "Chenildieu": 0.404,
+            "Cochepaille": 0.404,
+            "Pontmercy": 0.373,
+            "Boulatruelle": 0.342,
+            "Eponine": 0.396,
+            "Anzelma": 0.352,
+            "Woman2": 0.402,
+            "MotherInnocent": 0.398,
+            "Gribier": 0.288,
+            "MmeBurgon": 0.344,
+            "Jondrette": 0.257,
+            "Gavroche": 0.514,
+            "Gillenormand": 0.442,
+            "Magnon": 0.335,
+            "MlleGillenormand": 0.442,
+            "MmePontmercy": 0.315,
+            "MlleVaubois": 0.308,
+            "LtGillenormand": 0.365,
+            "Marius": 0.531,
+            "BaronessT": 0.352,
+            "Mabeuf": 0.396,
+            "Enjolras": 0.481,
+            "Combeferre": 0.392,
+            "Prouvaire": 0.357,
+            "Feuilly": 0.392,
+            "Courfeyrac": 0.400,
+            "Bahorel": 0.394,
+            "Bossuet": 0.475,
+            "Joly": 0.394,
+            "Grantaire": 0.358,
+            "MotherPlutarch": 0.285,
+            "Gueulemer": 0.463,
+            "Babet": 0.463,
+            "Claquesous": 0.452,
+            "Montparnasse": 0.458,
+            "Toussaint": 0.402,
+            "Child1": 0.342,
+            "Child2": 0.342,
+            "Brujon": 0.380,
+            "MmeHucheloup": 0.353,
+        }
+        for n in sorted(self.LM):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_weighted_closeness(self):
+        edges = [
+            ("s", "u", 10),
+            ("s", "x", 5),
+            ("u", "v", 1),
+            ("u", "x", 2),
+            ("v", "y", 1),
+            ("x", "u", 3),
+            ("x", "v", 5),
+            ("x", "y", 2),
+            ("y", "s", 7),
+            ("y", "v", 6),
+        ]
+        XG = nx.Graph()
+        XG.add_weighted_edges_from(edges)
+        c = nx.closeness_centrality(XG, distance="weight")
+        d = {"y": 0.200, "x": 0.286, "s": 0.138, "u": 0.235, "v": 0.200}
+        for n in sorted(XG):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    #
+    # Tests for incremental closeness centrality.
+    #
+    @staticmethod
+    def pick_add_edge(g):
+        u = nx.utils.arbitrary_element(g)
+        possible_nodes = set(g.nodes())
+        neighbors = list(g.neighbors(u)) + [u]
+        possible_nodes.difference_update(neighbors)
+        v = nx.utils.arbitrary_element(possible_nodes)
+        return (u, v)
+
+    @staticmethod
+    def pick_remove_edge(g):
+        u = nx.utils.arbitrary_element(g)
+        possible_nodes = list(g.neighbors(u))
+        v = nx.utils.arbitrary_element(possible_nodes)
+        return (u, v)
+
+    def test_directed_raises(self):
+        with pytest.raises(nx.NetworkXNotImplemented):
+            dir_G = nx.gn_graph(n=5)
+            prev_cc = None
+            edge = self.pick_add_edge(dir_G)
+            insert = True
+            nx.incremental_closeness_centrality(dir_G, edge, prev_cc, insert)
+
+    def test_wrong_size_prev_cc_raises(self):
+        with pytest.raises(nx.NetworkXError):
+            G = self.undirected_G.copy()
+            edge = self.pick_add_edge(G)
+            insert = True
+            prev_cc = self.undirected_G_cc.copy()
+            prev_cc.pop(0)
+            nx.incremental_closeness_centrality(G, edge, prev_cc, insert)
+
+    def test_wrong_nodes_prev_cc_raises(self):
+        with pytest.raises(nx.NetworkXError):
+            G = self.undirected_G.copy()
+            edge = self.pick_add_edge(G)
+            insert = True
+            prev_cc = self.undirected_G_cc.copy()
+            num_nodes = len(prev_cc)
+            prev_cc.pop(0)
+            prev_cc[num_nodes] = 0.5
+            nx.incremental_closeness_centrality(G, edge, prev_cc, insert)
+
+    def test_zero_centrality(self):
+        G = nx.path_graph(3)
+        prev_cc = nx.closeness_centrality(G)
+        edge = self.pick_remove_edge(G)
+        test_cc = nx.incremental_closeness_centrality(G, edge, prev_cc, insertion=False)
+        G.remove_edges_from([edge])
+        real_cc = nx.closeness_centrality(G)
+        shared_items = set(test_cc.items()) & set(real_cc.items())
+        assert len(shared_items) == len(real_cc)
+        assert 0 in test_cc.values()
+
+    def test_incremental(self):
+        # Check that incremental and regular give same output
+        G = self.undirected_G.copy()
+        prev_cc = None
+        for i in range(5):
+            if i % 2 == 0:
+                # Remove an edge
+                insert = False
+                edge = self.pick_remove_edge(G)
+            else:
+                # Add an edge
+                insert = True
+                edge = self.pick_add_edge(G)
+
+            # start = timeit.default_timer()
+            test_cc = nx.incremental_closeness_centrality(G, edge, prev_cc, insert)
+            # inc_elapsed = (timeit.default_timer() - start)
+            # print(f"incremental time: {inc_elapsed}")
+
+            if insert:
+                G.add_edges_from([edge])
+            else:
+                G.remove_edges_from([edge])
+
+            # start = timeit.default_timer()
+            real_cc = nx.closeness_centrality(G)
+            # reg_elapsed = (timeit.default_timer() - start)
+            # print(f"regular time: {reg_elapsed}")
+            # Example output:
+            # incremental time: 0.208
+            # regular time: 0.276
+            # incremental time: 0.00683
+            # regular time: 0.260
+            # incremental time: 0.0224
+            # regular time: 0.278
+            # incremental time: 0.00804
+            # regular time: 0.208
+            # incremental time: 0.00947
+            # regular time: 0.188
+
+            assert set(test_cc.items()) == set(real_cc.items())
+
+            prev_cc = test_cc

wemm/lib/python3.10/site-packages/networkx/algorithms/centrality/tests/test_laplacian_centrality.py

@@ -0,0 +1,221 @@
+import pytest
+
+import networkx as nx
+
+np = pytest.importorskip("numpy")
+sp = pytest.importorskip("scipy")
+
+
+def test_laplacian_centrality_null_graph():
+    G = nx.Graph()
+    with pytest.raises(nx.NetworkXPointlessConcept):
+        d = nx.laplacian_centrality(G, normalized=False)
+
+
+def test_laplacian_centrality_single_node():
+    """See gh-6571"""
+    G = nx.empty_graph(1)
+    assert nx.laplacian_centrality(G, normalized=False) == {0: 0}
+    with pytest.raises(ZeroDivisionError):
+        nx.laplacian_centrality(G, normalized=True)
+
+
+def test_laplacian_centrality_unconnected_nodes():
+    """laplacian_centrality on a unconnected node graph should return 0
+
+    For graphs without edges, the Laplacian energy is 0 and is unchanged with
+    node removal, so::
+
+        LC(v) = LE(G) - LE(G - v) = 0 - 0 = 0
+    """
+    G = nx.empty_graph(3)
+    assert nx.laplacian_centrality(G, normalized=False) == {0: 0, 1: 0, 2: 0}
+
+
+def test_laplacian_centrality_empty_graph():
+    G = nx.empty_graph(3)
+    with pytest.raises(ZeroDivisionError):
+        d = nx.laplacian_centrality(G, normalized=True)
+
+
+def test_laplacian_centrality_E():
+    E = nx.Graph()
+    E.add_weighted_edges_from(
+        [(0, 1, 4), (4, 5, 1), (0, 2, 2), (2, 1, 1), (1, 3, 2), (1, 4, 2)]
+    )
+    d = nx.laplacian_centrality(E)
+    exact = {
+        0: 0.700000,
+        1: 0.900000,
+        2: 0.280000,
+        3: 0.220000,
+        4: 0.260000,
+        5: 0.040000,
+    }
+
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check not normalized
+    full_energy = 200
+    dnn = nx.laplacian_centrality(E, normalized=False)
+    for n, dc in dnn.items():
+        assert exact[n] * full_energy == pytest.approx(dc, abs=1e-7)
+
+    # Check unweighted not-normalized version
+    duw_nn = nx.laplacian_centrality(E, normalized=False, weight=None)
+    print(duw_nn)
+    exact_uw_nn = {
+        0: 18,
+        1: 34,
+        2: 18,
+        3: 10,
+        4: 16,
+        5: 6,
+    }
+    for n, dc in duw_nn.items():
+        assert exact_uw_nn[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check unweighted version
+    duw = nx.laplacian_centrality(E, weight=None)
+    full_energy = 42
+    for n, dc in duw.items():
+        assert exact_uw_nn[n] / full_energy == pytest.approx(dc, abs=1e-7)
+
+
+def test_laplacian_centrality_KC():
+    KC = nx.karate_club_graph()
+    d = nx.laplacian_centrality(KC)
+    exact = {
+        0: 0.2543593,
+        1: 0.1724524,
+        2: 0.2166053,
+        3: 0.0964646,
+        4: 0.0350344,
+        5: 0.0571109,
+        6: 0.0540713,
+        7: 0.0788674,
+        8: 0.1222204,
+        9: 0.0217565,
+        10: 0.0308751,
+        11: 0.0215965,
+        12: 0.0174372,
+        13: 0.118861,
+        14: 0.0366341,
+        15: 0.0548712,
+        16: 0.0172772,
+        17: 0.0191969,
+        18: 0.0225564,
+        19: 0.0331147,
+        20: 0.0279955,
+        21: 0.0246361,
+        22: 0.0382339,
+        23: 0.1294193,
+        24: 0.0227164,
+        25: 0.0644697,
+        26: 0.0281555,
+        27: 0.075188,
+        28: 0.0364742,
+        29: 0.0707087,
+        30: 0.0708687,
+        31: 0.131019,
+        32: 0.2370821,
+        33: 0.3066709,
+    }
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check not normalized
+    full_energy = 12502
+    dnn = nx.laplacian_centrality(KC, normalized=False)
+    for n, dc in dnn.items():
+        assert exact[n] * full_energy == pytest.approx(dc, abs=1e-3)
+
+
+def test_laplacian_centrality_K():
+    K = nx.krackhardt_kite_graph()
+    d = nx.laplacian_centrality(K)
+    exact = {
+        0: 0.3010753,
+        1: 0.3010753,
+        2: 0.2258065,
+        3: 0.483871,
+        4: 0.2258065,
+        5: 0.3870968,
+        6: 0.3870968,
+        7: 0.1935484,
+        8: 0.0752688,
+        9: 0.0322581,
+    }
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check not normalized
+    full_energy = 186
+    dnn = nx.laplacian_centrality(K, normalized=False)
+    for n, dc in dnn.items():
+        assert exact[n] * full_energy == pytest.approx(dc, abs=1e-3)
+
+
+def test_laplacian_centrality_P3():
+    P3 = nx.path_graph(3)
+    d = nx.laplacian_centrality(P3)
+    exact = {0: 0.6, 1: 1.0, 2: 0.6}
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+
+def test_laplacian_centrality_K5():
+    K5 = nx.complete_graph(5)
+    d = nx.laplacian_centrality(K5)
+    exact = {0: 0.52, 1: 0.52, 2: 0.52, 3: 0.52, 4: 0.52}
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+
+def test_laplacian_centrality_FF():
+    FF = nx.florentine_families_graph()
+    d = nx.laplacian_centrality(FF)
+    exact = {
+        "Acciaiuoli": 0.0804598,
+        "Medici": 0.4022989,
+        "Castellani": 0.1724138,
+        "Peruzzi": 0.183908,
+        "Strozzi": 0.2528736,
+        "Barbadori": 0.137931,
+        "Ridolfi": 0.2183908,
+        "Tornabuoni": 0.2183908,
+        "Albizzi": 0.1954023,
+        "Salviati": 0.1149425,
+        "Pazzi": 0.0344828,
+        "Bischeri": 0.1954023,
+        "Guadagni": 0.2298851,
+        "Ginori": 0.045977,
+        "Lamberteschi": 0.0574713,
+    }
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+
+def test_laplacian_centrality_DG():
+    DG = nx.DiGraph([(0, 5), (1, 5), (2, 5), (3, 5), (4, 5), (5, 6), (5, 7), (5, 8)])
+    d = nx.laplacian_centrality(DG)
+    exact = {
+        0: 0.2123352,
+        5: 0.515391,
+        1: 0.2123352,
+        2: 0.2123352,
+        3: 0.2123352,
+        4: 0.2123352,
+        6: 0.2952031,
+        7: 0.2952031,
+        8: 0.2952031,
+    }
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check not normalized
+    full_energy = 9.50704
+    dnn = nx.laplacian_centrality(DG, normalized=False)
+    for n, dc in dnn.items():
+        assert exact[n] * full_energy == pytest.approx(dc, abs=1e-4)

wemm/lib/python3.10/site-packages/networkx/algorithms/clique.py

@@ -0,0 +1,755 @@
+"""Functions for finding and manipulating cliques.
+
+Finding the largest clique in a graph is NP-complete problem, so most of
+these algorithms have an exponential running time; for more information,
+see the Wikipedia article on the clique problem [1]_.
+
+.. [1] clique problem:: https://en.wikipedia.org/wiki/Clique_problem
+
+"""
+
+from collections import defaultdict, deque
+from itertools import chain, combinations, islice
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = [
+    "find_cliques",
+    "find_cliques_recursive",
+    "make_max_clique_graph",
+    "make_clique_bipartite",
+    "node_clique_number",
+    "number_of_cliques",
+    "enumerate_all_cliques",
+    "max_weight_clique",
+]
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def enumerate_all_cliques(G):
+    """Returns all cliques in an undirected graph.
+
+    This function returns an iterator over cliques, each of which is a
+    list of nodes. The iteration is ordered by cardinality of the
+    cliques: first all cliques of size one, then all cliques of size
+    two, etc.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected graph.
+
+    Returns
+    -------
+    iterator
+        An iterator over cliques, each of which is a list of nodes in
+        `G`. The cliques are ordered according to size.
+
+    Notes
+    -----
+    To obtain a list of all cliques, use
+    `list(enumerate_all_cliques(G))`. However, be aware that in the
+    worst-case, the length of this list can be exponential in the number
+    of nodes in the graph (for example, when the graph is the complete
+    graph). This function avoids storing all cliques in memory by only
+    keeping current candidate node lists in memory during its search.
+
+    The implementation is adapted from the algorithm by Zhang, et
+    al. (2005) [1]_ to output all cliques discovered.
+
+    This algorithm ignores self-loops and parallel edges, since cliques
+    are not conventionally defined with such edges.
+
+    References
+    ----------
+    .. [1] Yun Zhang, Abu-Khzam, F.N., Baldwin, N.E., Chesler, E.J.,
+           Langston, M.A., Samatova, N.F.,
+           "Genome-Scale Computational Approaches to Memory-Intensive
+           Applications in Systems Biology".
+           *Supercomputing*, 2005. Proceedings of the ACM/IEEE SC 2005
+           Conference, pp. 12, 12--18 Nov. 2005.
+           <https://doi.org/10.1109/SC.2005.29>.
+
+    """
+    index = {}
+    nbrs = {}
+    for u in G:
+        index[u] = len(index)
+        # Neighbors of u that appear after u in the iteration order of G.
+        nbrs[u] = {v for v in G[u] if v not in index}
+
+    queue = deque(([u], sorted(nbrs[u], key=index.__getitem__)) for u in G)
+    # Loop invariants:
+    # 1. len(base) is nondecreasing.
+    # 2. (base + cnbrs) is sorted with respect to the iteration order of G.
+    # 3. cnbrs is a set of common neighbors of nodes in base.
+    while queue:
+        base, cnbrs = map(list, queue.popleft())
+        yield base
+        for i, u in enumerate(cnbrs):
+            # Use generators to reduce memory consumption.
+            queue.append(
+                (
+                    chain(base, [u]),
+                    filter(nbrs[u].__contains__, islice(cnbrs, i + 1, None)),
+                )
+            )
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def find_cliques(G, nodes=None):
+    """Returns all maximal cliques in an undirected graph.
+
+    For each node *n*, a *maximal clique for n* is a largest complete
+    subgraph containing *n*. The largest maximal clique is sometimes
+    called the *maximum clique*.
+
+    This function returns an iterator over cliques, each of which is a
+    list of nodes. It is an iterative implementation, so should not
+    suffer from recursion depth issues.
+
+    This function accepts a list of `nodes` and only the maximal cliques
+    containing all of these `nodes` are returned. It can considerably speed up
+    the running time if some specific cliques are desired.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected graph.
+
+    nodes : list, optional (default=None)
+        If provided, only yield *maximal cliques* containing all nodes in `nodes`.
+        If `nodes` isn't a clique itself, a ValueError is raised.
+
+    Returns
+    -------
+    iterator
+        An iterator over maximal cliques, each of which is a list of
+        nodes in `G`. If `nodes` is provided, only the maximal cliques
+        containing all the nodes in `nodes` are returned. The order of
+        cliques is arbitrary.
+
+    Raises
+    ------
+    ValueError
+        If `nodes` is not a clique.
+
+    Examples
+    --------
+    >>> from pprint import pprint  # For nice dict formatting
+    >>> G = nx.karate_club_graph()
+    >>> sum(1 for c in nx.find_cliques(G))  # The number of maximal cliques in G
+    36
+    >>> max(nx.find_cliques(G), key=len)  # The largest maximal clique in G
+    [0, 1, 2, 3, 13]
+
+    The size of the largest maximal clique is known as the *clique number* of
+    the graph, which can be found directly with:
+
+    >>> max(len(c) for c in nx.find_cliques(G))
+    5
+
+    One can also compute the number of maximal cliques in `G` that contain a given
+    node. The following produces a dictionary keyed by node whose
+    values are the number of maximal cliques in `G` that contain the node:
+
+    >>> pprint({n: sum(1 for c in nx.find_cliques(G) if n in c) for n in G})
+    {0: 13,
+     1: 6,
+     2: 7,
+     3: 3,
+     4: 2,
+     5: 3,
+     6: 3,
+     7: 1,
+     8: 3,
+     9: 2,
+     10: 2,
+     11: 1,
+     12: 1,
+     13: 2,
+     14: 1,
+     15: 1,
+     16: 1,
+     17: 1,
+     18: 1,
+     19: 2,
+     20: 1,
+     21: 1,
+     22: 1,
+     23: 3,
+     24: 2,
+     25: 2,
+     26: 1,
+     27: 3,
+     28: 2,
+     29: 2,
+     30: 2,
+     31: 4,
+     32: 9,
+     33: 14}
+
+    Or, similarly, the maximal cliques in `G` that contain a given node.
+    For example, the 4 maximal cliques that contain node 31:
+
+    >>> [c for c in nx.find_cliques(G) if 31 in c]
+    [[0, 31], [33, 32, 31], [33, 28, 31], [24, 25, 31]]
+
+    See Also
+    --------
+    find_cliques_recursive
+        A recursive version of the same algorithm.
+
+    Notes
+    -----
+    To obtain a list of all maximal cliques, use
+    `list(find_cliques(G))`. However, be aware that in the worst-case,
+    the length of this list can be exponential in the number of nodes in
+    the graph. This function avoids storing all cliques in memory by
+    only keeping current candidate node lists in memory during its search.
+
+    This implementation is based on the algorithm published by Bron and
+    Kerbosch (1973) [1]_, as adapted by Tomita, Tanaka and Takahashi
+    (2006) [2]_ and discussed in Cazals and Karande (2008) [3]_. It
+    essentially unrolls the recursion used in the references to avoid
+    issues of recursion stack depth (for a recursive implementation, see
+    :func:`find_cliques_recursive`).
+
+    This algorithm ignores self-loops and parallel edges, since cliques
+    are not conventionally defined with such edges.
+
+    References
+    ----------
+    .. [1] Bron, C. and Kerbosch, J.
+       "Algorithm 457: finding all cliques of an undirected graph".
+       *Communications of the ACM* 16, 9 (Sep. 1973), 575--577.
+       <http://portal.acm.org/citation.cfm?doid=362342.362367>
+
+    .. [2] Etsuji Tomita, Akira Tanaka, Haruhisa Takahashi,
+       "The worst-case time complexity for generating all maximal
+       cliques and computational experiments",
+       *Theoretical Computer Science*, Volume 363, Issue 1,
+       Computing and Combinatorics,
+       10th Annual International Conference on
+       Computing and Combinatorics (COCOON 2004), 25 October 2006, Pages 28--42
+       <https://doi.org/10.1016/j.tcs.2006.06.015>
+
+    .. [3] F. Cazals, C. Karande,
+       "A note on the problem of reporting maximal cliques",
+       *Theoretical Computer Science*,
+       Volume 407, Issues 1--3, 6 November 2008, Pages 564--568,
+       <https://doi.org/10.1016/j.tcs.2008.05.010>
+
+    """
+    if len(G) == 0:
+        return
+
+    adj = {u: {v for v in G[u] if v != u} for u in G}
+
+    # Initialize Q with the given nodes and subg, cand with their nbrs
+    Q = nodes[:] if nodes is not None else []
+    cand = set(G)
+    for node in Q:
+        if node not in cand:
+            raise ValueError(f"The given `nodes` {nodes} do not form a clique")
+        cand &= adj[node]
+
+    if not cand:
+        yield Q[:]
+        return
+
+    subg = cand.copy()
+    stack = []
+    Q.append(None)
+
+    u = max(subg, key=lambda u: len(cand & adj[u]))
+    ext_u = cand - adj[u]
+
+    try:
+        while True:
+            if ext_u:
+                q = ext_u.pop()
+                cand.remove(q)
+                Q[-1] = q
+                adj_q = adj[q]
+                subg_q = subg & adj_q
+                if not subg_q:
+                    yield Q[:]
+                else:
+                    cand_q = cand & adj_q
+                    if cand_q:
+                        stack.append((subg, cand, ext_u))
+                        Q.append(None)
+                        subg = subg_q
+                        cand = cand_q
+                        u = max(subg, key=lambda u: len(cand & adj[u]))
+                        ext_u = cand - adj[u]
+            else:
+                Q.pop()
+                subg, cand, ext_u = stack.pop()
+    except IndexError:
+        pass
+
+
+# TODO Should this also be not implemented for directed graphs?
+@nx._dispatchable
+def find_cliques_recursive(G, nodes=None):
+    """Returns all maximal cliques in a graph.
+
+    For each node *v*, a *maximal clique for v* is a largest complete
+    subgraph containing *v*. The largest maximal clique is sometimes
+    called the *maximum clique*.
+
+    This function returns an iterator over cliques, each of which is a
+    list of nodes. It is a recursive implementation, so may suffer from
+    recursion depth issues, but is included for pedagogical reasons.
+    For a non-recursive implementation, see :func:`find_cliques`.
+
+    This function accepts a list of `nodes` and only the maximal cliques
+    containing all of these `nodes` are returned. It can considerably speed up
+    the running time if some specific cliques are desired.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    nodes : list, optional (default=None)
+        If provided, only yield *maximal cliques* containing all nodes in `nodes`.
+        If `nodes` isn't a clique itself, a ValueError is raised.
+
+    Returns
+    -------
+    iterator
+        An iterator over maximal cliques, each of which is a list of
+        nodes in `G`. If `nodes` is provided, only the maximal cliques
+        containing all the nodes in `nodes` are yielded. The order of
+        cliques is arbitrary.
+
+    Raises
+    ------
+    ValueError
+        If `nodes` is not a clique.
+
+    See Also
+    --------
+    find_cliques
+        An iterative version of the same algorithm. See docstring for examples.
+
+    Notes
+    -----
+    To obtain a list of all maximal cliques, use
+    `list(find_cliques_recursive(G))`. However, be aware that in the
+    worst-case, the length of this list can be exponential in the number
+    of nodes in the graph. This function avoids storing all cliques in memory
+    by only keeping current candidate node lists in memory during its search.
+
+    This implementation is based on the algorithm published by Bron and
+    Kerbosch (1973) [1]_, as adapted by Tomita, Tanaka and Takahashi
+    (2006) [2]_ and discussed in Cazals and Karande (2008) [3]_. For a
+    non-recursive implementation, see :func:`find_cliques`.
+
+    This algorithm ignores self-loops and parallel edges, since cliques
+    are not conventionally defined with such edges.
+
+    References
+    ----------
+    .. [1] Bron, C. and Kerbosch, J.
+       "Algorithm 457: finding all cliques of an undirected graph".
+       *Communications of the ACM* 16, 9 (Sep. 1973), 575--577.
+       <http://portal.acm.org/citation.cfm?doid=362342.362367>
+
+    .. [2] Etsuji Tomita, Akira Tanaka, Haruhisa Takahashi,
+       "The worst-case time complexity for generating all maximal
+       cliques and computational experiments",
+       *Theoretical Computer Science*, Volume 363, Issue 1,
+       Computing and Combinatorics,
+       10th Annual International Conference on
+       Computing and Combinatorics (COCOON 2004), 25 October 2006, Pages 28--42
+       <https://doi.org/10.1016/j.tcs.2006.06.015>
+
+    .. [3] F. Cazals, C. Karande,
+       "A note on the problem of reporting maximal cliques",
+       *Theoretical Computer Science*,
+       Volume 407, Issues 1--3, 6 November 2008, Pages 564--568,
+       <https://doi.org/10.1016/j.tcs.2008.05.010>
+
+    """
+    if len(G) == 0:
+        return iter([])
+
+    adj = {u: {v for v in G[u] if v != u} for u in G}
+
+    # Initialize Q with the given nodes and subg, cand with their nbrs
+    Q = nodes[:] if nodes is not None else []
+    cand_init = set(G)
+    for node in Q:
+        if node not in cand_init:
+            raise ValueError(f"The given `nodes` {nodes} do not form a clique")
+        cand_init &= adj[node]
+
+    if not cand_init:
+        return iter([Q])
+
+    subg_init = cand_init.copy()
+
+    def expand(subg, cand):
+        u = max(subg, key=lambda u: len(cand & adj[u]))
+        for q in cand - adj[u]:
+            cand.remove(q)
+            Q.append(q)
+            adj_q = adj[q]
+            subg_q = subg & adj_q
+            if not subg_q:
+                yield Q[:]
+            else:
+                cand_q = cand & adj_q
+                if cand_q:
+                    yield from expand(subg_q, cand_q)
+            Q.pop()
+
+    return expand(subg_init, cand_init)
+
+
+@nx._dispatchable(returns_graph=True)
+def make_max_clique_graph(G, create_using=None):
+    """Returns the maximal clique graph of the given graph.
+
+    The nodes of the maximal clique graph of `G` are the cliques of
+    `G` and an edge joins two cliques if the cliques are not disjoint.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    NetworkX graph
+        A graph whose nodes are the cliques of `G` and whose edges
+        join two cliques if they are not disjoint.
+
+    Notes
+    -----
+    This function behaves like the following code::
+
+        import networkx as nx
+
+        G = nx.make_clique_bipartite(G)
+        cliques = [v for v in G.nodes() if G.nodes[v]["bipartite"] == 0]
+        G = nx.bipartite.projected_graph(G, cliques)
+        G = nx.relabel_nodes(G, {-v: v - 1 for v in G})
+
+    It should be faster, though, since it skips all the intermediate
+    steps.
+
+    """
+    if create_using is None:
+        B = G.__class__()
+    else:
+        B = nx.empty_graph(0, create_using)
+    cliques = list(enumerate(set(c) for c in find_cliques(G)))
+    # Add a numbered node for each clique.
+    B.add_nodes_from(i for i, c in cliques)
+    # Join cliques by an edge if they share a node.
+    clique_pairs = combinations(cliques, 2)
+    B.add_edges_from((i, j) for (i, c1), (j, c2) in clique_pairs if c1 & c2)
+    return B
+
+
+@nx._dispatchable(returns_graph=True)
+def make_clique_bipartite(G, fpos=None, create_using=None, name=None):
+    """Returns the bipartite clique graph corresponding to `G`.
+
+    In the returned bipartite graph, the "bottom" nodes are the nodes of
+    `G` and the "top" nodes represent the maximal cliques of `G`.
+    There is an edge from node *v* to clique *C* in the returned graph
+    if and only if *v* is an element of *C*.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected graph.
+
+    fpos : bool
+        If True or not None, the returned graph will have an
+        additional attribute, `pos`, a dictionary mapping node to
+        position in the Euclidean plane.
+
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    NetworkX graph
+        A bipartite graph whose "bottom" set is the nodes of the graph
+        `G`, whose "top" set is the cliques of `G`, and whose edges
+        join nodes of `G` to the cliques that contain them.
+
+        The nodes of the graph `G` have the node attribute
+        'bipartite' set to 1 and the nodes representing cliques
+        have the node attribute 'bipartite' set to 0, as is the
+        convention for bipartite graphs in NetworkX.
+
+    """
+    B = nx.empty_graph(0, create_using)
+    B.clear()
+    # The "bottom" nodes in the bipartite graph are the nodes of the
+    # original graph, G.
+    B.add_nodes_from(G, bipartite=1)
+    for i, cl in enumerate(find_cliques(G)):
+        # The "top" nodes in the bipartite graph are the cliques. These
+        # nodes get negative numbers as labels.
+        name = -i - 1
+        B.add_node(name, bipartite=0)
+        B.add_edges_from((v, name) for v in cl)
+    return B
+
+
+@nx._dispatchable
+def node_clique_number(G, nodes=None, cliques=None, separate_nodes=False):
+    """Returns the size of the largest maximal clique containing each given node.
+
+    Returns a single or list depending on input nodes.
+    An optional list of cliques can be input if already computed.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected graph.
+
+    cliques : list, optional (default=None)
+        A list of cliques, each of which is itself a list of nodes.
+        If not specified, the list of all cliques will be computed
+        using :func:`find_cliques`.
+
+    Returns
+    -------
+    int or dict
+        If `nodes` is a single node, returns the size of the
+        largest maximal clique in `G` containing that node.
+        Otherwise return a dict keyed by node to the size
+        of the largest maximal clique containing that node.
+
+    See Also
+    --------
+    find_cliques
+        find_cliques yields the maximal cliques of G.
+        It accepts a `nodes` argument which restricts consideration to
+        maximal cliques containing all the given `nodes`.
+        The search for the cliques is optimized for `nodes`.
+    """
+    if cliques is None:
+        if nodes is not None:
+            # Use ego_graph to decrease size of graph
+            # check for single node
+            if nodes in G:
+                return max(len(c) for c in find_cliques(nx.ego_graph(G, nodes)))
+            # handle multiple nodes
+            return {
+                n: max(len(c) for c in find_cliques(nx.ego_graph(G, n))) for n in nodes
+            }
+
+        # nodes is None--find all cliques
+        cliques = list(find_cliques(G))
+
+    # single node requested
+    if nodes in G:
+        return max(len(c) for c in cliques if nodes in c)
+
+    # multiple nodes requested
+    # preprocess all nodes (faster than one at a time for even 2 nodes)
+    size_for_n = defaultdict(int)
+    for c in cliques:
+        size_of_c = len(c)
+        for n in c:
+            if size_for_n[n] < size_of_c:
+                size_for_n[n] = size_of_c
+    if nodes is None:
+        return size_for_n
+    return {n: size_for_n[n] for n in nodes}
+
+
+def number_of_cliques(G, nodes=None, cliques=None):
+    """Returns the number of maximal cliques for each node.
+
+    Returns a single or list depending on input nodes.
+    Optional list of cliques can be input if already computed.
+    """
+    if cliques is None:
+        cliques = list(find_cliques(G))
+
+    if nodes is None:
+        nodes = list(G.nodes())  # none, get entire graph
+
+    if not isinstance(nodes, list):  # check for a list
+        v = nodes
+        # assume it is a single value
+        numcliq = len([1 for c in cliques if v in c])
+    else:
+        numcliq = {}
+        for v in nodes:
+            numcliq[v] = len([1 for c in cliques if v in c])
+    return numcliq
+
+
+class MaxWeightClique:
+    """A class for the maximum weight clique algorithm.
+
+    This class is a helper for the `max_weight_clique` function.  The class
+    should not normally be used directly.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        The undirected graph for which a maximum weight clique is sought
+    weight : string or None, optional (default='weight')
+        The node attribute that holds the integer value used as a weight.
+        If None, then each node has weight 1.
+
+    Attributes
+    ----------
+    G : NetworkX graph
+        The undirected graph for which a maximum weight clique is sought
+    node_weights: dict
+        The weight of each node
+    incumbent_nodes : list
+        The nodes of the incumbent clique (the best clique found so far)
+    incumbent_weight: int
+        The weight of the incumbent clique
+    """
+
+    def __init__(self, G, weight):
+        self.G = G
+        self.incumbent_nodes = []
+        self.incumbent_weight = 0
+
+        if weight is None:
+            self.node_weights = {v: 1 for v in G.nodes()}
+        else:
+            for v in G.nodes():
+                if weight not in G.nodes[v]:
+                    errmsg = f"Node {v!r} does not have the requested weight field."
+                    raise KeyError(errmsg)
+                if not isinstance(G.nodes[v][weight], int):
+                    errmsg = f"The {weight!r} field of node {v!r} is not an integer."
+                    raise ValueError(errmsg)
+            self.node_weights = {v: G.nodes[v][weight] for v in G.nodes()}
+
+    def update_incumbent_if_improved(self, C, C_weight):
+        """Update the incumbent if the node set C has greater weight.
+
+        C is assumed to be a clique.
+        """
+        if C_weight > self.incumbent_weight:
+            self.incumbent_nodes = C[:]
+            self.incumbent_weight = C_weight
+
+    def greedily_find_independent_set(self, P):
+        """Greedily find an independent set of nodes from a set of
+        nodes P."""
+        independent_set = []
+        P = P[:]
+        while P:
+            v = P[0]
+            independent_set.append(v)
+            P = [w for w in P if v != w and not self.G.has_edge(v, w)]
+        return independent_set
+
+    def find_branching_nodes(self, P, target):
+        """Find a set of nodes to branch on."""
+        residual_wt = {v: self.node_weights[v] for v in P}
+        total_wt = 0
+        P = P[:]
+        while P:
+            independent_set = self.greedily_find_independent_set(P)
+            min_wt_in_class = min(residual_wt[v] for v in independent_set)
+            total_wt += min_wt_in_class
+            if total_wt > target:
+                break
+            for v in independent_set:
+                residual_wt[v] -= min_wt_in_class
+            P = [v for v in P if residual_wt[v] != 0]
+        return P
+
+    def expand(self, C, C_weight, P):
+        """Look for the best clique that contains all the nodes in C and zero or
+        more of the nodes in P, backtracking if it can be shown that no such
+        clique has greater weight than the incumbent.
+        """
+        self.update_incumbent_if_improved(C, C_weight)
+        branching_nodes = self.find_branching_nodes(P, self.incumbent_weight - C_weight)
+        while branching_nodes:
+            v = branching_nodes.pop()
+            P.remove(v)
+            new_C = C + [v]
+            new_C_weight = C_weight + self.node_weights[v]
+            new_P = [w for w in P if self.G.has_edge(v, w)]
+            self.expand(new_C, new_C_weight, new_P)
+
+    def find_max_weight_clique(self):
+        """Find a maximum weight clique."""
+        # Sort nodes in reverse order of degree for speed
+        nodes = sorted(self.G.nodes(), key=lambda v: self.G.degree(v), reverse=True)
+        nodes = [v for v in nodes if self.node_weights[v] > 0]
+        self.expand([], 0, nodes)
+
+
+@not_implemented_for("directed")
+@nx._dispatchable(node_attrs="weight")
+def max_weight_clique(G, weight="weight"):
+    """Find a maximum weight clique in G.
+
+    A *clique* in a graph is a set of nodes such that every two distinct nodes
+    are adjacent.  The *weight* of a clique is the sum of the weights of its
+    nodes.  A *maximum weight clique* of graph G is a clique C in G such that
+    no clique in G has weight greater than the weight of C.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Undirected graph
+    weight : string or None, optional (default='weight')
+        The node attribute that holds the integer value used as a weight.
+        If None, then each node has weight 1.
+
+    Returns
+    -------
+    clique : list
+        the nodes of a maximum weight clique
+    weight : int
+        the weight of a maximum weight clique
+
+    Notes
+    -----
+    The implementation is recursive, and therefore it may run into recursion
+    depth issues if G contains a clique whose number of nodes is close to the
+    recursion depth limit.
+
+    At each search node, the algorithm greedily constructs a weighted
+    independent set cover of part of the graph in order to find a small set of
+    nodes on which to branch.  The algorithm is very similar to the algorithm
+    of Tavares et al. [1]_, other than the fact that the NetworkX version does
+    not use bitsets.  This style of algorithm for maximum weight clique (and
+    maximum weight independent set, which is the same problem but on the
+    complement graph) has a decades-long history.  See Algorithm B of Warren
+    and Hicks [2]_ and the references in that paper.
+
+    References
+    ----------
+    .. [1] Tavares, W.A., Neto, M.B.C., Rodrigues, C.D., Michelon, P.: Um
+           algoritmo de branch and bound para o problema da clique máxima
+           ponderada.  Proceedings of XLVII SBPO 1 (2015).
+
+    .. [2] Warren, Jeffrey S, Hicks, Illya V.: Combinatorial Branch-and-Bound
+           for the Maximum Weight Independent Set Problem.  Technical Report,
+           Texas A&M University (2016).
+    """
+
+    mwc = MaxWeightClique(G, weight)
+    mwc.find_max_weight_clique()
+    return mwc.incumbent_nodes, mwc.incumbent_weight

wemm/lib/python3.10/site-packages/networkx/algorithms/cycles.py

@@ -0,0 +1,1230 @@
+"""
+========================
+Cycle finding algorithms
+========================
+"""
+
+from collections import Counter, defaultdict
+from itertools import combinations, product
+from math import inf
+
+import networkx as nx
+from networkx.utils import not_implemented_for, pairwise
+
+__all__ = [
+    "cycle_basis",
+    "simple_cycles",
+    "recursive_simple_cycles",
+    "find_cycle",
+    "minimum_cycle_basis",
+    "chordless_cycles",
+    "girth",
+]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def cycle_basis(G, root=None):
+    """Returns a list of cycles which form a basis for cycles of G.
+
+    A basis for cycles of a network is a minimal collection of
+    cycles such that any cycle in the network can be written
+    as a sum of cycles in the basis.  Here summation of cycles
+    is defined as "exclusive or" of the edges. Cycle bases are
+    useful, e.g. when deriving equations for electric circuits
+    using Kirchhoff's Laws.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+    root : node, optional
+       Specify starting node for basis.
+
+    Returns
+    -------
+    A list of cycle lists.  Each cycle list is a list of nodes
+    which forms a cycle (loop) in G.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> nx.add_cycle(G, [0, 1, 2, 3])
+    >>> nx.add_cycle(G, [0, 3, 4, 5])
+    >>> nx.cycle_basis(G, 0)
+    [[3, 4, 5, 0], [1, 2, 3, 0]]
+
+    Notes
+    -----
+    This is adapted from algorithm CACM 491 [1]_.
+
+    References
+    ----------
+    .. [1] Paton, K. An algorithm for finding a fundamental set of
+       cycles of a graph. Comm. ACM 12, 9 (Sept 1969), 514-518.
+
+    See Also
+    --------
+    simple_cycles
+    minimum_cycle_basis
+    """
+    gnodes = dict.fromkeys(G)  # set-like object that maintains node order
+    cycles = []
+    while gnodes:  # loop over connected components
+        if root is None:
+            root = gnodes.popitem()[0]
+        stack = [root]
+        pred = {root: root}
+        used = {root: set()}
+        while stack:  # walk the spanning tree finding cycles
+            z = stack.pop()  # use last-in so cycles easier to find
+            zused = used[z]
+            for nbr in G[z]:
+                if nbr not in used:  # new node
+                    pred[nbr] = z
+                    stack.append(nbr)
+                    used[nbr] = {z}
+                elif nbr == z:  # self loops
+                    cycles.append([z])
+                elif nbr not in zused:  # found a cycle
+                    pn = used[nbr]
+                    cycle = [nbr, z]
+                    p = pred[z]
+                    while p not in pn:
+                        cycle.append(p)
+                        p = pred[p]
+                    cycle.append(p)
+                    cycles.append(cycle)
+                    used[nbr].add(z)
+        for node in pred:
+            gnodes.pop(node, None)
+        root = None
+    return cycles
+
+
+@nx._dispatchable
+def simple_cycles(G, length_bound=None):
+    """Find simple cycles (elementary circuits) of a graph.
+
+    A "simple cycle", or "elementary circuit", is a closed path where
+    no node appears twice.  In a directed graph, two simple cycles are distinct
+    if they are not cyclic permutations of each other.  In an undirected graph,
+    two simple cycles are distinct if they are not cyclic permutations of each
+    other nor of the other's reversal.
+
+    Optionally, the cycles are bounded in length.  In the unbounded case, we use
+    a nonrecursive, iterator/generator version of Johnson's algorithm [1]_.  In
+    the bounded case, we use a version of the algorithm of Gupta and
+    Suzumura [2]_. There may be better algorithms for some cases [3]_ [4]_ [5]_.
+
+    The algorithms of Johnson, and Gupta and Suzumura, are enhanced by some
+    well-known preprocessing techniques.  When `G` is directed, we restrict our
+    attention to strongly connected components of `G`, generate all simple cycles
+    containing a certain node, remove that node, and further decompose the
+    remainder into strongly connected components.  When `G` is undirected, we
+    restrict our attention to biconnected components, generate all simple cycles
+    containing a particular edge, remove that edge, and further decompose the
+    remainder into biconnected components.
+
+    Note that multigraphs are supported by this function -- and in undirected
+    multigraphs, a pair of parallel edges is considered a cycle of length 2.
+    Likewise, self-loops are considered to be cycles of length 1.  We define
+    cycles as sequences of nodes; so the presence of loops and parallel edges
+    does not change the number of simple cycles in a graph.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+       A networkx graph. Undirected, directed, and multigraphs are all supported.
+
+    length_bound : int or None, optional (default=None)
+       If `length_bound` is an int, generate all simple cycles of `G` with length at
+       most `length_bound`.  Otherwise, generate all simple cycles of `G`.
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(0, 0), (0, 1), (0, 2), (1, 2), (2, 0), (2, 1), (2, 2)])
+    >>> sorted(nx.simple_cycles(G))
+    [[0], [0, 1, 2], [0, 2], [1, 2], [2]]
+
+    To filter the cycles so that they don't include certain nodes or edges,
+    copy your graph and eliminate those nodes or edges before calling.
+    For example, to exclude self-loops from the above example:
+
+    >>> H = G.copy()
+    >>> H.remove_edges_from(nx.selfloop_edges(G))
+    >>> sorted(nx.simple_cycles(H))
+    [[0, 1, 2], [0, 2], [1, 2]]
+
+    Notes
+    -----
+    When `length_bound` is None, the time complexity is $O((n+e)(c+1))$ for $n$
+    nodes, $e$ edges and $c$ simple circuits.  Otherwise, when ``length_bound > 1``,
+    the time complexity is $O((c+n)(k-1)d^k)$ where $d$ is the average degree of
+    the nodes of `G` and $k$ = `length_bound`.
+
+    Raises
+    ------
+    ValueError
+        when ``length_bound < 0``.
+
+    References
+    ----------
+    .. [1] Finding all the elementary circuits of a directed graph.
+       D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975.
+       https://doi.org/10.1137/0204007
+    .. [2] Finding All Bounded-Length Simple Cycles in a Directed Graph
+       A. Gupta and T. Suzumura https://arxiv.org/abs/2105.10094
+    .. [3] Enumerating the cycles of a digraph: a new preprocessing strategy.
+       G. Loizou and P. Thanish, Information Sciences, v. 27, 163-182, 1982.
+    .. [4] A search strategy for the elementary cycles of a directed graph.
+       J.L. Szwarcfiter and P.E. Lauer, BIT NUMERICAL MATHEMATICS,
+       v. 16, no. 2, 192-204, 1976.
+    .. [5] Optimal Listing of Cycles and st-Paths in Undirected Graphs
+        R. Ferreira and R. Grossi and A. Marino and N. Pisanti and R. Rizzi and
+        G. Sacomoto https://arxiv.org/abs/1205.2766
+
+    See Also
+    --------
+    cycle_basis
+    chordless_cycles
+    """
+
+    if length_bound is not None:
+        if length_bound == 0:
+            return
+        elif length_bound < 0:
+            raise ValueError("length bound must be non-negative")
+
+    directed = G.is_directed()
+    yield from ([v] for v, Gv in G.adj.items() if v in Gv)
+
+    if length_bound is not None and length_bound == 1:
+        return
+
+    if G.is_multigraph() and not directed:
+        visited = set()
+        for u, Gu in G.adj.items():
+            multiplicity = ((v, len(Guv)) for v, Guv in Gu.items() if v in visited)
+            yield from ([u, v] for v, m in multiplicity if m > 1)
+            visited.add(u)
+
+    # explicitly filter out loops; implicitly filter out parallel edges
+    if directed:
+        G = nx.DiGraph((u, v) for u, Gu in G.adj.items() for v in Gu if v != u)
+    else:
+        G = nx.Graph((u, v) for u, Gu in G.adj.items() for v in Gu if v != u)
+
+    # this case is not strictly necessary but improves performance
+    if length_bound is not None and length_bound == 2:
+        if directed:
+            visited = set()
+            for u, Gu in G.adj.items():
+                yield from (
+                    [v, u] for v in visited.intersection(Gu) if G.has_edge(v, u)
+                )
+                visited.add(u)
+        return
+
+    if directed:
+        yield from _directed_cycle_search(G, length_bound)
+    else:
+        yield from _undirected_cycle_search(G, length_bound)
+
+
+def _directed_cycle_search(G, length_bound):
+    """A dispatch function for `simple_cycles` for directed graphs.
+
+    We generate all cycles of G through binary partition.
+
+        1. Pick a node v in G which belongs to at least one cycle
+            a. Generate all cycles of G which contain the node v.
+            b. Recursively generate all cycles of G \\ v.
+
+    This is accomplished through the following:
+
+        1. Compute the strongly connected components SCC of G.
+        2. Select and remove a biconnected component C from BCC.  Select a
+           non-tree edge (u, v) of a depth-first search of G[C].
+        3. For each simple cycle P containing v in G[C], yield P.
+        4. Add the biconnected components of G[C \\ v] to BCC.
+
+    If the parameter length_bound is not None, then step 3 will be limited to
+    simple cycles of length at most length_bound.
+
+    Parameters
+    ----------
+    G : NetworkX DiGraph
+       A directed graph
+
+    length_bound : int or None
+       If length_bound is an int, generate all simple cycles of G with length at most length_bound.
+       Otherwise, generate all simple cycles of G.
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+    """
+
+    scc = nx.strongly_connected_components
+    components = [c for c in scc(G) if len(c) >= 2]
+    while components:
+        c = components.pop()
+        Gc = G.subgraph(c)
+        v = next(iter(c))
+        if length_bound is None:
+            yield from _johnson_cycle_search(Gc, [v])
+        else:
+            yield from _bounded_cycle_search(Gc, [v], length_bound)
+        # delete v after searching G, to make sure we can find v
+        G.remove_node(v)
+        components.extend(c for c in scc(Gc) if len(c) >= 2)
+
+
+def _undirected_cycle_search(G, length_bound):
+    """A dispatch function for `simple_cycles` for undirected graphs.
+
+    We generate all cycles of G through binary partition.
+
+        1. Pick an edge (u, v) in G which belongs to at least one cycle
+            a. Generate all cycles of G which contain the edge (u, v)
+            b. Recursively generate all cycles of G \\ (u, v)
+
+    This is accomplished through the following:
+
+        1. Compute the biconnected components BCC of G.
+        2. Select and remove a biconnected component C from BCC.  Select a
+           non-tree edge (u, v) of a depth-first search of G[C].
+        3. For each (v -> u) path P remaining in G[C] \\ (u, v), yield P.
+        4. Add the biconnected components of G[C] \\ (u, v) to BCC.
+
+    If the parameter length_bound is not None, then step 3 will be limited to simple paths
+    of length at most length_bound.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+       An undirected graph
+
+    length_bound : int or None
+       If length_bound is an int, generate all simple cycles of G with length at most length_bound.
+       Otherwise, generate all simple cycles of G.
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+    """
+
+    bcc = nx.biconnected_components
+    components = [c for c in bcc(G) if len(c) >= 3]
+    while components:
+        c = components.pop()
+        Gc = G.subgraph(c)
+        uv = list(next(iter(Gc.edges)))
+        G.remove_edge(*uv)
+        # delete (u, v) before searching G, to avoid fake 3-cycles [u, v, u]
+        if length_bound is None:
+            yield from _johnson_cycle_search(Gc, uv)
+        else:
+            yield from _bounded_cycle_search(Gc, uv, length_bound)
+        components.extend(c for c in bcc(Gc) if len(c) >= 3)
+
+
+class _NeighborhoodCache(dict):
+    """Very lightweight graph wrapper which caches neighborhoods as list.
+
+    This dict subclass uses the __missing__ functionality to query graphs for
+    their neighborhoods, and store the result as a list.  This is used to avoid
+    the performance penalty incurred by subgraph views.
+    """
+
+    def __init__(self, G):
+        self.G = G
+
+    def __missing__(self, v):
+        Gv = self[v] = list(self.G[v])
+        return Gv
+
+
+def _johnson_cycle_search(G, path):
+    """The main loop of the cycle-enumeration algorithm of Johnson.
+
+    Parameters
+    ----------
+    G : NetworkX Graph or DiGraph
+       A graph
+
+    path : list
+       A cycle prefix.  All cycles generated will begin with this prefix.
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+
+    References
+    ----------
+        .. [1] Finding all the elementary circuits of a directed graph.
+       D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975.
+       https://doi.org/10.1137/0204007
+
+    """
+
+    G = _NeighborhoodCache(G)
+    blocked = set(path)
+    B = defaultdict(set)  # graph portions that yield no elementary circuit
+    start = path[0]
+    stack = [iter(G[path[-1]])]
+    closed = [False]
+    while stack:
+        nbrs = stack[-1]
+        for w in nbrs:
+            if w == start:
+                yield path[:]
+                closed[-1] = True
+            elif w not in blocked:
+                path.append(w)
+                closed.append(False)
+                stack.append(iter(G[w]))
+                blocked.add(w)
+                break
+        else:  # no more nbrs
+            stack.pop()
+            v = path.pop()
+            if closed.pop():
+                if closed:
+                    closed[-1] = True
+                unblock_stack = {v}
+                while unblock_stack:
+                    u = unblock_stack.pop()
+                    if u in blocked:
+                        blocked.remove(u)
+                        unblock_stack.update(B[u])
+                        B[u].clear()
+            else:
+                for w in G[v]:
+                    B[w].add(v)
+
+
+def _bounded_cycle_search(G, path, length_bound):
+    """The main loop of the cycle-enumeration algorithm of Gupta and Suzumura.
+
+    Parameters
+    ----------
+    G : NetworkX Graph or DiGraph
+       A graph
+
+    path : list
+       A cycle prefix.  All cycles generated will begin with this prefix.
+
+    length_bound: int
+        A length bound.  All cycles generated will have length at most length_bound.
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+
+    References
+    ----------
+    .. [1] Finding All Bounded-Length Simple Cycles in a Directed Graph
+       A. Gupta and T. Suzumura https://arxiv.org/abs/2105.10094
+
+    """
+    G = _NeighborhoodCache(G)
+    lock = {v: 0 for v in path}
+    B = defaultdict(set)
+    start = path[0]
+    stack = [iter(G[path[-1]])]
+    blen = [length_bound]
+    while stack:
+        nbrs = stack[-1]
+        for w in nbrs:
+            if w == start:
+                yield path[:]
+                blen[-1] = 1
+            elif len(path) < lock.get(w, length_bound):
+                path.append(w)
+                blen.append(length_bound)
+                lock[w] = len(path)
+                stack.append(iter(G[w]))
+                break
+        else:
+            stack.pop()
+            v = path.pop()
+            bl = blen.pop()
+            if blen:
+                blen[-1] = min(blen[-1], bl)
+            if bl < length_bound:
+                relax_stack = [(bl, v)]
+                while relax_stack:
+                    bl, u = relax_stack.pop()
+                    if lock.get(u, length_bound) < length_bound - bl + 1:
+                        lock[u] = length_bound - bl + 1
+                        relax_stack.extend((bl + 1, w) for w in B[u].difference(path))
+            else:
+                for w in G[v]:
+                    B[w].add(v)
+
+
+@nx._dispatchable
+def chordless_cycles(G, length_bound=None):
+    """Find simple chordless cycles of a graph.
+
+    A `simple cycle` is a closed path where no node appears twice.  In a simple
+    cycle, a `chord` is an additional edge between two nodes in the cycle.  A
+    `chordless cycle` is a simple cycle without chords.  Said differently, a
+    chordless cycle is a cycle C in a graph G where the number of edges in the
+    induced graph G[C] is equal to the length of `C`.
+
+    Note that some care must be taken in the case that G is not a simple graph
+    nor a simple digraph.  Some authors limit the definition of chordless cycles
+    to have a prescribed minimum length; we do not.
+
+        1. We interpret self-loops to be chordless cycles, except in multigraphs
+           with multiple loops in parallel.  Likewise, in a chordless cycle of
+           length greater than 1, there can be no nodes with self-loops.
+
+        2. We interpret directed two-cycles to be chordless cycles, except in
+           multi-digraphs when any edge in a two-cycle has a parallel copy.
+
+        3. We interpret parallel pairs of undirected edges as two-cycles, except
+           when a third (or more) parallel edge exists between the two nodes.
+
+        4. Generalizing the above, edges with parallel clones may not occur in
+           chordless cycles.
+
+    In a directed graph, two chordless cycles are distinct if they are not
+    cyclic permutations of each other.  In an undirected graph, two chordless
+    cycles are distinct if they are not cyclic permutations of each other nor of
+    the other's reversal.
+
+    Optionally, the cycles are bounded in length.
+
+    We use an algorithm strongly inspired by that of Dias et al [1]_.  It has
+    been modified in the following ways:
+
+        1. Recursion is avoided, per Python's limitations
+
+        2. The labeling function is not necessary, because the starting paths
+            are chosen (and deleted from the host graph) to prevent multiple
+            occurrences of the same path
+
+        3. The search is optionally bounded at a specified length
+
+        4. Support for directed graphs is provided by extending cycles along
+            forward edges, and blocking nodes along forward and reverse edges
+
+        5. Support for multigraphs is provided by omitting digons from the set
+            of forward edges
+
+    Parameters
+    ----------
+    G : NetworkX DiGraph
+       A directed graph
+
+    length_bound : int or None, optional (default=None)
+       If length_bound is an int, generate all simple cycles of G with length at
+       most length_bound.  Otherwise, generate all simple cycles of G.
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+
+    Examples
+    --------
+    >>> sorted(list(nx.chordless_cycles(nx.complete_graph(4))))
+    [[1, 0, 2], [1, 0, 3], [2, 0, 3], [2, 1, 3]]
+
+    Notes
+    -----
+    When length_bound is None, and the graph is simple, the time complexity is
+    $O((n+e)(c+1))$ for $n$ nodes, $e$ edges and $c$ chordless cycles.
+
+    Raises
+    ------
+    ValueError
+        when length_bound < 0.
+
+    References
+    ----------
+    .. [1] Efficient enumeration of chordless cycles
+       E. Dias and D. Castonguay and H. Longo and W.A.R. Jradi
+       https://arxiv.org/abs/1309.1051
+
+    See Also
+    --------
+    simple_cycles
+    """
+
+    if length_bound is not None:
+        if length_bound == 0:
+            return
+        elif length_bound < 0:
+            raise ValueError("length bound must be non-negative")
+
+    directed = G.is_directed()
+    multigraph = G.is_multigraph()
+
+    if multigraph:
+        yield from ([v] for v, Gv in G.adj.items() if len(Gv.get(v, ())) == 1)
+    else:
+        yield from ([v] for v, Gv in G.adj.items() if v in Gv)
+
+    if length_bound is not None and length_bound == 1:
+        return
+
+    # Nodes with loops cannot belong to longer cycles.  Let's delete them here.
+    # also, we implicitly reduce the multiplicity of edges down to 1 in the case
+    # of multiedges.
+    if directed:
+        F = nx.DiGraph((u, v) for u, Gu in G.adj.items() if u not in Gu for v in Gu)
+        B = F.to_undirected(as_view=False)
+    else:
+        F = nx.Graph((u, v) for u, Gu in G.adj.items() if u not in Gu for v in Gu)
+        B = None
+
+    # If we're given a multigraph, we have a few cases to consider with parallel
+    # edges.
+    #
+    # 1. If we have 2 or more edges in parallel between the nodes (u, v), we
+    #    must not construct longer cycles along (u, v).
+    # 2. If G is not directed, then a pair of parallel edges between (u, v) is a
+    #    chordless cycle unless there exists a third (or more) parallel edge.
+    # 3. If G is directed, then parallel edges do not form cycles, but do
+    #    preclude back-edges from forming cycles (handled in the next section),
+    #    Thus, if an edge (u, v) is duplicated and the reverse (v, u) is also
+    #    present, then we remove both from F.
+    #
+    # In directed graphs, we need to consider both directions that edges can
+    # take, so iterate over all edges (u, v) and possibly (v, u).  In undirected
+    # graphs, we need to be a little careful to only consider every edge once,
+    # so we use a "visited" set to emulate node-order comparisons.
+
+    if multigraph:
+        if not directed:
+            B = F.copy()
+            visited = set()
+        for u, Gu in G.adj.items():
+            if directed:
+                multiplicity = ((v, len(Guv)) for v, Guv in Gu.items())
+                for v, m in multiplicity:
+                    if m > 1:
+                        F.remove_edges_from(((u, v), (v, u)))
+            else:
+                multiplicity = ((v, len(Guv)) for v, Guv in Gu.items() if v in visited)
+                for v, m in multiplicity:
+                    if m == 2:
+                        yield [u, v]
+                    if m > 1:
+                        F.remove_edge(u, v)
+                visited.add(u)
+
+    # If we're given a directed graphs, we need to think about digons.  If we
+    # have two edges (u, v) and (v, u), then that's a two-cycle.  If either edge
+    # was duplicated above, then we removed both from F.  So, any digons we find
+    # here are chordless.  After finding digons, we remove their edges from F
+    # to avoid traversing them in the search for chordless cycles.
+    if directed:
+        for u, Fu in F.adj.items():
+            digons = [[u, v] for v in Fu if F.has_edge(v, u)]
+            yield from digons
+            F.remove_edges_from(digons)
+            F.remove_edges_from(e[::-1] for e in digons)
+
+    if length_bound is not None and length_bound == 2:
+        return
+
+    # Now, we prepare to search for cycles.  We have removed all cycles of
+    # lengths 1 and 2, so F is a simple graph or simple digraph.  We repeatedly
+    # separate digraphs into their strongly connected components, and undirected
+    # graphs into their biconnected components.  For each component, we pick a
+    # node v, search for chordless cycles based at each "stem" (u, v, w), and
+    # then remove v from that component before separating the graph again.
+    if directed:
+        separate = nx.strongly_connected_components
+
+        # Directed stems look like (u -> v -> w), so we use the product of
+        # predecessors of v with successors of v.
+        def stems(C, v):
+            for u, w in product(C.pred[v], C.succ[v]):
+                if not G.has_edge(u, w):  # omit stems with acyclic chords
+                    yield [u, v, w], F.has_edge(w, u)
+
+    else:
+        separate = nx.biconnected_components
+
+        # Undirected stems look like (u ~ v ~ w), but we must not also search
+        # (w ~ v ~ u), so we use combinations of v's neighbors of length 2.
+        def stems(C, v):
+            yield from (([u, v, w], F.has_edge(w, u)) for u, w in combinations(C[v], 2))
+
+    components = [c for c in separate(F) if len(c) > 2]
+    while components:
+        c = components.pop()
+        v = next(iter(c))
+        Fc = F.subgraph(c)
+        Fcc = Bcc = None
+        for S, is_triangle in stems(Fc, v):
+            if is_triangle:
+                yield S
+            else:
+                if Fcc is None:
+                    Fcc = _NeighborhoodCache(Fc)
+                    Bcc = Fcc if B is None else _NeighborhoodCache(B.subgraph(c))
+                yield from _chordless_cycle_search(Fcc, Bcc, S, length_bound)
+
+        components.extend(c for c in separate(F.subgraph(c - {v})) if len(c) > 2)
+
+
+def _chordless_cycle_search(F, B, path, length_bound):
+    """The main loop for chordless cycle enumeration.
+
+    This algorithm is strongly inspired by that of Dias et al [1]_.  It has been
+    modified in the following ways:
+
+        1. Recursion is avoided, per Python's limitations
+
+        2. The labeling function is not necessary, because the starting paths
+            are chosen (and deleted from the host graph) to prevent multiple
+            occurrences of the same path
+
+        3. The search is optionally bounded at a specified length
+
+        4. Support for directed graphs is provided by extending cycles along
+            forward edges, and blocking nodes along forward and reverse edges
+
+        5. Support for multigraphs is provided by omitting digons from the set
+            of forward edges
+
+    Parameters
+    ----------
+    F : _NeighborhoodCache
+       A graph of forward edges to follow in constructing cycles
+
+    B : _NeighborhoodCache
+       A graph of blocking edges to prevent the production of chordless cycles
+
+    path : list
+       A cycle prefix.  All cycles generated will begin with this prefix.
+
+    length_bound : int
+       A length bound.  All cycles generated will have length at most length_bound.
+
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+
+    References
+    ----------
+    .. [1] Efficient enumeration of chordless cycles
+       E. Dias and D. Castonguay and H. Longo and W.A.R. Jradi
+       https://arxiv.org/abs/1309.1051
+
+    """
+    blocked = defaultdict(int)
+    target = path[0]
+    blocked[path[1]] = 1
+    for w in path[1:]:
+        for v in B[w]:
+            blocked[v] += 1
+
+    stack = [iter(F[path[2]])]
+    while stack:
+        nbrs = stack[-1]
+        for w in nbrs:
+            if blocked[w] == 1 and (length_bound is None or len(path) < length_bound):
+                Fw = F[w]
+                if target in Fw:
+                    yield path + [w]
+                else:
+                    Bw = B[w]
+                    if target in Bw:
+                        continue
+                    for v in Bw:
+                        blocked[v] += 1
+                    path.append(w)
+                    stack.append(iter(Fw))
+                    break
+        else:
+            stack.pop()
+            for v in B[path.pop()]:
+                blocked[v] -= 1
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable(mutates_input=True)
+def recursive_simple_cycles(G):
+    """Find simple cycles (elementary circuits) of a directed graph.
+
+    A `simple cycle`, or `elementary circuit`, is a closed path where
+    no node appears twice. Two elementary circuits are distinct if they
+    are not cyclic permutations of each other.
+
+    This version uses a recursive algorithm to build a list of cycles.
+    You should probably use the iterator version called simple_cycles().
+    Warning: This recursive version uses lots of RAM!
+    It appears in NetworkX for pedagogical value.
+
+    Parameters
+    ----------
+    G : NetworkX DiGraph
+       A directed graph
+
+    Returns
+    -------
+    A list of cycles, where each cycle is represented by a list of nodes
+    along the cycle.
+
+    Example:
+
+    >>> edges = [(0, 0), (0, 1), (0, 2), (1, 2), (2, 0), (2, 1), (2, 2)]
+    >>> G = nx.DiGraph(edges)
+    >>> nx.recursive_simple_cycles(G)
+    [[0], [2], [0, 1, 2], [0, 2], [1, 2]]
+
+    Notes
+    -----
+    The implementation follows pp. 79-80 in [1]_.
+
+    The time complexity is $O((n+e)(c+1))$ for $n$ nodes, $e$ edges and $c$
+    elementary circuits.
+
+    References
+    ----------
+    .. [1] Finding all the elementary circuits of a directed graph.
+       D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975.
+       https://doi.org/10.1137/0204007
+
+    See Also
+    --------
+    simple_cycles, cycle_basis
+    """
+
+    # Jon Olav Vik, 2010-08-09
+    def _unblock(thisnode):
+        """Recursively unblock and remove nodes from B[thisnode]."""
+        if blocked[thisnode]:
+            blocked[thisnode] = False
+            while B[thisnode]:
+                _unblock(B[thisnode].pop())
+
+    def circuit(thisnode, startnode, component):
+        closed = False  # set to True if elementary path is closed
+        path.append(thisnode)
+        blocked[thisnode] = True
+        for nextnode in component[thisnode]:  # direct successors of thisnode
+            if nextnode == startnode:
+                result.append(path[:])
+                closed = True
+            elif not blocked[nextnode]:
+                if circuit(nextnode, startnode, component):
+                    closed = True
+        if closed:
+            _unblock(thisnode)
+        else:
+            for nextnode in component[thisnode]:
+                if thisnode not in B[nextnode]:  # TODO: use set for speedup?
+                    B[nextnode].append(thisnode)
+        path.pop()  # remove thisnode from path
+        return closed
+
+    path = []  # stack of nodes in current path
+    blocked = defaultdict(bool)  # vertex: blocked from search?
+    B = defaultdict(list)  # graph portions that yield no elementary circuit
+    result = []  # list to accumulate the circuits found
+
+    # Johnson's algorithm exclude self cycle edges like (v, v)
+    # To be backward compatible, we record those cycles in advance
+    # and then remove from subG
+    for v in G:
+        if G.has_edge(v, v):
+            result.append([v])
+            G.remove_edge(v, v)
+
+    # Johnson's algorithm requires some ordering of the nodes.
+    # They might not be sortable so we assign an arbitrary ordering.
+    ordering = dict(zip(G, range(len(G))))
+    for s in ordering:
+        # Build the subgraph induced by s and following nodes in the ordering
+        subgraph = G.subgraph(node for node in G if ordering[node] >= ordering[s])
+        # Find the strongly connected component in the subgraph
+        # that contains the least node according to the ordering
+        strongcomp = nx.strongly_connected_components(subgraph)
+        mincomp = min(strongcomp, key=lambda ns: min(ordering[n] for n in ns))
+        component = G.subgraph(mincomp)
+        if len(component) > 1:
+            # smallest node in the component according to the ordering
+            startnode = min(component, key=ordering.__getitem__)
+            for node in component:
+                blocked[node] = False
+                B[node][:] = []
+            dummy = circuit(startnode, startnode, component)
+    return result
+
+
+@nx._dispatchable
+def find_cycle(G, source=None, orientation=None):
+    """Returns a cycle found via depth-first traversal.
+
+    The cycle is a list of edges indicating the cyclic path.
+    Orientation of directed edges is controlled by `orientation`.
+
+    Parameters
+    ----------
+    G : graph
+        A directed/undirected graph/multigraph.
+
+    source : node, list of nodes
+        The node from which the traversal begins. If None, then a source
+        is chosen arbitrarily and repeatedly until all edges from each node in
+        the graph are searched.
+
+    orientation : None | 'original' | 'reverse' | 'ignore' (default: None)
+        For directed graphs and directed multigraphs, edge traversals need not
+        respect the original orientation of the edges.
+        When set to 'reverse' every edge is traversed in the reverse direction.
+        When set to 'ignore', every edge is treated as undirected.
+        When set to 'original', every edge is treated as directed.
+        In all three cases, the yielded edge tuples add a last entry to
+        indicate the direction in which that edge was traversed.
+        If orientation is None, the yielded edge has no direction indicated.
+        The direction is respected, but not reported.
+
+    Returns
+    -------
+    edges : directed edges
+        A list of directed edges indicating the path taken for the loop.
+        If no cycle is found, then an exception is raised.
+        For graphs, an edge is of the form `(u, v)` where `u` and `v`
+        are the tail and head of the edge as determined by the traversal.
+        For multigraphs, an edge is of the form `(u, v, key)`, where `key` is
+        the key of the edge. When the graph is directed, then `u` and `v`
+        are always in the order of the actual directed edge.
+        If orientation is not None then the edge tuple is extended to include
+        the direction of traversal ('forward' or 'reverse') on that edge.
+
+    Raises
+    ------
+    NetworkXNoCycle
+        If no cycle was found.
+
+    Examples
+    --------
+    In this example, we construct a DAG and find, in the first call, that there
+    are no directed cycles, and so an exception is raised. In the second call,
+    we ignore edge orientations and find that there is an undirected cycle.
+    Note that the second call finds a directed cycle while effectively
+    traversing an undirected graph, and so, we found an "undirected cycle".
+    This means that this DAG structure does not form a directed tree (which
+    is also known as a polytree).
+
+    >>> G = nx.DiGraph([(0, 1), (0, 2), (1, 2)])
+    >>> nx.find_cycle(G, orientation="original")
+    Traceback (most recent call last):
+        ...
+    networkx.exception.NetworkXNoCycle: No cycle found.
+    >>> list(nx.find_cycle(G, orientation="ignore"))
+    [(0, 1, 'forward'), (1, 2, 'forward'), (0, 2, 'reverse')]
+
+    See Also
+    --------
+    simple_cycles
+    """
+    if not G.is_directed() or orientation in (None, "original"):
+
+        def tailhead(edge):
+            return edge[:2]
+
+    elif orientation == "reverse":
+
+        def tailhead(edge):
+            return edge[1], edge[0]
+
+    elif orientation == "ignore":
+
+        def tailhead(edge):
+            if edge[-1] == "reverse":
+                return edge[1], edge[0]
+            return edge[:2]
+
+    explored = set()
+    cycle = []
+    final_node = None
+    for start_node in G.nbunch_iter(source):
+        if start_node in explored:
+            # No loop is possible.
+            continue
+
+        edges = []
+        # All nodes seen in this iteration of edge_dfs
+        seen = {start_node}
+        # Nodes in active path.
+        active_nodes = {start_node}
+        previous_head = None
+
+        for edge in nx.edge_dfs(G, start_node, orientation):
+            # Determine if this edge is a continuation of the active path.
+            tail, head = tailhead(edge)
+            if head in explored:
+                # Then we've already explored it. No loop is possible.
+                continue
+            if previous_head is not None and tail != previous_head:
+                # This edge results from backtracking.
+                # Pop until we get a node whose head equals the current tail.
+                # So for example, we might have:
+                #  (0, 1), (1, 2), (2, 3), (1, 4)
+                # which must become:
+                #  (0, 1), (1, 4)
+                while True:
+                    try:
+                        popped_edge = edges.pop()
+                    except IndexError:
+                        edges = []
+                        active_nodes = {tail}
+                        break
+                    else:
+                        popped_head = tailhead(popped_edge)[1]
+                        active_nodes.remove(popped_head)
+
+                    if edges:
+                        last_head = tailhead(edges[-1])[1]
+                        if tail == last_head:
+                            break
+            edges.append(edge)
+
+            if head in active_nodes:
+                # We have a loop!
+                cycle.extend(edges)
+                final_node = head
+                break
+            else:
+                seen.add(head)
+                active_nodes.add(head)
+                previous_head = head
+
+        if cycle:
+            break
+        else:
+            explored.update(seen)
+
+    else:
+        assert len(cycle) == 0
+        raise nx.exception.NetworkXNoCycle("No cycle found.")
+
+    # We now have a list of edges which ends on a cycle.
+    # So we need to remove from the beginning edges that are not relevant.
+
+    for i, edge in enumerate(cycle):
+        tail, head = tailhead(edge)
+        if tail == final_node:
+            break
+
+    return cycle[i:]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def minimum_cycle_basis(G, weight=None):
+    """Returns a minimum weight cycle basis for G
+
+    Minimum weight means a cycle basis for which the total weight
+    (length for unweighted graphs) of all the cycles is minimum.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+    weight: string
+        name of the edge attribute to use for edge weights
+
+    Returns
+    -------
+    A list of cycle lists.  Each cycle list is a list of nodes
+    which forms a cycle (loop) in G. Note that the nodes are not
+    necessarily returned in a order by which they appear in the cycle
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> nx.add_cycle(G, [0, 1, 2, 3])
+    >>> nx.add_cycle(G, [0, 3, 4, 5])
+    >>> nx.minimum_cycle_basis(G)
+    [[5, 4, 3, 0], [3, 2, 1, 0]]
+
+    References:
+        [1] Kavitha, Telikepalli, et al. "An O(m^2n) Algorithm for
+        Minimum Cycle Basis of Graphs."
+        http://link.springer.com/article/10.1007/s00453-007-9064-z
+        [2] de Pina, J. 1995. Applications of shortest path methods.
+        Ph.D. thesis, University of Amsterdam, Netherlands
+
+    See Also
+    --------
+    simple_cycles, cycle_basis
+    """
+    # We first split the graph in connected subgraphs
+    return sum(
+        (_min_cycle_basis(G.subgraph(c), weight) for c in nx.connected_components(G)),
+        [],
+    )
+
+
+def _min_cycle_basis(G, weight):
+    cb = []
+    # We  extract the edges not in a spanning tree. We do not really need a
+    # *minimum* spanning tree. That is why we call the next function with
+    # weight=None. Depending on implementation, it may be faster as well
+    tree_edges = list(nx.minimum_spanning_edges(G, weight=None, data=False))
+    chords = G.edges - tree_edges - {(v, u) for u, v in tree_edges}
+
+    # We maintain a set of vectors orthogonal to sofar found cycles
+    set_orth = [{edge} for edge in chords]
+    while set_orth:
+        base = set_orth.pop()
+        # kth cycle is "parallel" to kth vector in set_orth
+        cycle_edges = _min_cycle(G, base, weight)
+        cb.append([v for u, v in cycle_edges])
+
+        # now update set_orth so that k+1,k+2... th elements are
+        # orthogonal to the newly found cycle, as per [p. 336, 1]
+        set_orth = [
+            (
+                {e for e in orth if e not in base if e[::-1] not in base}
+                | {e for e in base if e not in orth if e[::-1] not in orth}
+            )
+            if sum((e in orth or e[::-1] in orth) for e in cycle_edges) % 2
+            else orth
+            for orth in set_orth
+        ]
+    return cb
+
+
+def _min_cycle(G, orth, weight):
+    """
+    Computes the minimum weight cycle in G,
+    orthogonal to the vector orth as per [p. 338, 1]
+    Use (u, 1) to indicate the lifted copy of u (denoted u' in paper).
+    """
+    Gi = nx.Graph()
+
+    # Add 2 copies of each edge in G to Gi.
+    # If edge is in orth, add cross edge; otherwise in-plane edge
+    for u, v, wt in G.edges(data=weight, default=1):
+        if (u, v) in orth or (v, u) in orth:
+            Gi.add_edges_from([(u, (v, 1)), ((u, 1), v)], Gi_weight=wt)
+        else:
+            Gi.add_edges_from([(u, v), ((u, 1), (v, 1))], Gi_weight=wt)
+
+    # find the shortest length in Gi between n and (n, 1) for each n
+    # Note: Use "Gi_weight" for name of weight attribute
+    spl = nx.shortest_path_length
+    lift = {n: spl(Gi, source=n, target=(n, 1), weight="Gi_weight") for n in G}
+
+    # Now compute that short path in Gi, which translates to a cycle in G
+    start = min(lift, key=lift.get)
+    end = (start, 1)
+    min_path_i = nx.shortest_path(Gi, source=start, target=end, weight="Gi_weight")
+
+    # Now we obtain the actual path, re-map nodes in Gi to those in G
+    min_path = [n if n in G else n[0] for n in min_path_i]
+
+    # Now remove the edges that occur two times
+    # two passes: flag which edges get kept, then build it
+    edgelist = list(pairwise(min_path))
+    edgeset = set()
+    for e in edgelist:
+        if e in edgeset:
+            edgeset.remove(e)
+        elif e[::-1] in edgeset:
+            edgeset.remove(e[::-1])
+        else:
+            edgeset.add(e)
+
+    min_edgelist = []
+    for e in edgelist:
+        if e in edgeset:
+            min_edgelist.append(e)
+            edgeset.remove(e)
+        elif e[::-1] in edgeset:
+            min_edgelist.append(e[::-1])
+            edgeset.remove(e[::-1])
+
+    return min_edgelist
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def girth(G):
+    """Returns the girth of the graph.
+
+    The girth of a graph is the length of its shortest cycle, or infinity if
+    the graph is acyclic. The algorithm follows the description given on the
+    Wikipedia page [1]_, and runs in time O(mn) on a graph with m edges and n
+    nodes.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    Returns
+    -------
+    int or math.inf
+
+    Examples
+    --------
+    All examples below (except P_5) can easily be checked using Wikipedia,
+    which has a page for each of these famous graphs.
+
+    >>> nx.girth(nx.chvatal_graph())
+    4
+    >>> nx.girth(nx.tutte_graph())
+    4
+    >>> nx.girth(nx.petersen_graph())
+    5
+    >>> nx.girth(nx.heawood_graph())
+    6
+    >>> nx.girth(nx.pappus_graph())
+    6
+    >>> nx.girth(nx.path_graph(5))
+    inf
+
+    References
+    ----------
+    .. [1] `Wikipedia: Girth <https://en.wikipedia.org/wiki/Girth_(graph_theory)>`_
+
+    """
+    girth = depth_limit = inf
+    tree_edge = nx.algorithms.traversal.breadth_first_search.TREE_EDGE
+    level_edge = nx.algorithms.traversal.breadth_first_search.LEVEL_EDGE
+    for n in G:
+        # run a BFS from source n, keeping track of distances; since we want
+        # the shortest cycle, no need to explore beyond the current minimum length
+        depth = {n: 0}
+        for u, v, label in nx.bfs_labeled_edges(G, n):
+            du = depth[u]
+            if du > depth_limit:
+                break
+            if label is tree_edge:
+                depth[v] = du + 1
+            else:
+                # if (u, v) is a level edge, the length is du + du + 1 (odd)
+                # otherwise, it's a forward edge; length is du + (du + 1) + 1 (even)
+                delta = label is level_edge
+                length = du + du + 2 - delta
+                if length < girth:
+                    girth = length
+                    depth_limit = du - delta
+
+    return girth

wemm/lib/python3.10/site-packages/networkx/algorithms/distance_regular.py

@@ -0,0 +1,238 @@
+"""
+=======================
+Distance-regular graphs
+=======================
+"""
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+from .distance_measures import diameter
+
+__all__ = [
+    "is_distance_regular",
+    "is_strongly_regular",
+    "intersection_array",
+    "global_parameters",
+]
+
+
+@nx._dispatchable
+def is_distance_regular(G):
+    """Returns True if the graph is distance regular, False otherwise.
+
+    A connected graph G is distance-regular if for any nodes x,y
+    and any integers i,j=0,1,...,d (where d is the graph
+    diameter), the number of vertices at distance i from x and
+    distance j from y depends only on i,j and the graph distance
+    between x and y, independently of the choice of x and y.
+
+    Parameters
+    ----------
+    G: Networkx graph (undirected)
+
+    Returns
+    -------
+    bool
+      True if the graph is Distance Regular, False otherwise
+
+    Examples
+    --------
+    >>> G = nx.hypercube_graph(6)
+    >>> nx.is_distance_regular(G)
+    True
+
+    See Also
+    --------
+    intersection_array, global_parameters
+
+    Notes
+    -----
+    For undirected and simple graphs only
+
+    References
+    ----------
+    .. [1] Brouwer, A. E.; Cohen, A. M.; and Neumaier, A.
+        Distance-Regular Graphs. New York: Springer-Verlag, 1989.
+    .. [2] Weisstein, Eric W. "Distance-Regular Graph."
+        http://mathworld.wolfram.com/Distance-RegularGraph.html
+
+    """
+    try:
+        intersection_array(G)
+        return True
+    except nx.NetworkXError:
+        return False
+
+
+def global_parameters(b, c):
+    """Returns global parameters for a given intersection array.
+
+    Given a distance-regular graph G with integers b_i, c_i,i = 0,....,d
+    such that for any 2 vertices x,y in G at a distance i=d(x,y), there
+    are exactly c_i neighbors of y at a distance of i-1 from x and b_i
+    neighbors of y at a distance of i+1 from x.
+
+    Thus, a distance regular graph has the global parameters,
+    [[c_0,a_0,b_0],[c_1,a_1,b_1],......,[c_d,a_d,b_d]] for the
+    intersection array  [b_0,b_1,.....b_{d-1};c_1,c_2,.....c_d]
+    where a_i+b_i+c_i=k , k= degree of every vertex.
+
+    Parameters
+    ----------
+    b : list
+
+    c : list
+
+    Returns
+    -------
+    iterable
+       An iterable over three tuples.
+
+    Examples
+    --------
+    >>> G = nx.dodecahedral_graph()
+    >>> b, c = nx.intersection_array(G)
+    >>> list(nx.global_parameters(b, c))
+    [(0, 0, 3), (1, 0, 2), (1, 1, 1), (1, 1, 1), (2, 0, 1), (3, 0, 0)]
+
+    References
+    ----------
+    .. [1] Weisstein, Eric W. "Global Parameters."
+       From MathWorld--A Wolfram Web Resource.
+       http://mathworld.wolfram.com/GlobalParameters.html
+
+    See Also
+    --------
+    intersection_array
+    """
+    return ((y, b[0] - x - y, x) for x, y in zip(b + [0], [0] + c))
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def intersection_array(G):
+    """Returns the intersection array of a distance-regular graph.
+
+    Given a distance-regular graph G with integers b_i, c_i,i = 0,....,d
+    such that for any 2 vertices x,y in G at a distance i=d(x,y), there
+    are exactly c_i neighbors of y at a distance of i-1 from x and b_i
+    neighbors of y at a distance of i+1 from x.
+
+    A distance regular graph's intersection array is given by,
+    [b_0,b_1,.....b_{d-1};c_1,c_2,.....c_d]
+
+    Parameters
+    ----------
+    G: Networkx graph (undirected)
+
+    Returns
+    -------
+    b,c: tuple of lists
+
+    Examples
+    --------
+    >>> G = nx.icosahedral_graph()
+    >>> nx.intersection_array(G)
+    ([5, 2, 1], [1, 2, 5])
+
+    References
+    ----------
+    .. [1] Weisstein, Eric W. "Intersection Array."
+       From MathWorld--A Wolfram Web Resource.
+       http://mathworld.wolfram.com/IntersectionArray.html
+
+    See Also
+    --------
+    global_parameters
+    """
+    # test for regular graph (all degrees must be equal)
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept("Graph has no nodes.")
+    degree = iter(G.degree())
+    (_, k) = next(degree)
+    for _, knext in degree:
+        if knext != k:
+            raise nx.NetworkXError("Graph is not distance regular.")
+        k = knext
+    path_length = dict(nx.all_pairs_shortest_path_length(G))
+    diameter = max(max(path_length[n].values()) for n in path_length)
+    bint = {}  # 'b' intersection array
+    cint = {}  # 'c' intersection array
+    for u in G:
+        for v in G:
+            try:
+                i = path_length[u][v]
+            except KeyError as err:  # graph must be connected
+                raise nx.NetworkXError("Graph is not distance regular.") from err
+            # number of neighbors of v at a distance of i-1 from u
+            c = len([n for n in G[v] if path_length[n][u] == i - 1])
+            # number of neighbors of v at a distance of i+1 from u
+            b = len([n for n in G[v] if path_length[n][u] == i + 1])
+            # b,c are independent of u and v
+            if cint.get(i, c) != c or bint.get(i, b) != b:
+                raise nx.NetworkXError("Graph is not distance regular")
+            bint[i] = b
+            cint[i] = c
+    return (
+        [bint.get(j, 0) for j in range(diameter)],
+        [cint.get(j + 1, 0) for j in range(diameter)],
+    )
+
+
+# TODO There is a definition for directed strongly regular graphs.
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def is_strongly_regular(G):
+    """Returns True if and only if the given graph is strongly
+    regular.
+
+    An undirected graph is *strongly regular* if
+
+    * it is regular,
+    * each pair of adjacent vertices has the same number of neighbors in
+      common,
+    * each pair of nonadjacent vertices has the same number of neighbors
+      in common.
+
+    Each strongly regular graph is a distance-regular graph.
+    Conversely, if a distance-regular graph has diameter two, then it is
+    a strongly regular graph. For more information on distance-regular
+    graphs, see :func:`is_distance_regular`.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected graph.
+
+    Returns
+    -------
+    bool
+        Whether `G` is strongly regular.
+
+    Examples
+    --------
+
+    The cycle graph on five vertices is strongly regular. It is
+    two-regular, each pair of adjacent vertices has no shared neighbors,
+    and each pair of nonadjacent vertices has one shared neighbor::
+
+        >>> G = nx.cycle_graph(5)
+        >>> nx.is_strongly_regular(G)
+        True
+
+    """
+    # Here is an alternate implementation based directly on the
+    # definition of strongly regular graphs:
+    #
+    #     return (all_equal(G.degree().values())
+    #             and all_equal(len(common_neighbors(G, u, v))
+    #                           for u, v in G.edges())
+    #             and all_equal(len(common_neighbors(G, u, v))
+    #                           for u, v in non_edges(G)))
+    #
+    # We instead use the fact that a distance-regular graph of diameter
+    # two is strongly regular.
+    return is_distance_regular(G) and diameter(G) == 2

wemm/lib/python3.10/site-packages/networkx/algorithms/dominating.py

@@ -0,0 +1,95 @@
+"""Functions for computing dominating sets in a graph."""
+
+from itertools import chain
+
+import networkx as nx
+from networkx.utils import arbitrary_element
+
+__all__ = ["dominating_set", "is_dominating_set"]
+
+
+@nx._dispatchable
+def dominating_set(G, start_with=None):
+    r"""Finds a dominating set for the graph G.
+
+    A *dominating set* for a graph with node set *V* is a subset *D* of
+    *V* such that every node not in *D* is adjacent to at least one
+    member of *D* [1]_.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    start_with : node (default=None)
+        Node to use as a starting point for the algorithm.
+
+    Returns
+    -------
+    D : set
+        A dominating set for G.
+
+    Notes
+    -----
+    This function is an implementation of algorithm 7 in [2]_ which
+    finds some dominating set, not necessarily the smallest one.
+
+    See also
+    --------
+    is_dominating_set
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Dominating_set
+
+    .. [2] Abdol-Hossein Esfahanian. Connectivity Algorithms.
+        http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
+
+    """
+    all_nodes = set(G)
+    if start_with is None:
+        start_with = arbitrary_element(all_nodes)
+    if start_with not in G:
+        raise nx.NetworkXError(f"node {start_with} is not in G")
+    dominating_set = {start_with}
+    dominated_nodes = set(G[start_with])
+    remaining_nodes = all_nodes - dominated_nodes - dominating_set
+    while remaining_nodes:
+        # Choose an arbitrary node and determine its undominated neighbors.
+        v = remaining_nodes.pop()
+        undominated_nbrs = set(G[v]) - dominating_set
+        # Add the node to the dominating set and the neighbors to the
+        # dominated set. Finally, remove all of those nodes from the set
+        # of remaining nodes.
+        dominating_set.add(v)
+        dominated_nodes |= undominated_nbrs
+        remaining_nodes -= undominated_nbrs
+    return dominating_set
+
+
+@nx._dispatchable
+def is_dominating_set(G, nbunch):
+    """Checks if `nbunch` is a dominating set for `G`.
+
+    A *dominating set* for a graph with node set *V* is a subset *D* of
+    *V* such that every node not in *D* is adjacent to at least one
+    member of *D* [1]_.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    nbunch : iterable
+        An iterable of nodes in the graph `G`.
+
+    See also
+    --------
+    dominating_set
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Dominating_set
+
+    """
+    testset = {n for n in nbunch if n in G}
+    nbrs = set(chain.from_iterable(G[n] for n in testset))
+    return len(set(G) - testset - nbrs) == 0

wemm/lib/python3.10/site-packages/networkx/algorithms/euler.py

@@ -0,0 +1,470 @@
+"""
+Eulerian circuits and graphs.
+"""
+
+from itertools import combinations
+
+import networkx as nx
+
+from ..utils import arbitrary_element, not_implemented_for
+
+__all__ = [
+    "is_eulerian",
+    "eulerian_circuit",
+    "eulerize",
+    "is_semieulerian",
+    "has_eulerian_path",
+    "eulerian_path",
+]
+
+
+@nx._dispatchable
+def is_eulerian(G):
+    """Returns True if and only if `G` is Eulerian.
+
+    A graph is *Eulerian* if it has an Eulerian circuit. An *Eulerian
+    circuit* is a closed walk that includes each edge of a graph exactly
+    once.
+
+    Graphs with isolated vertices (i.e. vertices with zero degree) are not
+    considered to have Eulerian circuits. Therefore, if the graph is not
+    connected (or not strongly connected, for directed graphs), this function
+    returns False.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       A graph, either directed or undirected.
+
+    Examples
+    --------
+    >>> nx.is_eulerian(nx.DiGraph({0: [3], 1: [2], 2: [3], 3: [0, 1]}))
+    True
+    >>> nx.is_eulerian(nx.complete_graph(5))
+    True
+    >>> nx.is_eulerian(nx.petersen_graph())
+    False
+
+    If you prefer to allow graphs with isolated vertices to have Eulerian circuits,
+    you can first remove such vertices and then call `is_eulerian` as below example shows.
+
+    >>> G = nx.Graph([(0, 1), (1, 2), (0, 2)])
+    >>> G.add_node(3)
+    >>> nx.is_eulerian(G)
+    False
+
+    >>> G.remove_nodes_from(list(nx.isolates(G)))
+    >>> nx.is_eulerian(G)
+    True
+
+
+    """
+    if G.is_directed():
+        # Every node must have equal in degree and out degree and the
+        # graph must be strongly connected
+        return all(
+            G.in_degree(n) == G.out_degree(n) for n in G
+        ) and nx.is_strongly_connected(G)
+    # An undirected Eulerian graph has no vertices of odd degree and
+    # must be connected.
+    return all(d % 2 == 0 for v, d in G.degree()) and nx.is_connected(G)
+
+
+@nx._dispatchable
+def is_semieulerian(G):
+    """Return True iff `G` is semi-Eulerian.
+
+    G is semi-Eulerian if it has an Eulerian path but no Eulerian circuit.
+
+    See Also
+    --------
+    has_eulerian_path
+    is_eulerian
+    """
+    return has_eulerian_path(G) and not is_eulerian(G)
+
+
+def _find_path_start(G):
+    """Return a suitable starting vertex for an Eulerian path.
+
+    If no path exists, return None.
+    """
+    if not has_eulerian_path(G):
+        return None
+
+    if is_eulerian(G):
+        return arbitrary_element(G)
+
+    if G.is_directed():
+        v1, v2 = (v for v in G if G.in_degree(v) != G.out_degree(v))
+        # Determines which is the 'start' node (as opposed to the 'end')
+        if G.out_degree(v1) > G.in_degree(v1):
+            return v1
+        else:
+            return v2
+
+    else:
+        # In an undirected graph randomly choose one of the possibilities
+        start = [v for v in G if G.degree(v) % 2 != 0][0]
+        return start
+
+
+def _simplegraph_eulerian_circuit(G, source):
+    if G.is_directed():
+        degree = G.out_degree
+        edges = G.out_edges
+    else:
+        degree = G.degree
+        edges = G.edges
+    vertex_stack = [source]
+    last_vertex = None
+    while vertex_stack:
+        current_vertex = vertex_stack[-1]
+        if degree(current_vertex) == 0:
+            if last_vertex is not None:
+                yield (last_vertex, current_vertex)
+            last_vertex = current_vertex
+            vertex_stack.pop()
+        else:
+            _, next_vertex = arbitrary_element(edges(current_vertex))
+            vertex_stack.append(next_vertex)
+            G.remove_edge(current_vertex, next_vertex)
+
+
+def _multigraph_eulerian_circuit(G, source):
+    if G.is_directed():
+        degree = G.out_degree
+        edges = G.out_edges
+    else:
+        degree = G.degree
+        edges = G.edges
+    vertex_stack = [(source, None)]
+    last_vertex = None
+    last_key = None
+    while vertex_stack:
+        current_vertex, current_key = vertex_stack[-1]
+        if degree(current_vertex) == 0:
+            if last_vertex is not None:
+                yield (last_vertex, current_vertex, last_key)
+            last_vertex, last_key = current_vertex, current_key
+            vertex_stack.pop()
+        else:
+            triple = arbitrary_element(edges(current_vertex, keys=True))
+            _, next_vertex, next_key = triple
+            vertex_stack.append((next_vertex, next_key))
+            G.remove_edge(current_vertex, next_vertex, next_key)
+
+
+@nx._dispatchable
+def eulerian_circuit(G, source=None, keys=False):
+    """Returns an iterator over the edges of an Eulerian circuit in `G`.
+
+    An *Eulerian circuit* is a closed walk that includes each edge of a
+    graph exactly once.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       A graph, either directed or undirected.
+
+    source : node, optional
+       Starting node for circuit.
+
+    keys : bool
+       If False, edges generated by this function will be of the form
+       ``(u, v)``. Otherwise, edges will be of the form ``(u, v, k)``.
+       This option is ignored unless `G` is a multigraph.
+
+    Returns
+    -------
+    edges : iterator
+       An iterator over edges in the Eulerian circuit.
+
+    Raises
+    ------
+    NetworkXError
+       If the graph is not Eulerian.
+
+    See Also
+    --------
+    is_eulerian
+
+    Notes
+    -----
+    This is a linear time implementation of an algorithm adapted from [1]_.
+
+    For general information about Euler tours, see [2]_.
+
+    References
+    ----------
+    .. [1] J. Edmonds, E. L. Johnson.
+       Matching, Euler tours and the Chinese postman.
+       Mathematical programming, Volume 5, Issue 1 (1973), 111-114.
+    .. [2] https://en.wikipedia.org/wiki/Eulerian_path
+
+    Examples
+    --------
+    To get an Eulerian circuit in an undirected graph::
+
+        >>> G = nx.complete_graph(3)
+        >>> list(nx.eulerian_circuit(G))
+        [(0, 2), (2, 1), (1, 0)]
+        >>> list(nx.eulerian_circuit(G, source=1))
+        [(1, 2), (2, 0), (0, 1)]
+
+    To get the sequence of vertices in an Eulerian circuit::
+
+        >>> [u for u, v in nx.eulerian_circuit(G)]
+        [0, 2, 1]
+
+    """
+    if not is_eulerian(G):
+        raise nx.NetworkXError("G is not Eulerian.")
+    if G.is_directed():
+        G = G.reverse()
+    else:
+        G = G.copy()
+    if source is None:
+        source = arbitrary_element(G)
+    if G.is_multigraph():
+        for u, v, k in _multigraph_eulerian_circuit(G, source):
+            if keys:
+                yield u, v, k
+            else:
+                yield u, v
+    else:
+        yield from _simplegraph_eulerian_circuit(G, source)
+
+
+@nx._dispatchable
+def has_eulerian_path(G, source=None):
+    """Return True iff `G` has an Eulerian path.
+
+    An Eulerian path is a path in a graph which uses each edge of a graph
+    exactly once. If `source` is specified, then this function checks
+    whether an Eulerian path that starts at node `source` exists.
+
+    A directed graph has an Eulerian path iff:
+        - at most one vertex has out_degree - in_degree = 1,
+        - at most one vertex has in_degree - out_degree = 1,
+        - every other vertex has equal in_degree and out_degree,
+        - and all of its vertices belong to a single connected
+          component of the underlying undirected graph.
+
+    If `source` is not None, an Eulerian path starting at `source` exists if no
+    other node has out_degree - in_degree = 1. This is equivalent to either
+    there exists an Eulerian circuit or `source` has out_degree - in_degree = 1
+    and the conditions above hold.
+
+    An undirected graph has an Eulerian path iff:
+        - exactly zero or two vertices have odd degree,
+        - and all of its vertices belong to a single connected component.
+
+    If `source` is not None, an Eulerian path starting at `source` exists if
+    either there exists an Eulerian circuit or `source` has an odd degree and the
+    conditions above hold.
+
+    Graphs with isolated vertices (i.e. vertices with zero degree) are not considered
+    to have an Eulerian path. Therefore, if the graph is not connected (or not strongly
+    connected, for directed graphs), this function returns False.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        The graph to find an euler path in.
+
+    source : node, optional
+        Starting node for path.
+
+    Returns
+    -------
+    Bool : True if G has an Eulerian path.
+
+    Examples
+    --------
+    If you prefer to allow graphs with isolated vertices to have Eulerian path,
+    you can first remove such vertices and then call `has_eulerian_path` as below example shows.
+
+    >>> G = nx.Graph([(0, 1), (1, 2), (0, 2)])
+    >>> G.add_node(3)
+    >>> nx.has_eulerian_path(G)
+    False
+
+    >>> G.remove_nodes_from(list(nx.isolates(G)))
+    >>> nx.has_eulerian_path(G)
+    True
+
+    See Also
+    --------
+    is_eulerian
+    eulerian_path
+    """
+    if nx.is_eulerian(G):
+        return True
+
+    if G.is_directed():
+        ins = G.in_degree
+        outs = G.out_degree
+        # Since we know it is not eulerian, outs - ins must be 1 for source
+        if source is not None and outs[source] - ins[source] != 1:
+            return False
+
+        unbalanced_ins = 0
+        unbalanced_outs = 0
+        for v in G:
+            if ins[v] - outs[v] == 1:
+                unbalanced_ins += 1
+            elif outs[v] - ins[v] == 1:
+                unbalanced_outs += 1
+            elif ins[v] != outs[v]:
+                return False
+
+        return (
+            unbalanced_ins <= 1 and unbalanced_outs <= 1 and nx.is_weakly_connected(G)
+        )
+    else:
+        # We know it is not eulerian, so degree of source must be odd.
+        if source is not None and G.degree[source] % 2 != 1:
+            return False
+
+        # Sum is 2 since we know it is not eulerian (which implies sum is 0)
+        return sum(d % 2 == 1 for v, d in G.degree()) == 2 and nx.is_connected(G)
+
+
+@nx._dispatchable
+def eulerian_path(G, source=None, keys=False):
+    """Return an iterator over the edges of an Eulerian path in `G`.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        The graph in which to look for an eulerian path.
+    source : node or None (default: None)
+        The node at which to start the search. None means search over all
+        starting nodes.
+    keys : Bool (default: False)
+        Indicates whether to yield edge 3-tuples (u, v, edge_key).
+        The default yields edge 2-tuples
+
+    Yields
+    ------
+    Edge tuples along the eulerian path.
+
+    Warning: If `source` provided is not the start node of an Euler path
+    will raise error even if an Euler Path exists.
+    """
+    if not has_eulerian_path(G, source):
+        raise nx.NetworkXError("Graph has no Eulerian paths.")
+    if G.is_directed():
+        G = G.reverse()
+        if source is None or nx.is_eulerian(G) is False:
+            source = _find_path_start(G)
+        if G.is_multigraph():
+            for u, v, k in _multigraph_eulerian_circuit(G, source):
+                if keys:
+                    yield u, v, k
+                else:
+                    yield u, v
+        else:
+            yield from _simplegraph_eulerian_circuit(G, source)
+    else:
+        G = G.copy()
+        if source is None:
+            source = _find_path_start(G)
+        if G.is_multigraph():
+            if keys:
+                yield from reversed(
+                    [(v, u, k) for u, v, k in _multigraph_eulerian_circuit(G, source)]
+                )
+            else:
+                yield from reversed(
+                    [(v, u) for u, v, k in _multigraph_eulerian_circuit(G, source)]
+                )
+        else:
+            yield from reversed(
+                [(v, u) for u, v in _simplegraph_eulerian_circuit(G, source)]
+            )
+
+
+@not_implemented_for("directed")
+@nx._dispatchable(returns_graph=True)
+def eulerize(G):
+    """Transforms a graph into an Eulerian graph.
+
+    If `G` is Eulerian the result is `G` as a MultiGraph, otherwise the result is a smallest
+    (in terms of the number of edges) multigraph whose underlying simple graph is `G`.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph
+
+    Returns
+    -------
+    G : NetworkX multigraph
+
+    Raises
+    ------
+    NetworkXError
+       If the graph is not connected.
+
+    See Also
+    --------
+    is_eulerian
+    eulerian_circuit
+
+    References
+    ----------
+    .. [1] J. Edmonds, E. L. Johnson.
+       Matching, Euler tours and the Chinese postman.
+       Mathematical programming, Volume 5, Issue 1 (1973), 111-114.
+    .. [2] https://en.wikipedia.org/wiki/Eulerian_path
+    .. [3] http://web.math.princeton.edu/math_alive/5/Notes1.pdf
+
+    Examples
+    --------
+        >>> G = nx.complete_graph(10)
+        >>> H = nx.eulerize(G)
+        >>> nx.is_eulerian(H)
+        True
+
+    """
+    if G.order() == 0:
+        raise nx.NetworkXPointlessConcept("Cannot Eulerize null graph")
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("G is not connected")
+    odd_degree_nodes = [n for n, d in G.degree() if d % 2 == 1]
+    G = nx.MultiGraph(G)
+    if len(odd_degree_nodes) == 0:
+        return G
+
+    # get all shortest paths between vertices of odd degree
+    odd_deg_pairs_paths = [
+        (m, {n: nx.shortest_path(G, source=m, target=n)})
+        for m, n in combinations(odd_degree_nodes, 2)
+    ]
+
+    # use the number of vertices in a graph + 1 as an upper bound on
+    # the maximum length of a path in G
+    upper_bound_on_max_path_length = len(G) + 1
+
+    # use "len(G) + 1 - len(P)",
+    # where P is a shortest path between vertices n and m,
+    # as edge-weights in a new graph
+    # store the paths in the graph for easy indexing later
+    Gp = nx.Graph()
+    for n, Ps in odd_deg_pairs_paths:
+        for m, P in Ps.items():
+            if n != m:
+                Gp.add_edge(
+                    m, n, weight=upper_bound_on_max_path_length - len(P), path=P
+                )
+
+    # find the minimum weight matching of edges in the weighted graph
+    best_matching = nx.Graph(list(nx.max_weight_matching(Gp)))
+
+    # duplicate each edge along each path in the set of paths in Gp
+    for m, n in best_matching.edges():
+        path = Gp[m][n]["path"]
+        G.add_edges_from(nx.utils.pairwise(path))
+    return G

wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/__init__.py

@@ -0,0 +1,7 @@
+from networkx.algorithms.isomorphism.isomorph import *
+from networkx.algorithms.isomorphism.vf2userfunc import *
+from networkx.algorithms.isomorphism.matchhelpers import *
+from networkx.algorithms.isomorphism.temporalisomorphvf2 import *
+from networkx.algorithms.isomorphism.ismags import *
+from networkx.algorithms.isomorphism.tree_isomorphism import *
+from networkx.algorithms.isomorphism.vf2pp import *

wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/ismags.py

@@ -0,0 +1,1163 @@
+"""
+ISMAGS Algorithm
+================
+
+Provides a Python implementation of the ISMAGS algorithm. [1]_
+
+It is capable of finding (subgraph) isomorphisms between two graphs, taking the
+symmetry of the subgraph into account. In most cases the VF2 algorithm is
+faster (at least on small graphs) than this implementation, but in some cases
+there is an exponential number of isomorphisms that are symmetrically
+equivalent. In that case, the ISMAGS algorithm will provide only one solution
+per symmetry group.
+
+>>> petersen = nx.petersen_graph()
+>>> ismags = nx.isomorphism.ISMAGS(petersen, petersen)
+>>> isomorphisms = list(ismags.isomorphisms_iter(symmetry=False))
+>>> len(isomorphisms)
+120
+>>> isomorphisms = list(ismags.isomorphisms_iter(symmetry=True))
+>>> answer = [{0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9}]
+>>> answer == isomorphisms
+True
+
+In addition, this implementation also provides an interface to find the
+largest common induced subgraph [2]_ between any two graphs, again taking
+symmetry into account. Given `graph` and `subgraph` the algorithm will remove
+nodes from the `subgraph` until `subgraph` is isomorphic to a subgraph of
+`graph`. Since only the symmetry of `subgraph` is taken into account it is
+worth thinking about how you provide your graphs:
+
+>>> graph1 = nx.path_graph(4)
+>>> graph2 = nx.star_graph(3)
+>>> ismags = nx.isomorphism.ISMAGS(graph1, graph2)
+>>> ismags.is_isomorphic()
+False
+>>> largest_common_subgraph = list(ismags.largest_common_subgraph())
+>>> answer = [{1: 0, 0: 1, 2: 2}, {2: 0, 1: 1, 3: 2}]
+>>> answer == largest_common_subgraph
+True
+>>> ismags2 = nx.isomorphism.ISMAGS(graph2, graph1)
+>>> largest_common_subgraph = list(ismags2.largest_common_subgraph())
+>>> answer = [
+...     {1: 0, 0: 1, 2: 2},
+...     {1: 0, 0: 1, 3: 2},
+...     {2: 0, 0: 1, 1: 2},
+...     {2: 0, 0: 1, 3: 2},
+...     {3: 0, 0: 1, 1: 2},
+...     {3: 0, 0: 1, 2: 2},
+... ]
+>>> answer == largest_common_subgraph
+True
+
+However, when not taking symmetry into account, it doesn't matter:
+
+>>> largest_common_subgraph = list(ismags.largest_common_subgraph(symmetry=False))
+>>> answer = [
+...     {1: 0, 0: 1, 2: 2},
+...     {1: 0, 2: 1, 0: 2},
+...     {2: 0, 1: 1, 3: 2},
+...     {2: 0, 3: 1, 1: 2},
+...     {1: 0, 0: 1, 2: 3},
+...     {1: 0, 2: 1, 0: 3},
+...     {2: 0, 1: 1, 3: 3},
+...     {2: 0, 3: 1, 1: 3},
+...     {1: 0, 0: 2, 2: 3},
+...     {1: 0, 2: 2, 0: 3},
+...     {2: 0, 1: 2, 3: 3},
+...     {2: 0, 3: 2, 1: 3},
+... ]
+>>> answer == largest_common_subgraph
+True
+>>> largest_common_subgraph = list(ismags2.largest_common_subgraph(symmetry=False))
+>>> answer = [
+...     {1: 0, 0: 1, 2: 2},
+...     {1: 0, 0: 1, 3: 2},
+...     {2: 0, 0: 1, 1: 2},
+...     {2: 0, 0: 1, 3: 2},
+...     {3: 0, 0: 1, 1: 2},
+...     {3: 0, 0: 1, 2: 2},
+...     {1: 1, 0: 2, 2: 3},
+...     {1: 1, 0: 2, 3: 3},
+...     {2: 1, 0: 2, 1: 3},
+...     {2: 1, 0: 2, 3: 3},
+...     {3: 1, 0: 2, 1: 3},
+...     {3: 1, 0: 2, 2: 3},
+... ]
+>>> answer == largest_common_subgraph
+True
+
+Notes
+-----
+- The current implementation works for undirected graphs only. The algorithm
+  in general should work for directed graphs as well though.
+- Node keys for both provided graphs need to be fully orderable as well as
+  hashable.
+- Node and edge equality is assumed to be transitive: if A is equal to B, and
+  B is equal to C, then A is equal to C.
+
+References
+----------
+.. [1] M. Houbraken, S. Demeyer, T. Michoel, P. Audenaert, D. Colle,
+   M. Pickavet, "The Index-Based Subgraph Matching Algorithm with General
+   Symmetries (ISMAGS): Exploiting Symmetry for Faster Subgraph
+   Enumeration", PLoS One 9(5): e97896, 2014.
+   https://doi.org/10.1371/journal.pone.0097896
+.. [2] https://en.wikipedia.org/wiki/Maximum_common_induced_subgraph
+"""
+
+__all__ = ["ISMAGS"]
+
+import itertools
+from collections import Counter, defaultdict
+from functools import reduce, wraps
+
+
+def are_all_equal(iterable):
+    """
+    Returns ``True`` if and only if all elements in `iterable` are equal; and
+    ``False`` otherwise.
+
+    Parameters
+    ----------
+    iterable: collections.abc.Iterable
+        The container whose elements will be checked.
+
+    Returns
+    -------
+    bool
+        ``True`` iff all elements in `iterable` compare equal, ``False``
+        otherwise.
+    """
+    try:
+        shape = iterable.shape
+    except AttributeError:
+        pass
+    else:
+        if len(shape) > 1:
+            message = "The function does not works on multidimensional arrays."
+            raise NotImplementedError(message) from None
+
+    iterator = iter(iterable)
+    first = next(iterator, None)
+    return all(item == first for item in iterator)
+
+
+def make_partitions(items, test):
+    """
+    Partitions items into sets based on the outcome of ``test(item1, item2)``.
+    Pairs of items for which `test` returns `True` end up in the same set.
+
+    Parameters
+    ----------
+    items : collections.abc.Iterable[collections.abc.Hashable]
+        Items to partition
+    test : collections.abc.Callable[collections.abc.Hashable, collections.abc.Hashable]
+        A function that will be called with 2 arguments, taken from items.
+        Should return `True` if those 2 items need to end up in the same
+        partition, and `False` otherwise.
+
+    Returns
+    -------
+    list[set]
+        A list of sets, with each set containing part of the items in `items`,
+        such that ``all(test(*pair) for pair in  itertools.combinations(set, 2))
+        == True``
+
+    Notes
+    -----
+    The function `test` is assumed to be transitive: if ``test(a, b)`` and
+    ``test(b, c)`` return ``True``, then ``test(a, c)`` must also be ``True``.
+    """
+    partitions = []
+    for item in items:
+        for partition in partitions:
+            p_item = next(iter(partition))
+            if test(item, p_item):
+                partition.add(item)
+                break
+        else:  # No break
+            partitions.append({item})
+    return partitions
+
+
+def partition_to_color(partitions):
+    """
+    Creates a dictionary that maps each item in each partition to the index of
+    the partition to which it belongs.
+
+    Parameters
+    ----------
+    partitions: collections.abc.Sequence[collections.abc.Iterable]
+        As returned by :func:`make_partitions`.
+
+    Returns
+    -------
+    dict
+    """
+    colors = {}
+    for color, keys in enumerate(partitions):
+        for key in keys:
+            colors[key] = color
+    return colors
+
+
+def intersect(collection_of_sets):
+    """
+    Given an collection of sets, returns the intersection of those sets.
+
+    Parameters
+    ----------
+    collection_of_sets: collections.abc.Collection[set]
+        A collection of sets.
+
+    Returns
+    -------
+    set
+        An intersection of all sets in `collection_of_sets`. Will have the same
+        type as the item initially taken from `collection_of_sets`.
+    """
+    collection_of_sets = list(collection_of_sets)
+    first = collection_of_sets.pop()
+    out = reduce(set.intersection, collection_of_sets, set(first))
+    return type(first)(out)
+
+
+class ISMAGS:
+    """
+    Implements the ISMAGS subgraph matching algorithm. [1]_ ISMAGS stands for
+    "Index-based Subgraph Matching Algorithm with General Symmetries". As the
+    name implies, it is symmetry aware and will only generate non-symmetric
+    isomorphisms.
+
+    Notes
+    -----
+    The implementation imposes additional conditions compared to the VF2
+    algorithm on the graphs provided and the comparison functions
+    (:attr:`node_equality` and :attr:`edge_equality`):
+
+     - Node keys in both graphs must be orderable as well as hashable.
+     - Equality must be transitive: if A is equal to B, and B is equal to C,
+       then A must be equal to C.
+
+    Attributes
+    ----------
+    graph: networkx.Graph
+    subgraph: networkx.Graph
+    node_equality: collections.abc.Callable
+        The function called to see if two nodes should be considered equal.
+        It's signature looks like this:
+        ``f(graph1: networkx.Graph, node1, graph2: networkx.Graph, node2) -> bool``.
+        `node1` is a node in `graph1`, and `node2` a node in `graph2`.
+        Constructed from the argument `node_match`.
+    edge_equality: collections.abc.Callable
+        The function called to see if two edges should be considered equal.
+        It's signature looks like this:
+        ``f(graph1: networkx.Graph, edge1, graph2: networkx.Graph, edge2) -> bool``.
+        `edge1` is an edge in `graph1`, and `edge2` an edge in `graph2`.
+        Constructed from the argument `edge_match`.
+
+    References
+    ----------
+    .. [1] M. Houbraken, S. Demeyer, T. Michoel, P. Audenaert, D. Colle,
+       M. Pickavet, "The Index-Based Subgraph Matching Algorithm with General
+       Symmetries (ISMAGS): Exploiting Symmetry for Faster Subgraph
+       Enumeration", PLoS One 9(5): e97896, 2014.
+       https://doi.org/10.1371/journal.pone.0097896
+    """
+
+    def __init__(self, graph, subgraph, node_match=None, edge_match=None, cache=None):
+        """
+        Parameters
+        ----------
+        graph: networkx.Graph
+        subgraph: networkx.Graph
+        node_match: collections.abc.Callable or None
+            Function used to determine whether two nodes are equivalent. Its
+            signature should look like ``f(n1: dict, n2: dict) -> bool``, with
+            `n1` and `n2` node property dicts. See also
+            :func:`~networkx.algorithms.isomorphism.categorical_node_match` and
+            friends.
+            If `None`, all nodes are considered equal.
+        edge_match: collections.abc.Callable or None
+            Function used to determine whether two edges are equivalent. Its
+            signature should look like ``f(e1: dict, e2: dict) -> bool``, with
+            `e1` and `e2` edge property dicts. See also
+            :func:`~networkx.algorithms.isomorphism.categorical_edge_match` and
+            friends.
+            If `None`, all edges are considered equal.
+        cache: collections.abc.Mapping
+            A cache used for caching graph symmetries.
+        """
+        # TODO: graph and subgraph setter methods that invalidate the caches.
+        # TODO: allow for precomputed partitions and colors
+        self.graph = graph
+        self.subgraph = subgraph
+        self._symmetry_cache = cache
+        # Naming conventions are taken from the original paper. For your
+        # sanity:
+        #   sg: subgraph
+        #   g: graph
+        #   e: edge(s)
+        #   n: node(s)
+        # So: sgn means "subgraph nodes".
+        self._sgn_partitions_ = None
+        self._sge_partitions_ = None
+
+        self._sgn_colors_ = None
+        self._sge_colors_ = None
+
+        self._gn_partitions_ = None
+        self._ge_partitions_ = None
+
+        self._gn_colors_ = None
+        self._ge_colors_ = None
+
+        self._node_compat_ = None
+        self._edge_compat_ = None
+
+        if node_match is None:
+            self.node_equality = self._node_match_maker(lambda n1, n2: True)
+            self._sgn_partitions_ = [set(self.subgraph.nodes)]
+            self._gn_partitions_ = [set(self.graph.nodes)]
+            self._node_compat_ = {0: 0}
+        else:
+            self.node_equality = self._node_match_maker(node_match)
+        if edge_match is None:
+            self.edge_equality = self._edge_match_maker(lambda e1, e2: True)
+            self._sge_partitions_ = [set(self.subgraph.edges)]
+            self._ge_partitions_ = [set(self.graph.edges)]
+            self._edge_compat_ = {0: 0}
+        else:
+            self.edge_equality = self._edge_match_maker(edge_match)
+
+    @property
+    def _sgn_partitions(self):
+        if self._sgn_partitions_ is None:
+
+            def nodematch(node1, node2):
+                return self.node_equality(self.subgraph, node1, self.subgraph, node2)
+
+            self._sgn_partitions_ = make_partitions(self.subgraph.nodes, nodematch)
+        return self._sgn_partitions_
+
+    @property
+    def _sge_partitions(self):
+        if self._sge_partitions_ is None:
+
+            def edgematch(edge1, edge2):
+                return self.edge_equality(self.subgraph, edge1, self.subgraph, edge2)
+
+            self._sge_partitions_ = make_partitions(self.subgraph.edges, edgematch)
+        return self._sge_partitions_
+
+    @property
+    def _gn_partitions(self):
+        if self._gn_partitions_ is None:
+
+            def nodematch(node1, node2):
+                return self.node_equality(self.graph, node1, self.graph, node2)
+
+            self._gn_partitions_ = make_partitions(self.graph.nodes, nodematch)
+        return self._gn_partitions_
+
+    @property
+    def _ge_partitions(self):
+        if self._ge_partitions_ is None:
+
+            def edgematch(edge1, edge2):
+                return self.edge_equality(self.graph, edge1, self.graph, edge2)
+
+            self._ge_partitions_ = make_partitions(self.graph.edges, edgematch)
+        return self._ge_partitions_
+
+    @property
+    def _sgn_colors(self):
+        if self._sgn_colors_ is None:
+            self._sgn_colors_ = partition_to_color(self._sgn_partitions)
+        return self._sgn_colors_
+
+    @property
+    def _sge_colors(self):
+        if self._sge_colors_ is None:
+            self._sge_colors_ = partition_to_color(self._sge_partitions)
+        return self._sge_colors_
+
+    @property
+    def _gn_colors(self):
+        if self._gn_colors_ is None:
+            self._gn_colors_ = partition_to_color(self._gn_partitions)
+        return self._gn_colors_
+
+    @property
+    def _ge_colors(self):
+        if self._ge_colors_ is None:
+            self._ge_colors_ = partition_to_color(self._ge_partitions)
+        return self._ge_colors_
+
+    @property
+    def _node_compatibility(self):
+        if self._node_compat_ is not None:
+            return self._node_compat_
+        self._node_compat_ = {}
+        for sgn_part_color, gn_part_color in itertools.product(
+            range(len(self._sgn_partitions)), range(len(self._gn_partitions))
+        ):
+            sgn = next(iter(self._sgn_partitions[sgn_part_color]))
+            gn = next(iter(self._gn_partitions[gn_part_color]))
+            if self.node_equality(self.subgraph, sgn, self.graph, gn):
+                self._node_compat_[sgn_part_color] = gn_part_color
+        return self._node_compat_
+
+    @property
+    def _edge_compatibility(self):
+        if self._edge_compat_ is not None:
+            return self._edge_compat_
+        self._edge_compat_ = {}
+        for sge_part_color, ge_part_color in itertools.product(
+            range(len(self._sge_partitions)), range(len(self._ge_partitions))
+        ):
+            sge = next(iter(self._sge_partitions[sge_part_color]))
+            ge = next(iter(self._ge_partitions[ge_part_color]))
+            if self.edge_equality(self.subgraph, sge, self.graph, ge):
+                self._edge_compat_[sge_part_color] = ge_part_color
+        return self._edge_compat_
+
+    @staticmethod
+    def _node_match_maker(cmp):
+        @wraps(cmp)
+        def comparer(graph1, node1, graph2, node2):
+            return cmp(graph1.nodes[node1], graph2.nodes[node2])
+
+        return comparer
+
+    @staticmethod
+    def _edge_match_maker(cmp):
+        @wraps(cmp)
+        def comparer(graph1, edge1, graph2, edge2):
+            return cmp(graph1.edges[edge1], graph2.edges[edge2])
+
+        return comparer
+
+    def find_isomorphisms(self, symmetry=True):
+        """Find all subgraph isomorphisms between subgraph and graph
+
+        Finds isomorphisms where :attr:`subgraph` <= :attr:`graph`.
+
+        Parameters
+        ----------
+        symmetry: bool
+            Whether symmetry should be taken into account. If False, found
+            isomorphisms may be symmetrically equivalent.
+
+        Yields
+        ------
+        dict
+            The found isomorphism mappings of {graph_node: subgraph_node}.
+        """
+        # The networkx VF2 algorithm is slightly funny in when it yields an
+        # empty dict and when not.
+        if not self.subgraph:
+            yield {}
+            return
+        elif not self.graph:
+            return
+        elif len(self.graph) < len(self.subgraph):
+            return
+
+        if symmetry:
+            _, cosets = self.analyze_symmetry(
+                self.subgraph, self._sgn_partitions, self._sge_colors
+            )
+            constraints = self._make_constraints(cosets)
+        else:
+            constraints = []
+
+        candidates = self._find_nodecolor_candidates()
+        la_candidates = self._get_lookahead_candidates()
+        for sgn in self.subgraph:
+            extra_candidates = la_candidates[sgn]
+            if extra_candidates:
+                candidates[sgn] = candidates[sgn] | {frozenset(extra_candidates)}
+
+        if any(candidates.values()):
+            start_sgn = min(candidates, key=lambda n: min(candidates[n], key=len))
+            candidates[start_sgn] = (intersect(candidates[start_sgn]),)
+            yield from self._map_nodes(start_sgn, candidates, constraints)
+        else:
+            return
+
+    @staticmethod
+    def _find_neighbor_color_count(graph, node, node_color, edge_color):
+        """
+        For `node` in `graph`, count the number of edges of a specific color
+        it has to nodes of a specific color.
+        """
+        counts = Counter()
+        neighbors = graph[node]
+        for neighbor in neighbors:
+            n_color = node_color[neighbor]
+            if (node, neighbor) in edge_color:
+                e_color = edge_color[node, neighbor]
+            else:
+                e_color = edge_color[neighbor, node]
+            counts[e_color, n_color] += 1
+        return counts
+
+    def _get_lookahead_candidates(self):
+        """
+        Returns a mapping of {subgraph node: collection of graph nodes} for
+        which the graph nodes are feasible candidates for the subgraph node, as
+        determined by looking ahead one edge.
+        """
+        g_counts = {}
+        for gn in self.graph:
+            g_counts[gn] = self._find_neighbor_color_count(
+                self.graph, gn, self._gn_colors, self._ge_colors
+            )
+        candidates = defaultdict(set)
+        for sgn in self.subgraph:
+            sg_count = self._find_neighbor_color_count(
+                self.subgraph, sgn, self._sgn_colors, self._sge_colors
+            )
+            new_sg_count = Counter()
+            for (sge_color, sgn_color), count in sg_count.items():
+                try:
+                    ge_color = self._edge_compatibility[sge_color]
+                    gn_color = self._node_compatibility[sgn_color]
+                except KeyError:
+                    pass
+                else:
+                    new_sg_count[ge_color, gn_color] = count
+
+            for gn, g_count in g_counts.items():
+                if all(new_sg_count[x] <= g_count[x] for x in new_sg_count):
+                    # Valid candidate
+                    candidates[sgn].add(gn)
+        return candidates
+
+    def largest_common_subgraph(self, symmetry=True):
+        """
+        Find the largest common induced subgraphs between :attr:`subgraph` and
+        :attr:`graph`.
+
+        Parameters
+        ----------
+        symmetry: bool
+            Whether symmetry should be taken into account. If False, found
+            largest common subgraphs may be symmetrically equivalent.
+
+        Yields
+        ------
+        dict
+            The found isomorphism mappings of {graph_node: subgraph_node}.
+        """
+        # The networkx VF2 algorithm is slightly funny in when it yields an
+        # empty dict and when not.
+        if not self.subgraph:
+            yield {}
+            return
+        elif not self.graph:
+            return
+
+        if symmetry:
+            _, cosets = self.analyze_symmetry(
+                self.subgraph, self._sgn_partitions, self._sge_colors
+            )
+            constraints = self._make_constraints(cosets)
+        else:
+            constraints = []
+
+        candidates = self._find_nodecolor_candidates()
+
+        if any(candidates.values()):
+            yield from self._largest_common_subgraph(candidates, constraints)
+        else:
+            return
+
+    def analyze_symmetry(self, graph, node_partitions, edge_colors):
+        """
+        Find a minimal set of permutations and corresponding co-sets that
+        describe the symmetry of `graph`, given the node and edge equalities
+        given by `node_partitions` and `edge_colors`, respectively.
+
+        Parameters
+        ----------
+        graph : networkx.Graph
+            The graph whose symmetry should be analyzed.
+        node_partitions : list of sets
+            A list of sets containing node keys. Node keys in the same set
+            are considered equivalent. Every node key in `graph` should be in
+            exactly one of the sets. If all nodes are equivalent, this should
+            be ``[set(graph.nodes)]``.
+        edge_colors : dict mapping edges to their colors
+            A dict mapping every edge in `graph` to its corresponding color.
+            Edges with the same color are considered equivalent. If all edges
+            are equivalent, this should be ``{e: 0 for e in graph.edges}``.
+
+
+        Returns
+        -------
+        set[frozenset]
+            The found permutations. This is a set of frozensets of pairs of node
+            keys which can be exchanged without changing :attr:`subgraph`.
+        dict[collections.abc.Hashable, set[collections.abc.Hashable]]
+            The found co-sets. The co-sets is a dictionary of
+            ``{node key: set of node keys}``.
+            Every key-value pair describes which ``values`` can be interchanged
+            without changing nodes less than ``key``.
+        """
+        if self._symmetry_cache is not None:
+            key = hash(
+                (
+                    tuple(graph.nodes),
+                    tuple(graph.edges),
+                    tuple(map(tuple, node_partitions)),
+                    tuple(edge_colors.items()),
+                )
+            )
+            if key in self._symmetry_cache:
+                return self._symmetry_cache[key]
+        node_partitions = list(
+            self._refine_node_partitions(graph, node_partitions, edge_colors)
+        )
+        assert len(node_partitions) == 1
+        node_partitions = node_partitions[0]
+        permutations, cosets = self._process_ordered_pair_partitions(
+            graph, node_partitions, node_partitions, edge_colors
+        )
+        if self._symmetry_cache is not None:
+            self._symmetry_cache[key] = permutations, cosets
+        return permutations, cosets
+
+    def is_isomorphic(self, symmetry=False):
+        """
+        Returns True if :attr:`graph` is isomorphic to :attr:`subgraph` and
+        False otherwise.
+
+        Returns
+        -------
+        bool
+        """
+        return len(self.subgraph) == len(self.graph) and self.subgraph_is_isomorphic(
+            symmetry
+        )
+
+    def subgraph_is_isomorphic(self, symmetry=False):
+        """
+        Returns True if a subgraph of :attr:`graph` is isomorphic to
+        :attr:`subgraph` and False otherwise.
+
+        Returns
+        -------
+        bool
+        """
+        # symmetry=False, since we only need to know whether there is any
+        # example; figuring out all symmetry elements probably costs more time
+        # than it gains.
+        isom = next(self.subgraph_isomorphisms_iter(symmetry=symmetry), None)
+        return isom is not None
+
+    def isomorphisms_iter(self, symmetry=True):
+        """
+        Does the same as :meth:`find_isomorphisms` if :attr:`graph` and
+        :attr:`subgraph` have the same number of nodes.
+        """
+        if len(self.graph) == len(self.subgraph):
+            yield from self.subgraph_isomorphisms_iter(symmetry=symmetry)
+
+    def subgraph_isomorphisms_iter(self, symmetry=True):
+        """Alternative name for :meth:`find_isomorphisms`."""
+        return self.find_isomorphisms(symmetry)
+
+    def _find_nodecolor_candidates(self):
+        """
+        Per node in subgraph find all nodes in graph that have the same color.
+        """
+        candidates = defaultdict(set)
+        for sgn in self.subgraph.nodes:
+            sgn_color = self._sgn_colors[sgn]
+            if sgn_color in self._node_compatibility:
+                gn_color = self._node_compatibility[sgn_color]
+                candidates[sgn].add(frozenset(self._gn_partitions[gn_color]))
+            else:
+                candidates[sgn].add(frozenset())
+        candidates = dict(candidates)
+        for sgn, options in candidates.items():
+            candidates[sgn] = frozenset(options)
+        return candidates
+
+    @staticmethod
+    def _make_constraints(cosets):
+        """
+        Turn cosets into constraints.
+        """
+        constraints = []
+        for node_i, node_ts in cosets.items():
+            for node_t in node_ts:
+                if node_i != node_t:
+                    # Node i must be smaller than node t.
+                    constraints.append((node_i, node_t))
+        return constraints
+
+    @staticmethod
+    def _find_node_edge_color(graph, node_colors, edge_colors):
+        """
+        For every node in graph, come up with a color that combines 1) the
+        color of the node, and 2) the number of edges of a color to each type
+        of node.
+        """
+        counts = defaultdict(lambda: defaultdict(int))
+        for node1, node2 in graph.edges:
+            if (node1, node2) in edge_colors:
+                # FIXME directed graphs
+                ecolor = edge_colors[node1, node2]
+            else:
+                ecolor = edge_colors[node2, node1]
+            # Count per node how many edges it has of what color to nodes of
+            # what color
+            counts[node1][ecolor, node_colors[node2]] += 1
+            counts[node2][ecolor, node_colors[node1]] += 1
+
+        node_edge_colors = {}
+        for node in graph.nodes:
+            node_edge_colors[node] = node_colors[node], set(counts[node].items())
+
+        return node_edge_colors
+
+    @staticmethod
+    def _get_permutations_by_length(items):
+        """
+        Get all permutations of items, but only permute items with the same
+        length.
+
+        >>> found = list(ISMAGS._get_permutations_by_length([[1], [2], [3, 4], [4, 5]]))
+        >>> answer = [
+        ...     (([1], [2]), ([3, 4], [4, 5])),
+        ...     (([1], [2]), ([4, 5], [3, 4])),
+        ...     (([2], [1]), ([3, 4], [4, 5])),
+        ...     (([2], [1]), ([4, 5], [3, 4])),
+        ... ]
+        >>> found == answer
+        True
+        """
+        by_len = defaultdict(list)
+        for item in items:
+            by_len[len(item)].append(item)
+
+        yield from itertools.product(
+            *(itertools.permutations(by_len[l]) for l in sorted(by_len))
+        )
+
+    @classmethod
+    def _refine_node_partitions(cls, graph, node_partitions, edge_colors, branch=False):
+        """
+        Given a partition of nodes in graph, make the partitions smaller such
+        that all nodes in a partition have 1) the same color, and 2) the same
+        number of edges to specific other partitions.
+        """
+
+        def equal_color(node1, node2):
+            return node_edge_colors[node1] == node_edge_colors[node2]
+
+        node_partitions = list(node_partitions)
+        node_colors = partition_to_color(node_partitions)
+        node_edge_colors = cls._find_node_edge_color(graph, node_colors, edge_colors)
+        if all(
+            are_all_equal(node_edge_colors[node] for node in partition)
+            for partition in node_partitions
+        ):
+            yield node_partitions
+            return
+
+        new_partitions = []
+        output = [new_partitions]
+        for partition in node_partitions:
+            if not are_all_equal(node_edge_colors[node] for node in partition):
+                refined = make_partitions(partition, equal_color)
+                if (
+                    branch
+                    and len(refined) != 1
+                    and len({len(r) for r in refined}) != len([len(r) for r in refined])
+                ):
+                    # This is where it breaks. There are multiple new cells
+                    # in refined with the same length, and their order
+                    # matters.
+                    # So option 1) Hit it with a big hammer and simply make all
+                    # orderings.
+                    permutations = cls._get_permutations_by_length(refined)
+                    new_output = []
+                    for n_p in output:
+                        for permutation in permutations:
+                            new_output.append(n_p + list(permutation[0]))
+                    output = new_output
+                else:
+                    for n_p in output:
+                        n_p.extend(sorted(refined, key=len))
+            else:
+                for n_p in output:
+                    n_p.append(partition)
+        for n_p in output:
+            yield from cls._refine_node_partitions(graph, n_p, edge_colors, branch)
+
+    def _edges_of_same_color(self, sgn1, sgn2):
+        """
+        Returns all edges in :attr:`graph` that have the same colour as the
+        edge between sgn1 and sgn2 in :attr:`subgraph`.
+        """
+        if (sgn1, sgn2) in self._sge_colors:
+            # FIXME directed graphs
+            sge_color = self._sge_colors[sgn1, sgn2]
+        else:
+            sge_color = self._sge_colors[sgn2, sgn1]
+        if sge_color in self._edge_compatibility:
+            ge_color = self._edge_compatibility[sge_color]
+            g_edges = self._ge_partitions[ge_color]
+        else:
+            g_edges = []
+        return g_edges
+
+    def _map_nodes(self, sgn, candidates, constraints, mapping=None, to_be_mapped=None):
+        """
+        Find all subgraph isomorphisms honoring constraints.
+        """
+        if mapping is None:
+            mapping = {}
+        else:
+            mapping = mapping.copy()
+        if to_be_mapped is None:
+            to_be_mapped = set(self.subgraph.nodes)
+
+        # Note, we modify candidates here. Doesn't seem to affect results, but
+        # remember this.
+        # candidates = candidates.copy()
+        sgn_candidates = intersect(candidates[sgn])
+        candidates[sgn] = frozenset([sgn_candidates])
+        for gn in sgn_candidates:
+            # We're going to try to map sgn to gn.
+            if gn in mapping.values() or sgn not in to_be_mapped:
+                # gn is already mapped to something
+                continue  # pragma: no cover
+
+            # REDUCTION and COMBINATION
+            mapping[sgn] = gn
+            # BASECASE
+            if to_be_mapped == set(mapping.keys()):
+                yield {v: k for k, v in mapping.items()}
+                continue
+            left_to_map = to_be_mapped - set(mapping.keys())
+
+            new_candidates = candidates.copy()
+            sgn_nbrs = set(self.subgraph[sgn])
+            not_gn_nbrs = set(self.graph.nodes) - set(self.graph[gn])
+            for sgn2 in left_to_map:
+                if sgn2 not in sgn_nbrs:
+                    gn2_options = not_gn_nbrs
+                else:
+                    # Get all edges to gn of the right color:
+                    g_edges = self._edges_of_same_color(sgn, sgn2)
+                    # FIXME directed graphs
+                    # And all nodes involved in those which are connected to gn
+                    gn2_options = {n for e in g_edges for n in e if gn in e}
+                # Node color compatibility should be taken care of by the
+                # initial candidate lists made by find_subgraphs
+
+                # Add gn2_options to the right collection. Since new_candidates
+                # is a dict of frozensets of frozensets of node indices it's
+                # a bit clunky. We can't do .add, and + also doesn't work. We
+                # could do |, but I deem union to be clearer.
+                new_candidates[sgn2] = new_candidates[sgn2].union(
+                    [frozenset(gn2_options)]
+                )
+
+                if (sgn, sgn2) in constraints:
+                    gn2_options = {gn2 for gn2 in self.graph if gn2 > gn}
+                elif (sgn2, sgn) in constraints:
+                    gn2_options = {gn2 for gn2 in self.graph if gn2 < gn}
+                else:
+                    continue  # pragma: no cover
+                new_candidates[sgn2] = new_candidates[sgn2].union(
+                    [frozenset(gn2_options)]
+                )
+
+            # The next node is the one that is unmapped and has fewest
+            # candidates
+            next_sgn = min(left_to_map, key=lambda n: min(new_candidates[n], key=len))
+            yield from self._map_nodes(
+                next_sgn,
+                new_candidates,
+                constraints,
+                mapping=mapping,
+                to_be_mapped=to_be_mapped,
+            )
+            # Unmap sgn-gn. Strictly not necessary since it'd get overwritten
+            # when making a new mapping for sgn.
+            # del mapping[sgn]
+
+    def _largest_common_subgraph(self, candidates, constraints, to_be_mapped=None):
+        """
+        Find all largest common subgraphs honoring constraints.
+        """
+        if to_be_mapped is None:
+            to_be_mapped = {frozenset(self.subgraph.nodes)}
+
+        # The LCS problem is basically a repeated subgraph isomorphism problem
+        # with smaller and smaller subgraphs. We store the nodes that are
+        # "part of" the subgraph in to_be_mapped, and we make it a little
+        # smaller every iteration.
+
+        current_size = len(next(iter(to_be_mapped), []))
+
+        found_iso = False
+        if current_size <= len(self.graph):
+            # There's no point in trying to find isomorphisms of
+            # graph >= subgraph if subgraph has more nodes than graph.
+
+            # Try the isomorphism first with the nodes with lowest ID. So sort
+            # them. Those are more likely to be part of the final
+            # correspondence. This makes finding the first answer(s) faster. In
+            # theory.
+            for nodes in sorted(to_be_mapped, key=sorted):
+                # Find the isomorphism between subgraph[to_be_mapped] <= graph
+                next_sgn = min(nodes, key=lambda n: min(candidates[n], key=len))
+                isomorphs = self._map_nodes(
+                    next_sgn, candidates, constraints, to_be_mapped=nodes
+                )
+
+                # This is effectively `yield from isomorphs`, except that we look
+                # whether an item was yielded.
+                try:
+                    item = next(isomorphs)
+                except StopIteration:
+                    pass
+                else:
+                    yield item
+                    yield from isomorphs
+                    found_iso = True
+
+        # BASECASE
+        if found_iso or current_size == 1:
+            # Shrinking has no point because either 1) we end up with a smaller
+            # common subgraph (and we want the largest), or 2) there'll be no
+            # more subgraph.
+            return
+
+        left_to_be_mapped = set()
+        for nodes in to_be_mapped:
+            for sgn in nodes:
+                # We're going to remove sgn from to_be_mapped, but subject to
+                # symmetry constraints. We know that for every constraint we
+                # have those subgraph nodes are equal. So whenever we would
+                # remove the lower part of a constraint, remove the higher
+                # instead. This is all dealth with by _remove_node. And because
+                # left_to_be_mapped is a set, we don't do double work.
+
+                # And finally, make the subgraph one node smaller.
+                # REDUCTION
+                new_nodes = self._remove_node(sgn, nodes, constraints)
+                left_to_be_mapped.add(new_nodes)
+        # COMBINATION
+        yield from self._largest_common_subgraph(
+            candidates, constraints, to_be_mapped=left_to_be_mapped
+        )
+
+    @staticmethod
+    def _remove_node(node, nodes, constraints):
+        """
+        Returns a new set where node has been removed from nodes, subject to
+        symmetry constraints. We know, that for every constraint we have
+        those subgraph nodes are equal. So whenever we would remove the
+        lower part of a constraint, remove the higher instead.
+        """
+        while True:
+            for low, high in constraints:
+                if low == node and high in nodes:
+                    node = high
+                    break
+            else:  # no break, couldn't find node in constraints
+                break
+        return frozenset(nodes - {node})
+
+    @staticmethod
+    def _find_permutations(top_partitions, bottom_partitions):
+        """
+        Return the pairs of top/bottom partitions where the partitions are
+        different. Ensures that all partitions in both top and bottom
+        partitions have size 1.
+        """
+        # Find permutations
+        permutations = set()
+        for top, bot in zip(top_partitions, bottom_partitions):
+            # top and bot have only one element
+            if len(top) != 1 or len(bot) != 1:
+                raise IndexError(
+                    "Not all nodes are coupled. This is"
+                    f" impossible: {top_partitions}, {bottom_partitions}"
+                )
+            if top != bot:
+                permutations.add(frozenset((next(iter(top)), next(iter(bot)))))
+        return permutations
+
+    @staticmethod
+    def _update_orbits(orbits, permutations):
+        """
+        Update orbits based on permutations. Orbits is modified in place.
+        For every pair of items in permutations their respective orbits are
+        merged.
+        """
+        for permutation in permutations:
+            node, node2 = permutation
+            # Find the orbits that contain node and node2, and replace the
+            # orbit containing node with the union
+            first = second = None
+            for idx, orbit in enumerate(orbits):
+                if first is not None and second is not None:
+                    break
+                if node in orbit:
+                    first = idx
+                if node2 in orbit:
+                    second = idx
+            if first != second:
+                orbits[first].update(orbits[second])
+                del orbits[second]
+
+    def _couple_nodes(
+        self,
+        top_partitions,
+        bottom_partitions,
+        pair_idx,
+        t_node,
+        b_node,
+        graph,
+        edge_colors,
+    ):
+        """
+        Generate new partitions from top and bottom_partitions where t_node is
+        coupled to b_node. pair_idx is the index of the partitions where t_ and
+        b_node can be found.
+        """
+        t_partition = top_partitions[pair_idx]
+        b_partition = bottom_partitions[pair_idx]
+        assert t_node in t_partition and b_node in b_partition
+        # Couple node to node2. This means they get their own partition
+        new_top_partitions = [top.copy() for top in top_partitions]
+        new_bottom_partitions = [bot.copy() for bot in bottom_partitions]
+        new_t_groups = {t_node}, t_partition - {t_node}
+        new_b_groups = {b_node}, b_partition - {b_node}
+        # Replace the old partitions with the coupled ones
+        del new_top_partitions[pair_idx]
+        del new_bottom_partitions[pair_idx]
+        new_top_partitions[pair_idx:pair_idx] = new_t_groups
+        new_bottom_partitions[pair_idx:pair_idx] = new_b_groups
+
+        new_top_partitions = self._refine_node_partitions(
+            graph, new_top_partitions, edge_colors
+        )
+        new_bottom_partitions = self._refine_node_partitions(
+            graph, new_bottom_partitions, edge_colors, branch=True
+        )
+        new_top_partitions = list(new_top_partitions)
+        assert len(new_top_partitions) == 1
+        new_top_partitions = new_top_partitions[0]
+        for bot in new_bottom_partitions:
+            yield list(new_top_partitions), bot
+
+    def _process_ordered_pair_partitions(
+        self,
+        graph,
+        top_partitions,
+        bottom_partitions,
+        edge_colors,
+        orbits=None,
+        cosets=None,
+    ):
+        """
+        Processes ordered pair partitions as per the reference paper. Finds and
+        returns all permutations and cosets that leave the graph unchanged.
+        """
+        if orbits is None:
+            orbits = [{node} for node in graph.nodes]
+        else:
+            # Note that we don't copy orbits when we are given one. This means
+            # we leak information between the recursive branches. This is
+            # intentional!
+            orbits = orbits
+        if cosets is None:
+            cosets = {}
+        else:
+            cosets = cosets.copy()
+
+        assert all(
+            len(t_p) == len(b_p) for t_p, b_p in zip(top_partitions, bottom_partitions)
+        )
+
+        # BASECASE
+        if all(len(top) == 1 for top in top_partitions):
+            # All nodes are mapped
+            permutations = self._find_permutations(top_partitions, bottom_partitions)
+            self._update_orbits(orbits, permutations)
+            if permutations:
+                return [permutations], cosets
+            else:
+                return [], cosets
+
+        permutations = []
+        unmapped_nodes = {
+            (node, idx)
+            for idx, t_partition in enumerate(top_partitions)
+            for node in t_partition
+            if len(t_partition) > 1
+        }
+        node, pair_idx = min(unmapped_nodes)
+        b_partition = bottom_partitions[pair_idx]
+
+        for node2 in sorted(b_partition):
+            if len(b_partition) == 1:
+                # Can never result in symmetry
+                continue
+            if node != node2 and any(
+                node in orbit and node2 in orbit for orbit in orbits
+            ):
+                # Orbit prune branch
+                continue
+            # REDUCTION
+            # Couple node to node2
+            partitions = self._couple_nodes(
+                top_partitions,
+                bottom_partitions,
+                pair_idx,
+                node,
+                node2,
+                graph,
+                edge_colors,
+            )
+            for opp in partitions:
+                new_top_partitions, new_bottom_partitions = opp
+
+                new_perms, new_cosets = self._process_ordered_pair_partitions(
+                    graph,
+                    new_top_partitions,
+                    new_bottom_partitions,
+                    edge_colors,
+                    orbits,
+                    cosets,
+                )
+                # COMBINATION
+                permutations += new_perms
+                cosets.update(new_cosets)
+
+        mapped = {
+            k
+            for top, bottom in zip(top_partitions, bottom_partitions)
+            for k in top
+            if len(top) == 1 and top == bottom
+        }
+        ks = {k for k in graph.nodes if k < node}
+        # Have all nodes with ID < node been mapped?
+        find_coset = ks <= mapped and node not in cosets
+        if find_coset:
+            # Find the orbit that contains node
+            for orbit in orbits:
+                if node in orbit:
+                    cosets[node] = orbit.copy()
+        return permutations, cosets

wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/isomorph.py

@@ -0,0 +1,249 @@
+"""
+Graph isomorphism functions.
+"""
+
+import networkx as nx
+from networkx.exception import NetworkXError
+
+__all__ = [
+    "could_be_isomorphic",
+    "fast_could_be_isomorphic",
+    "faster_could_be_isomorphic",
+    "is_isomorphic",
+]
+
+
+@nx._dispatchable(graphs={"G1": 0, "G2": 1})
+def could_be_isomorphic(G1, G2):
+    """Returns False if graphs are definitely not isomorphic.
+    True does NOT guarantee isomorphism.
+
+    Parameters
+    ----------
+    G1, G2 : graphs
+       The two graphs G1 and G2 must be the same type.
+
+    Notes
+    -----
+    Checks for matching degree, triangle, and number of cliques sequences.
+    The triangle sequence contains the number of triangles each node is part of.
+    The clique sequence contains for each node the number of maximal cliques
+    involving that node.
+
+    """
+
+    # Check global properties
+    if G1.order() != G2.order():
+        return False
+
+    # Check local properties
+    d1 = G1.degree()
+    t1 = nx.triangles(G1)
+    clqs_1 = list(nx.find_cliques(G1))
+    c1 = {n: sum(1 for c in clqs_1 if n in c) for n in G1}  # number of cliques
+    props1 = [[d, t1[v], c1[v]] for v, d in d1]
+    props1.sort()
+
+    d2 = G2.degree()
+    t2 = nx.triangles(G2)
+    clqs_2 = list(nx.find_cliques(G2))
+    c2 = {n: sum(1 for c in clqs_2 if n in c) for n in G2}  # number of cliques
+    props2 = [[d, t2[v], c2[v]] for v, d in d2]
+    props2.sort()
+
+    if props1 != props2:
+        return False
+
+    # OK...
+    return True
+
+
+graph_could_be_isomorphic = could_be_isomorphic
+
+
+@nx._dispatchable(graphs={"G1": 0, "G2": 1})
+def fast_could_be_isomorphic(G1, G2):
+    """Returns False if graphs are definitely not isomorphic.
+
+    True does NOT guarantee isomorphism.
+
+    Parameters
+    ----------
+    G1, G2 : graphs
+       The two graphs G1 and G2 must be the same type.
+
+    Notes
+    -----
+    Checks for matching degree and triangle sequences. The triangle
+    sequence contains the number of triangles each node is part of.
+    """
+    # Check global properties
+    if G1.order() != G2.order():
+        return False
+
+    # Check local properties
+    d1 = G1.degree()
+    t1 = nx.triangles(G1)
+    props1 = [[d, t1[v]] for v, d in d1]
+    props1.sort()
+
+    d2 = G2.degree()
+    t2 = nx.triangles(G2)
+    props2 = [[d, t2[v]] for v, d in d2]
+    props2.sort()
+
+    if props1 != props2:
+        return False
+
+    # OK...
+    return True
+
+
+fast_graph_could_be_isomorphic = fast_could_be_isomorphic
+
+
+@nx._dispatchable(graphs={"G1": 0, "G2": 1})
+def faster_could_be_isomorphic(G1, G2):
+    """Returns False if graphs are definitely not isomorphic.
+
+    True does NOT guarantee isomorphism.
+
+    Parameters
+    ----------
+    G1, G2 : graphs
+       The two graphs G1 and G2 must be the same type.
+
+    Notes
+    -----
+    Checks for matching degree sequences.
+    """
+    # Check global properties
+    if G1.order() != G2.order():
+        return False
+
+    # Check local properties
+    d1 = sorted(d for n, d in G1.degree())
+    d2 = sorted(d for n, d in G2.degree())
+
+    if d1 != d2:
+        return False
+
+    # OK...
+    return True
+
+
+faster_graph_could_be_isomorphic = faster_could_be_isomorphic
+
+
+@nx._dispatchable(
+    graphs={"G1": 0, "G2": 1},
+    preserve_edge_attrs="edge_match",
+    preserve_node_attrs="node_match",
+)
+def is_isomorphic(G1, G2, node_match=None, edge_match=None):
+    """Returns True if the graphs G1 and G2 are isomorphic and False otherwise.
+
+    Parameters
+    ----------
+    G1, G2: graphs
+        The two graphs G1 and G2 must be the same type.
+
+    node_match : callable
+        A function that returns True if node n1 in G1 and n2 in G2 should
+        be considered equal during the isomorphism test.
+        If node_match is not specified then node attributes are not considered.
+
+        The function will be called like
+
+           node_match(G1.nodes[n1], G2.nodes[n2]).
+
+        That is, the function will receive the node attribute dictionaries
+        for n1 and n2 as inputs.
+
+    edge_match : callable
+        A function that returns True if the edge attribute dictionary
+        for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should
+        be considered equal during the isomorphism test.  If edge_match is
+        not specified then edge attributes are not considered.
+
+        The function will be called like
+
+           edge_match(G1[u1][v1], G2[u2][v2]).
+
+        That is, the function will receive the edge attribute dictionaries
+        of the edges under consideration.
+
+    Notes
+    -----
+    Uses the vf2 algorithm [1]_.
+
+    Examples
+    --------
+    >>> import networkx.algorithms.isomorphism as iso
+
+    For digraphs G1 and G2, using 'weight' edge attribute (default: 1)
+
+    >>> G1 = nx.DiGraph()
+    >>> G2 = nx.DiGraph()
+    >>> nx.add_path(G1, [1, 2, 3, 4], weight=1)
+    >>> nx.add_path(G2, [10, 20, 30, 40], weight=2)
+    >>> em = iso.numerical_edge_match("weight", 1)
+    >>> nx.is_isomorphic(G1, G2)  # no weights considered
+    True
+    >>> nx.is_isomorphic(G1, G2, edge_match=em)  # match weights
+    False
+
+    For multidigraphs G1 and G2, using 'fill' node attribute (default: '')
+
+    >>> G1 = nx.MultiDiGraph()
+    >>> G2 = nx.MultiDiGraph()
+    >>> G1.add_nodes_from([1, 2, 3], fill="red")
+    >>> G2.add_nodes_from([10, 20, 30, 40], fill="red")
+    >>> nx.add_path(G1, [1, 2, 3, 4], weight=3, linewidth=2.5)
+    >>> nx.add_path(G2, [10, 20, 30, 40], weight=3)
+    >>> nm = iso.categorical_node_match("fill", "red")
+    >>> nx.is_isomorphic(G1, G2, node_match=nm)
+    True
+
+    For multidigraphs G1 and G2, using 'weight' edge attribute (default: 7)
+
+    >>> G1.add_edge(1, 2, weight=7)
+    1
+    >>> G2.add_edge(10, 20)
+    1
+    >>> em = iso.numerical_multiedge_match("weight", 7, rtol=1e-6)
+    >>> nx.is_isomorphic(G1, G2, edge_match=em)
+    True
+
+    For multigraphs G1 and G2, using 'weight' and 'linewidth' edge attributes
+    with default values 7 and 2.5. Also using 'fill' node attribute with
+    default value 'red'.
+
+    >>> em = iso.numerical_multiedge_match(["weight", "linewidth"], [7, 2.5])
+    >>> nm = iso.categorical_node_match("fill", "red")
+    >>> nx.is_isomorphic(G1, G2, edge_match=em, node_match=nm)
+    True
+
+    See Also
+    --------
+    numerical_node_match, numerical_edge_match, numerical_multiedge_match
+    categorical_node_match, categorical_edge_match, categorical_multiedge_match
+
+    References
+    ----------
+    .. [1]  L. P. Cordella, P. Foggia, C. Sansone, M. Vento,
+       "An Improved Algorithm for Matching Large Graphs",
+       3rd IAPR-TC15 Workshop  on Graph-based Representations in
+       Pattern Recognition, Cuen, pp. 149-159, 2001.
+       https://www.researchgate.net/publication/200034365_An_Improved_Algorithm_for_Matching_Large_Graphs
+    """
+    if G1.is_directed() and G2.is_directed():
+        GM = nx.algorithms.isomorphism.DiGraphMatcher
+    elif (not G1.is_directed()) and (not G2.is_directed()):
+        GM = nx.algorithms.isomorphism.GraphMatcher
+    else:
+        raise NetworkXError("Graphs G1 and G2 are not of the same type.")
+
+    gm = GM(G1, G2, node_match=node_match, edge_match=edge_match)
+
+    return gm.is_isomorphic()

wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_ismags.py

@@ -0,0 +1,327 @@
+"""
+Tests for ISMAGS isomorphism algorithm.
+"""
+
+import pytest
+
+import networkx as nx
+from networkx.algorithms import isomorphism as iso
+
+
+def _matches_to_sets(matches):
+    """
+    Helper function to facilitate comparing collections of dictionaries in
+    which order does not matter.
+    """
+    return {frozenset(m.items()) for m in matches}
+
+
+class TestSelfIsomorphism:
+    data = [
+        (
+            [
+                (0, {"name": "a"}),
+                (1, {"name": "a"}),
+                (2, {"name": "b"}),
+                (3, {"name": "b"}),
+                (4, {"name": "a"}),
+                (5, {"name": "a"}),
+            ],
+            [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5)],
+        ),
+        (range(1, 5), [(1, 2), (2, 4), (4, 3), (3, 1)]),
+        (
+            [],
+            [
+                (0, 1),
+                (1, 2),
+                (2, 3),
+                (3, 4),
+                (4, 5),
+                (5, 0),
+                (0, 6),
+                (6, 7),
+                (2, 8),
+                (8, 9),
+                (4, 10),
+                (10, 11),
+            ],
+        ),
+        ([], [(0, 1), (1, 2), (1, 4), (2, 3), (3, 5), (3, 6)]),
+    ]
+
+    def test_self_isomorphism(self):
+        """
+        For some small, symmetric graphs, make sure that 1) they are isomorphic
+        to themselves, and 2) that only the identity mapping is found.
+        """
+        for node_data, edge_data in self.data:
+            graph = nx.Graph()
+            graph.add_nodes_from(node_data)
+            graph.add_edges_from(edge_data)
+
+            ismags = iso.ISMAGS(
+                graph, graph, node_match=iso.categorical_node_match("name", None)
+            )
+            assert ismags.is_isomorphic()
+            assert ismags.subgraph_is_isomorphic()
+            assert list(ismags.subgraph_isomorphisms_iter(symmetry=True)) == [
+                {n: n for n in graph.nodes}
+            ]
+
+    def test_edgecase_self_isomorphism(self):
+        """
+        This edgecase is one of the cases in which it is hard to find all
+        symmetry elements.
+        """
+        graph = nx.Graph()
+        nx.add_path(graph, range(5))
+        graph.add_edges_from([(2, 5), (5, 6)])
+
+        ismags = iso.ISMAGS(graph, graph)
+        ismags_answer = list(ismags.find_isomorphisms(True))
+        assert ismags_answer == [{n: n for n in graph.nodes}]
+
+        graph = nx.relabel_nodes(graph, {0: 0, 1: 1, 2: 2, 3: 3, 4: 6, 5: 4, 6: 5})
+        ismags = iso.ISMAGS(graph, graph)
+        ismags_answer = list(ismags.find_isomorphisms(True))
+        assert ismags_answer == [{n: n for n in graph.nodes}]
+
+    def test_directed_self_isomorphism(self):
+        """
+        For some small, directed, symmetric graphs, make sure that 1) they are
+        isomorphic to themselves, and 2) that only the identity mapping is
+        found.
+        """
+        for node_data, edge_data in self.data:
+            graph = nx.Graph()
+            graph.add_nodes_from(node_data)
+            graph.add_edges_from(edge_data)
+
+            ismags = iso.ISMAGS(
+                graph, graph, node_match=iso.categorical_node_match("name", None)
+            )
+            assert ismags.is_isomorphic()
+            assert ismags.subgraph_is_isomorphic()
+            assert list(ismags.subgraph_isomorphisms_iter(symmetry=True)) == [
+                {n: n for n in graph.nodes}
+            ]
+
+
+class TestSubgraphIsomorphism:
+    def test_isomorphism(self):
+        g1 = nx.Graph()
+        nx.add_cycle(g1, range(4))
+
+        g2 = nx.Graph()
+        nx.add_cycle(g2, range(4))
+        g2.add_edges_from(list(zip(g2, range(4, 8))))
+        ismags = iso.ISMAGS(g2, g1)
+        assert list(ismags.subgraph_isomorphisms_iter(symmetry=True)) == [
+            {n: n for n in g1.nodes}
+        ]
+
+    def test_isomorphism2(self):
+        g1 = nx.Graph()
+        nx.add_path(g1, range(3))
+
+        g2 = g1.copy()
+        g2.add_edge(1, 3)
+
+        ismags = iso.ISMAGS(g2, g1)
+        matches = ismags.subgraph_isomorphisms_iter(symmetry=True)
+        expected_symmetric = [
+            {0: 0, 1: 1, 2: 2},
+            {0: 0, 1: 1, 3: 2},
+            {2: 0, 1: 1, 3: 2},
+        ]
+        assert _matches_to_sets(matches) == _matches_to_sets(expected_symmetric)
+
+        matches = ismags.subgraph_isomorphisms_iter(symmetry=False)
+        expected_asymmetric = [
+            {0: 2, 1: 1, 2: 0},
+            {0: 2, 1: 1, 3: 0},
+            {2: 2, 1: 1, 3: 0},
+        ]
+        assert _matches_to_sets(matches) == _matches_to_sets(
+            expected_symmetric + expected_asymmetric
+        )
+
+    def test_labeled_nodes(self):
+        g1 = nx.Graph()
+        nx.add_cycle(g1, range(3))
+        g1.nodes[1]["attr"] = True
+
+        g2 = g1.copy()
+        g2.add_edge(1, 3)
+        ismags = iso.ISMAGS(g2, g1, node_match=lambda x, y: x == y)
+        matches = ismags.subgraph_isomorphisms_iter(symmetry=True)
+        expected_symmetric = [{0: 0, 1: 1, 2: 2}]
+        assert _matches_to_sets(matches) == _matches_to_sets(expected_symmetric)
+
+        matches = ismags.subgraph_isomorphisms_iter(symmetry=False)
+        expected_asymmetric = [{0: 2, 1: 1, 2: 0}]
+        assert _matches_to_sets(matches) == _matches_to_sets(
+            expected_symmetric + expected_asymmetric
+        )
+
+    def test_labeled_edges(self):
+        g1 = nx.Graph()
+        nx.add_cycle(g1, range(3))
+        g1.edges[1, 2]["attr"] = True
+
+        g2 = g1.copy()
+        g2.add_edge(1, 3)
+        ismags = iso.ISMAGS(g2, g1, edge_match=lambda x, y: x == y)
+        matches = ismags.subgraph_isomorphisms_iter(symmetry=True)
+        expected_symmetric = [{0: 0, 1: 1, 2: 2}]
+        assert _matches_to_sets(matches) == _matches_to_sets(expected_symmetric)
+
+        matches = ismags.subgraph_isomorphisms_iter(symmetry=False)
+        expected_asymmetric = [{1: 2, 0: 0, 2: 1}]
+        assert _matches_to_sets(matches) == _matches_to_sets(
+            expected_symmetric + expected_asymmetric
+        )
+
+
+class TestWikipediaExample:
+    # Nodes 'a', 'b', 'c' and 'd' form a column.
+    # Nodes 'g', 'h', 'i' and 'j' form a column.
+    g1edges = [
+        ["a", "g"],
+        ["a", "h"],
+        ["a", "i"],
+        ["b", "g"],
+        ["b", "h"],
+        ["b", "j"],
+        ["c", "g"],
+        ["c", "i"],
+        ["c", "j"],
+        ["d", "h"],
+        ["d", "i"],
+        ["d", "j"],
+    ]
+
+    # Nodes 1,2,3,4 form the clockwise corners of a large square.
+    # Nodes 5,6,7,8 form the clockwise corners of a small square
+    g2edges = [
+        [1, 2],
+        [2, 3],
+        [3, 4],
+        [4, 1],
+        [5, 6],
+        [6, 7],
+        [7, 8],
+        [8, 5],
+        [1, 5],
+        [2, 6],
+        [3, 7],
+        [4, 8],
+    ]
+
+    def test_graph(self):
+        g1 = nx.Graph()
+        g2 = nx.Graph()
+        g1.add_edges_from(self.g1edges)
+        g2.add_edges_from(self.g2edges)
+        gm = iso.ISMAGS(g1, g2)
+        assert gm.is_isomorphic()
+
+
+class TestLargestCommonSubgraph:
+    def test_mcis(self):
+        # Example graphs from DOI: 10.1002/spe.588
+        graph1 = nx.Graph()
+        graph1.add_edges_from([(1, 2), (2, 3), (2, 4), (3, 4), (4, 5)])
+        graph1.nodes[1]["color"] = 0
+
+        graph2 = nx.Graph()
+        graph2.add_edges_from(
+            [(1, 2), (2, 3), (2, 4), (3, 4), (3, 5), (5, 6), (5, 7), (6, 7)]
+        )
+        graph2.nodes[1]["color"] = 1
+        graph2.nodes[6]["color"] = 2
+        graph2.nodes[7]["color"] = 2
+
+        ismags = iso.ISMAGS(
+            graph1, graph2, node_match=iso.categorical_node_match("color", None)
+        )
+        assert list(ismags.subgraph_isomorphisms_iter(True)) == []
+        assert list(ismags.subgraph_isomorphisms_iter(False)) == []
+        found_mcis = _matches_to_sets(ismags.largest_common_subgraph())
+        expected = _matches_to_sets(
+            [{2: 2, 3: 4, 4: 3, 5: 5}, {2: 4, 3: 2, 4: 3, 5: 5}]
+        )
+        assert expected == found_mcis
+
+        ismags = iso.ISMAGS(
+            graph2, graph1, node_match=iso.categorical_node_match("color", None)
+        )
+        assert list(ismags.subgraph_isomorphisms_iter(True)) == []
+        assert list(ismags.subgraph_isomorphisms_iter(False)) == []
+        found_mcis = _matches_to_sets(ismags.largest_common_subgraph())
+        # Same answer, but reversed.
+        expected = _matches_to_sets(
+            [{2: 2, 3: 4, 4: 3, 5: 5}, {4: 2, 2: 3, 3: 4, 5: 5}]
+        )
+        assert expected == found_mcis
+
+    def test_symmetry_mcis(self):
+        graph1 = nx.Graph()
+        nx.add_path(graph1, range(4))
+
+        graph2 = nx.Graph()
+        nx.add_path(graph2, range(3))
+        graph2.add_edge(1, 3)
+
+        # Only the symmetry of graph2 is taken into account here.
+        ismags1 = iso.ISMAGS(
+            graph1, graph2, node_match=iso.categorical_node_match("color", None)
+        )
+        assert list(ismags1.subgraph_isomorphisms_iter(True)) == []
+        found_mcis = _matches_to_sets(ismags1.largest_common_subgraph())
+        expected = _matches_to_sets([{0: 0, 1: 1, 2: 2}, {1: 0, 3: 2, 2: 1}])
+        assert expected == found_mcis
+
+        # Only the symmetry of graph1 is taken into account here.
+        ismags2 = iso.ISMAGS(
+            graph2, graph1, node_match=iso.categorical_node_match("color", None)
+        )
+        assert list(ismags2.subgraph_isomorphisms_iter(True)) == []
+        found_mcis = _matches_to_sets(ismags2.largest_common_subgraph())
+        expected = _matches_to_sets(
+            [
+                {3: 2, 0: 0, 1: 1},
+                {2: 0, 0: 2, 1: 1},
+                {3: 0, 0: 2, 1: 1},
+                {3: 0, 1: 1, 2: 2},
+                {0: 0, 1: 1, 2: 2},
+                {2: 0, 3: 2, 1: 1},
+            ]
+        )
+
+        assert expected == found_mcis
+
+        found_mcis1 = _matches_to_sets(ismags1.largest_common_subgraph(False))
+        found_mcis2 = ismags2.largest_common_subgraph(False)
+        found_mcis2 = [{v: k for k, v in d.items()} for d in found_mcis2]
+        found_mcis2 = _matches_to_sets(found_mcis2)
+
+        expected = _matches_to_sets(
+            [
+                {3: 2, 1: 3, 2: 1},
+                {2: 0, 0: 2, 1: 1},
+                {1: 2, 3: 3, 2: 1},
+                {3: 0, 1: 3, 2: 1},
+                {0: 2, 2: 3, 1: 1},
+                {3: 0, 1: 2, 2: 1},
+                {2: 0, 0: 3, 1: 1},
+                {0: 0, 2: 3, 1: 1},
+                {1: 0, 3: 3, 2: 1},
+                {1: 0, 3: 2, 2: 1},
+                {0: 3, 1: 1, 2: 2},
+                {0: 0, 1: 1, 2: 2},
+            ]
+        )
+        assert expected == found_mcis1
+        assert expected == found_mcis2

wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_isomorphism.py

@@ -0,0 +1,48 @@
+import pytest
+
+import networkx as nx
+from networkx.algorithms import isomorphism as iso
+
+
+class TestIsomorph:
+    @classmethod
+    def setup_class(cls):
+        cls.G1 = nx.Graph()
+        cls.G2 = nx.Graph()
+        cls.G3 = nx.Graph()
+        cls.G4 = nx.Graph()
+        cls.G5 = nx.Graph()
+        cls.G6 = nx.Graph()
+        cls.G1.add_edges_from([[1, 2], [1, 3], [1, 5], [2, 3]])
+        cls.G2.add_edges_from([[10, 20], [20, 30], [10, 30], [10, 50]])
+        cls.G3.add_edges_from([[1, 2], [1, 3], [1, 5], [2, 5]])
+        cls.G4.add_edges_from([[1, 2], [1, 3], [1, 5], [2, 4]])
+        cls.G5.add_edges_from([[1, 2], [1, 3]])
+        cls.G6.add_edges_from([[10, 20], [20, 30], [10, 30], [10, 50], [20, 50]])
+
+    def test_could_be_isomorphic(self):
+        assert iso.could_be_isomorphic(self.G1, self.G2)
+        assert iso.could_be_isomorphic(self.G1, self.G3)
+        assert not iso.could_be_isomorphic(self.G1, self.G4)
+        assert iso.could_be_isomorphic(self.G3, self.G2)
+        assert not iso.could_be_isomorphic(self.G1, self.G6)
+
+    def test_fast_could_be_isomorphic(self):
+        assert iso.fast_could_be_isomorphic(self.G3, self.G2)
+        assert not iso.fast_could_be_isomorphic(self.G3, self.G5)
+        assert not iso.fast_could_be_isomorphic(self.G1, self.G6)
+
+    def test_faster_could_be_isomorphic(self):
+        assert iso.faster_could_be_isomorphic(self.G3, self.G2)
+        assert not iso.faster_could_be_isomorphic(self.G3, self.G5)
+        assert not iso.faster_could_be_isomorphic(self.G1, self.G6)
+
+    def test_is_isomorphic(self):
+        assert iso.is_isomorphic(self.G1, self.G2)
+        assert not iso.is_isomorphic(self.G1, self.G4)
+        assert iso.is_isomorphic(self.G1.to_directed(), self.G2.to_directed())
+        assert not iso.is_isomorphic(self.G1.to_directed(), self.G4.to_directed())
+        with pytest.raises(
+            nx.NetworkXError, match="Graphs G1 and G2 are not of the same type."
+        ):
+            iso.is_isomorphic(self.G1.to_directed(), self.G1)

wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_temporalisomorphvf2.py

@@ -0,0 +1,212 @@
+"""
+Tests for the temporal aspect of the Temporal VF2 isomorphism algorithm.
+"""
+
+from datetime import date, datetime, timedelta
+
+import networkx as nx
+from networkx.algorithms import isomorphism as iso
+
+
+def provide_g1_edgelist():
+    return [(0, 1), (0, 2), (1, 2), (2, 4), (1, 3), (3, 4), (4, 5)]
+
+
+def put_same_time(G, att_name):
+    for e in G.edges(data=True):
+        e[2][att_name] = date(2015, 1, 1)
+    return G
+
+
+def put_same_datetime(G, att_name):
+    for e in G.edges(data=True):
+        e[2][att_name] = datetime(2015, 1, 1)
+    return G
+
+
+def put_sequence_time(G, att_name):
+    current_date = date(2015, 1, 1)
+    for e in G.edges(data=True):
+        current_date += timedelta(days=1)
+        e[2][att_name] = current_date
+    return G
+
+
+def put_time_config_0(G, att_name):
+    G[0][1][att_name] = date(2015, 1, 2)
+    G[0][2][att_name] = date(2015, 1, 2)
+    G[1][2][att_name] = date(2015, 1, 3)
+    G[1][3][att_name] = date(2015, 1, 1)
+    G[2][4][att_name] = date(2015, 1, 1)
+    G[3][4][att_name] = date(2015, 1, 3)
+    G[4][5][att_name] = date(2015, 1, 3)
+    return G
+
+
+def put_time_config_1(G, att_name):
+    G[0][1][att_name] = date(2015, 1, 2)
+    G[0][2][att_name] = date(2015, 1, 1)
+    G[1][2][att_name] = date(2015, 1, 3)
+    G[1][3][att_name] = date(2015, 1, 1)
+    G[2][4][att_name] = date(2015, 1, 2)
+    G[3][4][att_name] = date(2015, 1, 4)
+    G[4][5][att_name] = date(2015, 1, 3)
+    return G
+
+
+def put_time_config_2(G, att_name):
+    G[0][1][att_name] = date(2015, 1, 1)
+    G[0][2][att_name] = date(2015, 1, 1)
+    G[1][2][att_name] = date(2015, 1, 3)
+    G[1][3][att_name] = date(2015, 1, 2)
+    G[2][4][att_name] = date(2015, 1, 2)
+    G[3][4][att_name] = date(2015, 1, 3)
+    G[4][5][att_name] = date(2015, 1, 2)
+    return G
+
+
+class TestTimeRespectingGraphMatcher:
+    """
+    A test class for the undirected temporal graph matcher.
+    """
+
+    def provide_g1_topology(self):
+        G1 = nx.Graph()
+        G1.add_edges_from(provide_g1_edgelist())
+        return G1
+
+    def provide_g2_path_3edges(self):
+        G2 = nx.Graph()
+        G2.add_edges_from([(0, 1), (1, 2), (2, 3)])
+        return G2
+
+    def test_timdelta_zero_timeRespecting_returnsTrue(self):
+        G1 = self.provide_g1_topology()
+        temporal_name = "date"
+        G1 = put_same_time(G1, temporal_name)
+        G2 = self.provide_g2_path_3edges()
+        d = timedelta()
+        gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d)
+        assert gm.subgraph_is_isomorphic()
+
+    def test_timdelta_zero_datetime_timeRespecting_returnsTrue(self):
+        G1 = self.provide_g1_topology()
+        temporal_name = "date"
+        G1 = put_same_datetime(G1, temporal_name)
+        G2 = self.provide_g2_path_3edges()
+        d = timedelta()
+        gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d)
+        assert gm.subgraph_is_isomorphic()
+
+    def test_attNameStrange_timdelta_zero_timeRespecting_returnsTrue(self):
+        G1 = self.provide_g1_topology()
+        temporal_name = "strange_name"
+        G1 = put_same_time(G1, temporal_name)
+        G2 = self.provide_g2_path_3edges()
+        d = timedelta()
+        gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d)
+        assert gm.subgraph_is_isomorphic()
+
+    def test_notTimeRespecting_returnsFalse(self):
+        G1 = self.provide_g1_topology()
+        temporal_name = "date"
+        G1 = put_sequence_time(G1, temporal_name)
+        G2 = self.provide_g2_path_3edges()
+        d = timedelta()
+        gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d)
+        assert not gm.subgraph_is_isomorphic()
+
+    def test_timdelta_one_config0_returns_no_embeddings(self):
+        G1 = self.provide_g1_topology()
+        temporal_name = "date"
+        G1 = put_time_config_0(G1, temporal_name)
+        G2 = self.provide_g2_path_3edges()
+        d = timedelta(days=1)
+        gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d)
+        count_match = len(list(gm.subgraph_isomorphisms_iter()))
+        assert count_match == 0
+
+    def test_timdelta_one_config1_returns_four_embedding(self):
+        G1 = self.provide_g1_topology()
+        temporal_name = "date"
+        G1 = put_time_config_1(G1, temporal_name)
+        G2 = self.provide_g2_path_3edges()
+        d = timedelta(days=1)
+        gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d)
+        count_match = len(list(gm.subgraph_isomorphisms_iter()))
+        assert count_match == 4
+
+    def test_timdelta_one_config2_returns_ten_embeddings(self):
+        G1 = self.provide_g1_topology()
+        temporal_name = "date"
+        G1 = put_time_config_2(G1, temporal_name)
+        G2 = self.provide_g2_path_3edges()
+        d = timedelta(days=1)
+        gm = iso.TimeRespectingGraphMatcher(G1, G2, temporal_name, d)
+        L = list(gm.subgraph_isomorphisms_iter())
+        count_match = len(list(gm.subgraph_isomorphisms_iter()))
+        assert count_match == 10
+
+
+class TestDiTimeRespectingGraphMatcher:
+    """
+    A test class for the directed time-respecting graph matcher.
+    """
+
+    def provide_g1_topology(self):
+        G1 = nx.DiGraph()
+        G1.add_edges_from(provide_g1_edgelist())
+        return G1
+
+    def provide_g2_path_3edges(self):
+        G2 = nx.DiGraph()
+        G2.add_edges_from([(0, 1), (1, 2), (2, 3)])
+        return G2
+
+    def test_timdelta_zero_same_dates_returns_true(self):
+        G1 = self.provide_g1_topology()
+        temporal_name = "date"
+        G1 = put_same_time(G1, temporal_name)
+        G2 = self.provide_g2_path_3edges()
+        d = timedelta()
+        gm = iso.TimeRespectingDiGraphMatcher(G1, G2, temporal_name, d)
+        assert gm.subgraph_is_isomorphic()
+
+    def test_attNameStrange_timdelta_zero_same_dates_returns_true(self):
+        G1 = self.provide_g1_topology()
+        temporal_name = "strange"
+        G1 = put_same_time(G1, temporal_name)
+        G2 = self.provide_g2_path_3edges()
+        d = timedelta()
+        gm = iso.TimeRespectingDiGraphMatcher(G1, G2, temporal_name, d)
+        assert gm.subgraph_is_isomorphic()
+
+    def test_timdelta_one_config0_returns_no_embeddings(self):
+        G1 = self.provide_g1_topology()
+        temporal_name = "date"
+        G1 = put_time_config_0(G1, temporal_name)
+        G2 = self.provide_g2_path_3edges()
+        d = timedelta(days=1)
+        gm = iso.TimeRespectingDiGraphMatcher(G1, G2, temporal_name, d)
+        count_match = len(list(gm.subgraph_isomorphisms_iter()))
+        assert count_match == 0
+
+    def test_timdelta_one_config1_returns_one_embedding(self):
+        G1 = self.provide_g1_topology()
+        temporal_name = "date"
+        G1 = put_time_config_1(G1, temporal_name)
+        G2 = self.provide_g2_path_3edges()
+        d = timedelta(days=1)
+        gm = iso.TimeRespectingDiGraphMatcher(G1, G2, temporal_name, d)
+        count_match = len(list(gm.subgraph_isomorphisms_iter()))
+        assert count_match == 1
+
+    def test_timdelta_one_config2_returns_two_embeddings(self):
+        G1 = self.provide_g1_topology()
+        temporal_name = "date"
+        G1 = put_time_config_2(G1, temporal_name)
+        G2 = self.provide_g2_path_3edges()
+        d = timedelta(days=1)
+        gm = iso.TimeRespectingDiGraphMatcher(G1, G2, temporal_name, d)
+        count_match = len(list(gm.subgraph_isomorphisms_iter()))
+        assert count_match == 2

wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_tree_isomorphism.py

@@ -0,0 +1,292 @@
+import random
+import time
+
+import pytest
+
+import networkx as nx
+from networkx.algorithms.isomorphism.tree_isomorphism import (
+    rooted_tree_isomorphism,
+    tree_isomorphism,
+)
+from networkx.classes.function import is_directed
+
+
+@pytest.mark.parametrize("graph_constructor", (nx.DiGraph, nx.MultiGraph))
+def test_tree_isomorphism_raises_on_directed_and_multigraphs(graph_constructor):
+    t1 = graph_constructor([(0, 1)])
+    t2 = graph_constructor([(1, 2)])
+    with pytest.raises(nx.NetworkXNotImplemented):
+        nx.isomorphism.tree_isomorphism(t1, t2)
+
+
+# have this work for graph
+# given two trees (either the directed or undirected)
+# transform t2 according to the isomorphism
+# and confirm it is identical to t1
+# randomize the order of the edges when constructing
+def check_isomorphism(t1, t2, isomorphism):
+    # get the name of t1, given the name in t2
+    mapping = {v2: v1 for (v1, v2) in isomorphism}
+
+    # these should be the same
+    d1 = is_directed(t1)
+    d2 = is_directed(t2)
+    assert d1 == d2
+
+    edges_1 = []
+    for u, v in t1.edges():
+        if d1:
+            edges_1.append((u, v))
+        else:
+            # if not directed, then need to
+            # put the edge in a consistent direction
+            if u < v:
+                edges_1.append((u, v))
+            else:
+                edges_1.append((v, u))
+
+    edges_2 = []
+    for u, v in t2.edges():
+        # translate to names for t1
+        u = mapping[u]
+        v = mapping[v]
+        if d2:
+            edges_2.append((u, v))
+        else:
+            if u < v:
+                edges_2.append((u, v))
+            else:
+                edges_2.append((v, u))
+
+    return sorted(edges_1) == sorted(edges_2)
+
+
+def test_hardcoded():
+    print("hardcoded test")
+
+    # define a test problem
+    edges_1 = [
+        ("a", "b"),
+        ("a", "c"),
+        ("a", "d"),
+        ("b", "e"),
+        ("b", "f"),
+        ("e", "j"),
+        ("e", "k"),
+        ("c", "g"),
+        ("c", "h"),
+        ("g", "m"),
+        ("d", "i"),
+        ("f", "l"),
+    ]
+
+    edges_2 = [
+        ("v", "y"),
+        ("v", "z"),
+        ("u", "x"),
+        ("q", "u"),
+        ("q", "v"),
+        ("p", "t"),
+        ("n", "p"),
+        ("n", "q"),
+        ("n", "o"),
+        ("o", "r"),
+        ("o", "s"),
+        ("s", "w"),
+    ]
+
+    # there are two possible correct isomorphisms
+    # it currently returns isomorphism1
+    # but the second is also correct
+    isomorphism1 = [
+        ("a", "n"),
+        ("b", "q"),
+        ("c", "o"),
+        ("d", "p"),
+        ("e", "v"),
+        ("f", "u"),
+        ("g", "s"),
+        ("h", "r"),
+        ("i", "t"),
+        ("j", "y"),
+        ("k", "z"),
+        ("l", "x"),
+        ("m", "w"),
+    ]
+
+    # could swap y and z
+    isomorphism2 = [
+        ("a", "n"),
+        ("b", "q"),
+        ("c", "o"),
+        ("d", "p"),
+        ("e", "v"),
+        ("f", "u"),
+        ("g", "s"),
+        ("h", "r"),
+        ("i", "t"),
+        ("j", "z"),
+        ("k", "y"),
+        ("l", "x"),
+        ("m", "w"),
+    ]
+
+    t1 = nx.Graph()
+    t1.add_edges_from(edges_1)
+    root1 = "a"
+
+    t2 = nx.Graph()
+    t2.add_edges_from(edges_2)
+    root2 = "n"
+
+    isomorphism = sorted(rooted_tree_isomorphism(t1, root1, t2, root2))
+
+    # is correct by hand
+    assert isomorphism in (isomorphism1, isomorphism2)
+
+    # check algorithmically
+    assert check_isomorphism(t1, t2, isomorphism)
+
+    # try again as digraph
+    t1 = nx.DiGraph()
+    t1.add_edges_from(edges_1)
+    root1 = "a"
+
+    t2 = nx.DiGraph()
+    t2.add_edges_from(edges_2)
+    root2 = "n"
+
+    isomorphism = sorted(rooted_tree_isomorphism(t1, root1, t2, root2))
+
+    # is correct by hand
+    assert isomorphism in (isomorphism1, isomorphism2)
+
+    # check algorithmically
+    assert check_isomorphism(t1, t2, isomorphism)
+
+
+# randomly swap a tuple (a,b)
+def random_swap(t):
+    (a, b) = t
+    if random.randint(0, 1) == 1:
+        return (a, b)
+    else:
+        return (b, a)
+
+
+# given a tree t1, create a new tree t2
+# that is isomorphic to t1, with a known isomorphism
+# and test that our algorithm found the right one
+def positive_single_tree(t1):
+    assert nx.is_tree(t1)
+
+    nodes1 = list(t1.nodes())
+    # get a random permutation of this
+    nodes2 = nodes1.copy()
+    random.shuffle(nodes2)
+
+    # this is one isomorphism, however they may be multiple
+    # so we don't necessarily get this one back
+    someisomorphism = list(zip(nodes1, nodes2))
+
+    # map from old to new
+    map1to2 = dict(someisomorphism)
+
+    # get the edges with the transformed names
+    edges2 = [random_swap((map1to2[u], map1to2[v])) for (u, v) in t1.edges()]
+    # randomly permute, to ensure we're not relying on edge order somehow
+    random.shuffle(edges2)
+
+    # so t2 is isomorphic to t1
+    t2 = nx.Graph()
+    t2.add_edges_from(edges2)
+
+    # lets call our code to see if t1 and t2 are isomorphic
+    isomorphism = tree_isomorphism(t1, t2)
+
+    # make sure we got a correct solution
+    # although not necessarily someisomorphism
+    assert len(isomorphism) > 0
+    assert check_isomorphism(t1, t2, isomorphism)
+
+
+# run positive_single_tree over all the
+# non-isomorphic trees for k from 4 to maxk
+# k = 4 is the first level that has more than 1 non-isomorphic tree
+# k = 13 takes about 2.86 seconds to run on my laptop
+# larger values run slow down significantly
+# as the number of trees grows rapidly
+def test_positive(maxk=14):
+    print("positive test")
+
+    for k in range(2, maxk + 1):
+        start_time = time.time()
+        trial = 0
+        for t in nx.nonisomorphic_trees(k):
+            positive_single_tree(t)
+            trial += 1
+        print(k, trial, time.time() - start_time)
+
+
+# test the trivial case of a single node in each tree
+# note that nonisomorphic_trees doesn't work for k = 1
+def test_trivial():
+    print("trivial test")
+
+    # back to an undirected graph
+    t1 = nx.Graph()
+    t1.add_node("a")
+    root1 = "a"
+
+    t2 = nx.Graph()
+    t2.add_node("n")
+    root2 = "n"
+
+    isomorphism = rooted_tree_isomorphism(t1, root1, t2, root2)
+
+    assert isomorphism == [("a", "n")]
+
+    assert check_isomorphism(t1, t2, isomorphism)
+
+
+# test another trivial case where the two graphs have
+# different numbers of nodes
+def test_trivial_2():
+    print("trivial test 2")
+
+    edges_1 = [("a", "b"), ("a", "c")]
+
+    edges_2 = [("v", "y")]
+
+    t1 = nx.Graph()
+    t1.add_edges_from(edges_1)
+
+    t2 = nx.Graph()
+    t2.add_edges_from(edges_2)
+
+    isomorphism = tree_isomorphism(t1, t2)
+
+    # they cannot be isomorphic,
+    # since they have different numbers of nodes
+    assert isomorphism == []
+
+
+# the function nonisomorphic_trees generates all the non-isomorphic
+# trees of a given size.  Take each pair of these and verify that
+# they are not isomorphic
+# k = 4 is the first level that has more than 1 non-isomorphic tree
+# k = 11 takes about 4.76 seconds to run on my laptop
+# larger values run slow down significantly
+# as the number of trees grows rapidly
+def test_negative(maxk=11):
+    print("negative test")
+
+    for k in range(4, maxk + 1):
+        test_trees = list(nx.nonisomorphic_trees(k))
+        start_time = time.time()
+        trial = 0
+        for i in range(len(test_trees) - 1):
+            for j in range(i + 1, len(test_trees)):
+                trial += 1
+                assert tree_isomorphism(test_trees[i], test_trees[j]) == []
+        print(k, trial, time.time() - start_time)

wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_vf2pp.py

@@ -0,0 +1,1608 @@
+import itertools as it
+
+import pytest
+
+import networkx as nx
+from networkx import vf2pp_is_isomorphic, vf2pp_isomorphism
+
+labels_same = ["blue"]
+
+labels_many = [
+    "white",
+    "red",
+    "blue",
+    "green",
+    "orange",
+    "black",
+    "purple",
+    "yellow",
+    "brown",
+    "cyan",
+    "solarized",
+    "pink",
+    "none",
+]
+
+
+class TestPreCheck:
+    def test_first_graph_empty(self):
+        G1 = nx.Graph()
+        G2 = nx.Graph([(0, 1), (1, 2)])
+        assert not vf2pp_is_isomorphic(G1, G2)
+
+    def test_second_graph_empty(self):
+        G1 = nx.Graph([(0, 1), (1, 2)])
+        G2 = nx.Graph()
+        assert not vf2pp_is_isomorphic(G1, G2)
+
+    def test_different_order1(self):
+        G1 = nx.path_graph(5)
+        G2 = nx.path_graph(6)
+        assert not vf2pp_is_isomorphic(G1, G2)
+
+    def test_different_order2(self):
+        G1 = nx.barbell_graph(100, 20)
+        G2 = nx.barbell_graph(101, 20)
+        assert not vf2pp_is_isomorphic(G1, G2)
+
+    def test_different_order3(self):
+        G1 = nx.complete_graph(7)
+        G2 = nx.complete_graph(8)
+        assert not vf2pp_is_isomorphic(G1, G2)
+
+    def test_different_degree_sequences1(self):
+        G1 = nx.Graph([(0, 1), (0, 2), (1, 2), (1, 3), (0, 4)])
+        G2 = nx.Graph([(0, 1), (0, 2), (1, 2), (1, 3), (0, 4), (2, 5)])
+        assert not vf2pp_is_isomorphic(G1, G2)
+
+        G2.remove_node(3)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(["a"]))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle("a"))), "label")
+
+        assert vf2pp_is_isomorphic(G1, G2)
+
+    def test_different_degree_sequences2(self):
+        G1 = nx.Graph(
+            [
+                (0, 1),
+                (1, 2),
+                (0, 2),
+                (2, 3),
+                (3, 4),
+                (4, 5),
+                (5, 6),
+                (6, 3),
+                (4, 7),
+                (7, 8),
+                (8, 3),
+            ]
+        )
+        G2 = G1.copy()
+        G2.add_edge(8, 0)
+        assert not vf2pp_is_isomorphic(G1, G2)
+
+        G1.add_edge(6, 1)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(["a"]))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle("a"))), "label")
+
+        assert vf2pp_is_isomorphic(G1, G2)
+
+    def test_different_degree_sequences3(self):
+        G1 = nx.Graph([(0, 1), (0, 2), (1, 2), (2, 3), (2, 4), (3, 4), (2, 5), (2, 6)])
+        G2 = nx.Graph(
+            [(0, 1), (0, 6), (0, 2), (1, 2), (2, 3), (2, 4), (3, 4), (2, 5), (2, 6)]
+        )
+        assert not vf2pp_is_isomorphic(G1, G2)
+
+        G1.add_edge(3, 5)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(["a"]))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle("a"))), "label")
+
+        assert vf2pp_is_isomorphic(G1, G2)
+
+    def test_label_distribution(self):
+        G1 = nx.Graph([(0, 1), (0, 2), (1, 2), (2, 3), (2, 4), (3, 4), (2, 5), (2, 6)])
+        G2 = nx.Graph([(0, 1), (0, 2), (1, 2), (2, 3), (2, 4), (3, 4), (2, 5), (2, 6)])
+
+        colors1 = ["blue", "blue", "blue", "yellow", "black", "purple", "purple"]
+        colors2 = ["blue", "blue", "yellow", "yellow", "black", "purple", "purple"]
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(colors1[::-1]))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(colors2[::-1]))), "label")
+
+        assert not vf2pp_is_isomorphic(G1, G2, node_label="label")
+        G2.nodes[3]["label"] = "blue"
+        assert vf2pp_is_isomorphic(G1, G2, node_label="label")
+
+
+class TestAllGraphTypesEdgeCases:
+    @pytest.mark.parametrize("graph_type", (nx.Graph, nx.MultiGraph, nx.DiGraph))
+    def test_both_graphs_empty(self, graph_type):
+        G = graph_type()
+        H = graph_type()
+        assert vf2pp_isomorphism(G, H) is None
+
+        G.add_node(0)
+
+        assert vf2pp_isomorphism(G, H) is None
+        assert vf2pp_isomorphism(H, G) is None
+
+        H.add_node(0)
+        assert vf2pp_isomorphism(G, H) == {0: 0}
+
+    @pytest.mark.parametrize("graph_type", (nx.Graph, nx.MultiGraph, nx.DiGraph))
+    def test_first_graph_empty(self, graph_type):
+        G = graph_type()
+        H = graph_type([(0, 1)])
+        assert vf2pp_isomorphism(G, H) is None
+
+    @pytest.mark.parametrize("graph_type", (nx.Graph, nx.MultiGraph, nx.DiGraph))
+    def test_second_graph_empty(self, graph_type):
+        G = graph_type([(0, 1)])
+        H = graph_type()
+        assert vf2pp_isomorphism(G, H) is None
+
+
+class TestGraphISOVF2pp:
+    def test_custom_graph1_same_labels(self):
+        G1 = nx.Graph()
+
+        mapped = {1: "A", 2: "B", 3: "C", 4: "D", 5: "Z", 6: "E"}
+        edges1 = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 6), (3, 4), (5, 1), (5, 2)]
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label")
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Add edge making G1 symmetrical
+        G1.add_edge(3, 7)
+        G1.nodes[7]["label"] = "blue"
+        assert vf2pp_isomorphism(G1, G2, node_label="label") is None
+
+        # Make G2 isomorphic to G1
+        G2.add_edges_from([(mapped[3], "X"), (mapped[6], mapped[5])])
+        G1.add_edge(4, 7)
+        G2.nodes["X"]["label"] = "blue"
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Re-structure maintaining isomorphism
+        G1.remove_edges_from([(1, 4), (1, 3)])
+        G2.remove_edges_from([(mapped[1], mapped[5]), (mapped[1], mapped[2])])
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+    def test_custom_graph1_different_labels(self):
+        G1 = nx.Graph()
+
+        mapped = {1: "A", 2: "B", 3: "C", 4: "D", 5: "Z", 6: "E"}
+        edges1 = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 6), (3, 4), (5, 1), (5, 2)]
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label")
+        nx.set_node_attributes(
+            G2,
+            dict(zip([mapped[n] for n in G1], it.cycle(labels_many))),
+            "label",
+        )
+        assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped
+
+    def test_custom_graph2_same_labels(self):
+        G1 = nx.Graph()
+
+        mapped = {1: "A", 2: "C", 3: "D", 4: "E", 5: "G", 7: "B", 6: "F"}
+        edges1 = [(1, 2), (1, 5), (5, 6), (2, 3), (2, 4), (3, 4), (4, 5), (2, 7)]
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label")
+
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Obtain two isomorphic subgraphs from the graph
+        G2.remove_edge(mapped[1], mapped[2])
+        G2.add_edge(mapped[1], mapped[4])
+        H1 = nx.Graph(G1.subgraph([2, 3, 4, 7]))
+        H2 = nx.Graph(G2.subgraph([mapped[1], mapped[4], mapped[5], mapped[6]]))
+        assert vf2pp_isomorphism(H1, H2, node_label="label")
+
+        # Add edges maintaining isomorphism
+        H1.add_edges_from([(3, 7), (4, 7)])
+        H2.add_edges_from([(mapped[1], mapped[6]), (mapped[4], mapped[6])])
+        assert vf2pp_isomorphism(H1, H2, node_label="label")
+
+    def test_custom_graph2_different_labels(self):
+        G1 = nx.Graph()
+
+        mapped = {1: "A", 2: "C", 3: "D", 4: "E", 5: "G", 7: "B", 6: "F"}
+        edges1 = [(1, 2), (1, 5), (5, 6), (2, 3), (2, 4), (3, 4), (4, 5), (2, 7)]
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label")
+        nx.set_node_attributes(
+            G2,
+            dict(zip([mapped[n] for n in G1], it.cycle(labels_many))),
+            "label",
+        )
+
+        # Adding new nodes
+        G1.add_node(0)
+        G2.add_node("Z")
+        G1.nodes[0]["label"] = G1.nodes[1]["label"]
+        G2.nodes["Z"]["label"] = G1.nodes[1]["label"]
+        mapped.update({0: "Z"})
+
+        assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped
+
+        # Change the color of one of the nodes
+        G2.nodes["Z"]["label"] = G1.nodes[2]["label"]
+        assert vf2pp_isomorphism(G1, G2, node_label="label") is None
+
+        # Add an extra edge
+        G1.nodes[0]["label"] = "blue"
+        G2.nodes["Z"]["label"] = "blue"
+        G1.add_edge(0, 1)
+
+        assert vf2pp_isomorphism(G1, G2, node_label="label") is None
+
+        # Add extra edge to both
+        G2.add_edge("Z", "A")
+        assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped
+
+    def test_custom_graph3_same_labels(self):
+        G1 = nx.Graph()
+
+        mapped = {1: 9, 2: 8, 3: 7, 4: 6, 5: 3, 8: 5, 9: 4, 7: 1, 6: 2}
+        edges1 = [
+            (1, 2),
+            (1, 3),
+            (2, 3),
+            (3, 4),
+            (4, 5),
+            (4, 7),
+            (4, 9),
+            (5, 8),
+            (8, 9),
+            (5, 6),
+            (6, 7),
+            (5, 2),
+        ]
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label")
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Connect nodes maintaining symmetry
+        G1.add_edges_from([(6, 9), (7, 8)])
+        G2.add_edges_from([(mapped[6], mapped[8]), (mapped[7], mapped[9])])
+        assert vf2pp_isomorphism(G1, G2, node_label="label") is None
+
+        # Make isomorphic
+        G1.add_edges_from([(6, 8), (7, 9)])
+        G2.add_edges_from([(mapped[6], mapped[9]), (mapped[7], mapped[8])])
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Connect more nodes
+        G1.add_edges_from([(2, 7), (3, 6)])
+        G2.add_edges_from([(mapped[2], mapped[7]), (mapped[3], mapped[6])])
+        G1.add_node(10)
+        G2.add_node("Z")
+        G1.nodes[10]["label"] = "blue"
+        G2.nodes["Z"]["label"] = "blue"
+
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Connect the newly added node, to opposite sides of the graph
+        G1.add_edges_from([(10, 1), (10, 5), (10, 8)])
+        G2.add_edges_from([("Z", mapped[1]), ("Z", mapped[4]), ("Z", mapped[9])])
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Get two subgraphs that are not isomorphic but are easy to make
+        H1 = nx.Graph(G1.subgraph([2, 3, 4, 5, 6, 7, 10]))
+        H2 = nx.Graph(
+            G2.subgraph(
+                [mapped[4], mapped[5], mapped[6], mapped[7], mapped[8], mapped[9], "Z"]
+            )
+        )
+        assert vf2pp_isomorphism(H1, H2, node_label="label") is None
+
+        # Restructure both to make them isomorphic
+        H1.add_edges_from([(10, 2), (10, 6), (3, 6), (2, 7), (2, 6), (3, 7)])
+        H2.add_edges_from(
+            [("Z", mapped[7]), (mapped[6], mapped[9]), (mapped[7], mapped[8])]
+        )
+        assert vf2pp_isomorphism(H1, H2, node_label="label")
+
+        # Add edges with opposite direction in each Graph
+        H1.add_edge(3, 5)
+        H2.add_edge(mapped[5], mapped[7])
+        assert vf2pp_isomorphism(H1, H2, node_label="label") is None
+
+    def test_custom_graph3_different_labels(self):
+        G1 = nx.Graph()
+
+        mapped = {1: 9, 2: 8, 3: 7, 4: 6, 5: 3, 8: 5, 9: 4, 7: 1, 6: 2}
+        edges1 = [
+            (1, 2),
+            (1, 3),
+            (2, 3),
+            (3, 4),
+            (4, 5),
+            (4, 7),
+            (4, 9),
+            (5, 8),
+            (8, 9),
+            (5, 6),
+            (6, 7),
+            (5, 2),
+        ]
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label")
+        nx.set_node_attributes(
+            G2,
+            dict(zip([mapped[n] for n in G1], it.cycle(labels_many))),
+            "label",
+        )
+        assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped
+
+        # Add extra edge to G1
+        G1.add_edge(1, 7)
+        assert vf2pp_isomorphism(G1, G2, node_label="label") is None
+
+        # Compensate in G2
+        G2.add_edge(9, 1)
+        assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped
+
+        # Add extra node
+        G1.add_node("A")
+        G2.add_node("K")
+        G1.nodes["A"]["label"] = "green"
+        G2.nodes["K"]["label"] = "green"
+        mapped.update({"A": "K"})
+
+        assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped
+
+        # Connect A to one side of G1 and K to the opposite
+        G1.add_edge("A", 6)
+        G2.add_edge("K", 5)
+        assert vf2pp_isomorphism(G1, G2, node_label="label") is None
+
+        # Make the graphs symmetrical
+        G1.add_edge(1, 5)
+        G1.add_edge(2, 9)
+        G2.add_edge(9, 3)
+        G2.add_edge(8, 4)
+        assert vf2pp_isomorphism(G1, G2, node_label="label") is None
+
+        # Assign same colors so the two opposite sides are identical
+        for node in G1.nodes():
+            color = "red"
+            G1.nodes[node]["label"] = color
+            G2.nodes[mapped[node]]["label"] = color
+
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+    def test_custom_graph4_different_labels(self):
+        G1 = nx.Graph()
+        edges1 = [
+            (1, 2),
+            (2, 3),
+            (3, 8),
+            (3, 4),
+            (4, 5),
+            (4, 6),
+            (3, 6),
+            (8, 7),
+            (8, 9),
+            (5, 9),
+            (10, 11),
+            (11, 12),
+            (12, 13),
+            (11, 13),
+        ]
+
+        mapped = {
+            1: "n",
+            2: "m",
+            3: "l",
+            4: "j",
+            5: "k",
+            6: "i",
+            7: "g",
+            8: "h",
+            9: "f",
+            10: "b",
+            11: "a",
+            12: "d",
+            13: "e",
+        }
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label")
+        nx.set_node_attributes(
+            G2,
+            dict(zip([mapped[n] for n in G1], it.cycle(labels_many))),
+            "label",
+        )
+        assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped
+
+    def test_custom_graph4_same_labels(self):
+        G1 = nx.Graph()
+        edges1 = [
+            (1, 2),
+            (2, 3),
+            (3, 8),
+            (3, 4),
+            (4, 5),
+            (4, 6),
+            (3, 6),
+            (8, 7),
+            (8, 9),
+            (5, 9),
+            (10, 11),
+            (11, 12),
+            (12, 13),
+            (11, 13),
+        ]
+
+        mapped = {
+            1: "n",
+            2: "m",
+            3: "l",
+            4: "j",
+            5: "k",
+            6: "i",
+            7: "g",
+            8: "h",
+            9: "f",
+            10: "b",
+            11: "a",
+            12: "d",
+            13: "e",
+        }
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label")
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Add nodes of different label
+        G1.add_node(0)
+        G2.add_node("z")
+        G1.nodes[0]["label"] = "green"
+        G2.nodes["z"]["label"] = "blue"
+
+        assert vf2pp_isomorphism(G1, G2, node_label="label") is None
+
+        # Make the labels identical
+        G2.nodes["z"]["label"] = "green"
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Change the structure of the graphs, keeping them isomorphic
+        G1.add_edge(2, 5)
+        G2.remove_edge("i", "l")
+        G2.add_edge("g", "l")
+        G2.add_edge("m", "f")
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Change the structure of the disconnected sub-graph, keeping it isomorphic
+        G1.remove_node(13)
+        G2.remove_node("d")
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Connect the newly added node to the disconnected graph, which now is just a path of size 3
+        G1.add_edge(0, 10)
+        G2.add_edge("e", "z")
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Connect the two disconnected sub-graphs, forming a single graph
+        G1.add_edge(11, 3)
+        G1.add_edge(0, 8)
+        G2.add_edge("a", "l")
+        G2.add_edge("z", "j")
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+    def test_custom_graph5_same_labels(self):
+        G1 = nx.Graph()
+        edges1 = [
+            (1, 5),
+            (1, 2),
+            (1, 4),
+            (2, 3),
+            (2, 6),
+            (3, 4),
+            (3, 7),
+            (4, 8),
+            (5, 8),
+            (5, 6),
+            (6, 7),
+            (7, 8),
+        ]
+        mapped = {1: "a", 2: "h", 3: "d", 4: "i", 5: "g", 6: "b", 7: "j", 8: "c"}
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label")
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Add different edges in each graph, maintaining symmetry
+        G1.add_edges_from([(3, 6), (2, 7), (2, 5), (1, 3), (4, 7), (6, 8)])
+        G2.add_edges_from(
+            [
+                (mapped[6], mapped[3]),
+                (mapped[2], mapped[7]),
+                (mapped[1], mapped[6]),
+                (mapped[5], mapped[7]),
+                (mapped[3], mapped[8]),
+                (mapped[2], mapped[4]),
+            ]
+        )
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+        # Obtain two different but isomorphic subgraphs from G1 and G2
+        H1 = nx.Graph(G1.subgraph([1, 5, 8, 6, 7, 3]))
+        H2 = nx.Graph(
+            G2.subgraph(
+                [mapped[1], mapped[4], mapped[8], mapped[7], mapped[3], mapped[5]]
+            )
+        )
+        assert vf2pp_isomorphism(H1, H2, node_label="label")
+
+        # Delete corresponding node from the two graphs
+        H1.remove_node(8)
+        H2.remove_node(mapped[7])
+        assert vf2pp_isomorphism(H1, H2, node_label="label")
+
+        # Re-orient, maintaining isomorphism
+        H1.add_edge(1, 6)
+        H1.remove_edge(3, 6)
+        assert vf2pp_isomorphism(H1, H2, node_label="label")
+
+    def test_custom_graph5_different_labels(self):
+        G1 = nx.Graph()
+        edges1 = [
+            (1, 5),
+            (1, 2),
+            (1, 4),
+            (2, 3),
+            (2, 6),
+            (3, 4),
+            (3, 7),
+            (4, 8),
+            (5, 8),
+            (5, 6),
+            (6, 7),
+            (7, 8),
+        ]
+        mapped = {1: "a", 2: "h", 3: "d", 4: "i", 5: "g", 6: "b", 7: "j", 8: "c"}
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        colors = ["red", "blue", "grey", "none", "brown", "solarized", "yellow", "pink"]
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label")
+        nx.set_node_attributes(
+            G2,
+            dict(zip([mapped[n] for n in G1], it.cycle(labels_many))),
+            "label",
+        )
+        assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped
+
+        # Assign different colors to matching nodes
+        c = 0
+        for node in G1.nodes():
+            color1 = colors[c]
+            color2 = colors[(c + 3) % len(colors)]
+            G1.nodes[node]["label"] = color1
+            G2.nodes[mapped[node]]["label"] = color2
+            c += 1
+
+        assert vf2pp_isomorphism(G1, G2, node_label="label") is None
+
+        # Get symmetrical sub-graphs of G1,G2 and compare them
+        H1 = G1.subgraph([1, 5])
+        H2 = G2.subgraph(["i", "c"])
+        c = 0
+        for node1, node2 in zip(H1.nodes(), H2.nodes()):
+            H1.nodes[node1]["label"] = "red"
+            H2.nodes[node2]["label"] = "red"
+            c += 1
+
+        assert vf2pp_isomorphism(H1, H2, node_label="label")
+
+    def test_disconnected_graph_all_same_labels(self):
+        G1 = nx.Graph()
+        G1.add_nodes_from(list(range(10)))
+
+        mapped = {0: 9, 1: 8, 2: 7, 3: 6, 4: 5, 5: 4, 6: 3, 7: 2, 8: 1, 9: 0}
+        G2 = nx.relabel_nodes(G1, mapped)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label")
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+    def test_disconnected_graph_all_different_labels(self):
+        G1 = nx.Graph()
+        G1.add_nodes_from(list(range(10)))
+
+        mapped = {0: 9, 1: 8, 2: 7, 3: 6, 4: 5, 5: 4, 6: 3, 7: 2, 8: 1, 9: 0}
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label")
+        nx.set_node_attributes(
+            G2,
+            dict(zip([mapped[n] for n in G1], it.cycle(labels_many))),
+            "label",
+        )
+        assert vf2pp_isomorphism(G1, G2, node_label="label") == mapped
+
+    def test_disconnected_graph_some_same_labels(self):
+        G1 = nx.Graph()
+        G1.add_nodes_from(list(range(10)))
+
+        mapped = {0: 9, 1: 8, 2: 7, 3: 6, 4: 5, 5: 4, 6: 3, 7: 2, 8: 1, 9: 0}
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        colors = [
+            "white",
+            "white",
+            "white",
+            "purple",
+            "purple",
+            "red",
+            "red",
+            "pink",
+            "pink",
+            "pink",
+        ]
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(colors))), "label")
+        nx.set_node_attributes(
+            G2, dict(zip([mapped[n] for n in G1], it.cycle(colors))), "label"
+        )
+
+        assert vf2pp_isomorphism(G1, G2, node_label="label")
+
+
+class TestMultiGraphISOVF2pp:
+    def test_custom_multigraph1_same_labels(self):
+        G1 = nx.MultiGraph()
+
+        mapped = {1: "A", 2: "B", 3: "C", 4: "D", 5: "Z", 6: "E"}
+        edges1 = [
+            (1, 2),
+            (1, 3),
+            (1, 4),
+            (1, 4),
+            (1, 4),
+            (2, 3),
+            (2, 6),
+            (2, 6),
+            (3, 4),
+            (3, 4),
+            (5, 1),
+            (5, 1),
+            (5, 2),
+            (5, 2),
+        ]
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label")
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Transfer the 2-clique to the right side of G1
+        G1.remove_edges_from([(2, 6), (2, 6)])
+        G1.add_edges_from([(3, 6), (3, 6)])
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Delete an edges, making them symmetrical, so the position of the 2-clique doesn't matter
+        G2.remove_edge(mapped[1], mapped[4])
+        G1.remove_edge(1, 4)
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Add self-loops
+        G1.add_edges_from([(5, 5), (5, 5), (1, 1)])
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Compensate in G2
+        G2.add_edges_from(
+            [(mapped[1], mapped[1]), (mapped[4], mapped[4]), (mapped[4], mapped[4])]
+        )
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+    def test_custom_multigraph1_different_labels(self):
+        G1 = nx.MultiGraph()
+
+        mapped = {1: "A", 2: "B", 3: "C", 4: "D", 5: "Z", 6: "E"}
+        edges1 = [
+            (1, 2),
+            (1, 3),
+            (1, 4),
+            (1, 4),
+            (1, 4),
+            (2, 3),
+            (2, 6),
+            (2, 6),
+            (3, 4),
+            (3, 4),
+            (5, 1),
+            (5, 1),
+            (5, 2),
+            (5, 2),
+        ]
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label")
+        nx.set_node_attributes(
+            G2,
+            dict(zip([mapped[n] for n in G1], it.cycle(labels_many))),
+            "label",
+        )
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+        assert m == mapped
+
+        # Re-structure G1, maintaining the degree sequence
+        G1.remove_edge(1, 4)
+        G1.add_edge(1, 5)
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Restructure G2, making it isomorphic to G1
+        G2.remove_edge("A", "D")
+        G2.add_edge("A", "Z")
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+        assert m == mapped
+
+        # Add edge from node to itself
+        G1.add_edges_from([(6, 6), (6, 6), (6, 6)])
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Same for G2
+        G2.add_edges_from([("E", "E"), ("E", "E"), ("E", "E")])
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+        assert m == mapped
+
+    def test_custom_multigraph2_same_labels(self):
+        G1 = nx.MultiGraph()
+
+        mapped = {1: "A", 2: "C", 3: "D", 4: "E", 5: "G", 7: "B", 6: "F"}
+        edges1 = [
+            (1, 2),
+            (1, 2),
+            (1, 5),
+            (1, 5),
+            (1, 5),
+            (5, 6),
+            (2, 3),
+            (2, 3),
+            (2, 4),
+            (3, 4),
+            (3, 4),
+            (4, 5),
+            (4, 5),
+            (4, 5),
+            (2, 7),
+            (2, 7),
+            (2, 7),
+        ]
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label")
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Obtain two non-isomorphic subgraphs from the graph
+        G2.remove_edges_from([(mapped[1], mapped[2]), (mapped[1], mapped[2])])
+        G2.add_edge(mapped[1], mapped[4])
+        H1 = nx.MultiGraph(G1.subgraph([2, 3, 4, 7]))
+        H2 = nx.MultiGraph(G2.subgraph([mapped[1], mapped[4], mapped[5], mapped[6]]))
+
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert not m
+
+        # Make them isomorphic
+        H1.remove_edge(3, 4)
+        H1.add_edges_from([(2, 3), (2, 4), (2, 4)])
+        H2.add_edges_from([(mapped[5], mapped[6]), (mapped[5], mapped[6])])
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+        # Remove triangle edge
+        H1.remove_edges_from([(2, 3), (2, 3), (2, 3)])
+        H2.remove_edges_from([(mapped[5], mapped[4])] * 3)
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+        # Change the edge orientation such that H1 is rotated H2
+        H1.remove_edges_from([(2, 7), (2, 7)])
+        H1.add_edges_from([(3, 4), (3, 4)])
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+        # Add extra edges maintaining degree sequence, but in a non-symmetrical manner
+        H2.add_edge(mapped[5], mapped[1])
+        H1.add_edge(3, 4)
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert not m
+
+    def test_custom_multigraph2_different_labels(self):
+        G1 = nx.MultiGraph()
+
+        mapped = {1: "A", 2: "C", 3: "D", 4: "E", 5: "G", 7: "B", 6: "F"}
+        edges1 = [
+            (1, 2),
+            (1, 2),
+            (1, 5),
+            (1, 5),
+            (1, 5),
+            (5, 6),
+            (2, 3),
+            (2, 3),
+            (2, 4),
+            (3, 4),
+            (3, 4),
+            (4, 5),
+            (4, 5),
+            (4, 5),
+            (2, 7),
+            (2, 7),
+            (2, 7),
+        ]
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label")
+        nx.set_node_attributes(
+            G2,
+            dict(zip([mapped[n] for n in G1], it.cycle(labels_many))),
+            "label",
+        )
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+        assert m == mapped
+
+        # Re-structure G1
+        G1.remove_edge(2, 7)
+        G1.add_edge(5, 6)
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Same for G2
+        G2.remove_edge("B", "C")
+        G2.add_edge("G", "F")
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+        assert m == mapped
+
+        # Delete node from G1 and G2, keeping them isomorphic
+        G1.remove_node(3)
+        G2.remove_node("D")
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Change G1 edges
+        G1.remove_edge(1, 2)
+        G1.remove_edge(2, 7)
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Make G2 identical to G1, but with different edge orientation and different labels
+        G2.add_edges_from([("A", "C"), ("C", "E"), ("C", "E")])
+        G2.remove_edges_from(
+            [("A", "G"), ("A", "G"), ("F", "G"), ("E", "G"), ("E", "G")]
+        )
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Make all labels the same, so G1 and G2 are also isomorphic
+        for n1, n2 in zip(G1.nodes(), G2.nodes()):
+            G1.nodes[n1]["label"] = "blue"
+            G2.nodes[n2]["label"] = "blue"
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+    def test_custom_multigraph3_same_labels(self):
+        G1 = nx.MultiGraph()
+
+        mapped = {1: 9, 2: 8, 3: 7, 4: 6, 5: 3, 8: 5, 9: 4, 7: 1, 6: 2}
+        edges1 = [
+            (1, 2),
+            (1, 3),
+            (1, 3),
+            (2, 3),
+            (2, 3),
+            (3, 4),
+            (4, 5),
+            (4, 7),
+            (4, 9),
+            (4, 9),
+            (4, 9),
+            (5, 8),
+            (5, 8),
+            (8, 9),
+            (8, 9),
+            (5, 6),
+            (6, 7),
+            (6, 7),
+            (6, 7),
+            (5, 2),
+        ]
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label")
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Connect nodes maintaining symmetry
+        G1.add_edges_from([(6, 9), (7, 8), (5, 8), (4, 9), (4, 9)])
+        G2.add_edges_from(
+            [
+                (mapped[6], mapped[8]),
+                (mapped[7], mapped[9]),
+                (mapped[5], mapped[8]),
+                (mapped[4], mapped[9]),
+                (mapped[4], mapped[9]),
+            ]
+        )
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Make isomorphic
+        G1.add_edges_from([(6, 8), (6, 8), (7, 9), (7, 9), (7, 9)])
+        G2.add_edges_from(
+            [
+                (mapped[6], mapped[8]),
+                (mapped[6], mapped[9]),
+                (mapped[7], mapped[8]),
+                (mapped[7], mapped[9]),
+                (mapped[7], mapped[9]),
+            ]
+        )
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Connect more nodes
+        G1.add_edges_from([(2, 7), (2, 7), (3, 6), (3, 6)])
+        G2.add_edges_from(
+            [
+                (mapped[2], mapped[7]),
+                (mapped[2], mapped[7]),
+                (mapped[3], mapped[6]),
+                (mapped[3], mapped[6]),
+            ]
+        )
+        G1.add_node(10)
+        G2.add_node("Z")
+        G1.nodes[10]["label"] = "blue"
+        G2.nodes["Z"]["label"] = "blue"
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Connect the newly added node, to opposite sides of the graph
+        G1.add_edges_from([(10, 1), (10, 5), (10, 8), (10, 10), (10, 10)])
+        G2.add_edges_from(
+            [
+                ("Z", mapped[1]),
+                ("Z", mapped[4]),
+                ("Z", mapped[9]),
+                ("Z", "Z"),
+                ("Z", "Z"),
+            ]
+        )
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # We connected the new node to opposite sides, so G1 must be symmetrical to G2. Re-structure them to be so
+        G1.remove_edges_from([(1, 3), (4, 9), (4, 9), (7, 9)])
+        G2.remove_edges_from(
+            [
+                (mapped[1], mapped[3]),
+                (mapped[4], mapped[9]),
+                (mapped[4], mapped[9]),
+                (mapped[7], mapped[9]),
+            ]
+        )
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Get two subgraphs that are not isomorphic but are easy to make
+        H1 = nx.Graph(G1.subgraph([2, 3, 4, 5, 6, 7, 10]))
+        H2 = nx.Graph(
+            G2.subgraph(
+                [mapped[4], mapped[5], mapped[6], mapped[7], mapped[8], mapped[9], "Z"]
+            )
+        )
+
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert not m
+
+        # Restructure both to make them isomorphic
+        H1.add_edges_from([(10, 2), (10, 6), (3, 6), (2, 7), (2, 6), (3, 7)])
+        H2.add_edges_from(
+            [("Z", mapped[7]), (mapped[6], mapped[9]), (mapped[7], mapped[8])]
+        )
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+        # Remove one self-loop in H2
+        H2.remove_edge("Z", "Z")
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert not m
+
+        # Compensate in H1
+        H1.remove_edge(10, 10)
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+    def test_custom_multigraph3_different_labels(self):
+        G1 = nx.MultiGraph()
+
+        mapped = {1: 9, 2: 8, 3: 7, 4: 6, 5: 3, 8: 5, 9: 4, 7: 1, 6: 2}
+        edges1 = [
+            (1, 2),
+            (1, 3),
+            (1, 3),
+            (2, 3),
+            (2, 3),
+            (3, 4),
+            (4, 5),
+            (4, 7),
+            (4, 9),
+            (4, 9),
+            (4, 9),
+            (5, 8),
+            (5, 8),
+            (8, 9),
+            (8, 9),
+            (5, 6),
+            (6, 7),
+            (6, 7),
+            (6, 7),
+            (5, 2),
+        ]
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label")
+        nx.set_node_attributes(
+            G2,
+            dict(zip([mapped[n] for n in G1], it.cycle(labels_many))),
+            "label",
+        )
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+        assert m == mapped
+
+        # Delete edge maintaining isomorphism
+        G1.remove_edge(4, 9)
+        G2.remove_edge(4, 6)
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+        assert m == mapped
+
+        # Change edge orientation such that G1 mirrors G2
+        G1.add_edges_from([(4, 9), (1, 2), (1, 2)])
+        G1.remove_edges_from([(1, 3), (1, 3)])
+        G2.add_edges_from([(3, 5), (7, 9)])
+        G2.remove_edge(8, 9)
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Make all labels the same, so G1 and G2 are also isomorphic
+        for n1, n2 in zip(G1.nodes(), G2.nodes()):
+            G1.nodes[n1]["label"] = "blue"
+            G2.nodes[n2]["label"] = "blue"
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        G1.add_node(10)
+        G2.add_node("Z")
+        G1.nodes[10]["label"] = "green"
+        G2.nodes["Z"]["label"] = "green"
+
+        # Add different number of edges between the new nodes and themselves
+        G1.add_edges_from([(10, 10), (10, 10)])
+        G2.add_edges_from([("Z", "Z")])
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Make the number of self-edges equal
+        G1.remove_edge(10, 10)
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Connect the new node to the graph
+        G1.add_edges_from([(10, 3), (10, 4)])
+        G2.add_edges_from([("Z", 8), ("Z", 3)])
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Remove central node
+        G1.remove_node(4)
+        G2.remove_node(3)
+        G1.add_edges_from([(5, 6), (5, 6), (5, 7)])
+        G2.add_edges_from([(1, 6), (1, 6), (6, 2)])
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+    def test_custom_multigraph4_same_labels(self):
+        G1 = nx.MultiGraph()
+        edges1 = [
+            (1, 2),
+            (1, 2),
+            (2, 2),
+            (2, 3),
+            (3, 8),
+            (3, 8),
+            (3, 4),
+            (4, 5),
+            (4, 5),
+            (4, 5),
+            (4, 6),
+            (3, 6),
+            (3, 6),
+            (6, 6),
+            (8, 7),
+            (7, 7),
+            (8, 9),
+            (9, 9),
+            (8, 9),
+            (8, 9),
+            (5, 9),
+            (10, 11),
+            (11, 12),
+            (12, 13),
+            (11, 13),
+            (10, 10),
+            (10, 11),
+            (11, 13),
+        ]
+
+        mapped = {
+            1: "n",
+            2: "m",
+            3: "l",
+            4: "j",
+            5: "k",
+            6: "i",
+            7: "g",
+            8: "h",
+            9: "f",
+            10: "b",
+            11: "a",
+            12: "d",
+            13: "e",
+        }
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label")
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Add extra but corresponding edges to both graphs
+        G1.add_edges_from([(2, 2), (2, 3), (2, 8), (3, 4)])
+        G2.add_edges_from([("m", "m"), ("m", "l"), ("m", "h"), ("l", "j")])
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Obtain subgraphs
+        H1 = nx.MultiGraph(G1.subgraph([2, 3, 4, 6, 10, 11, 12, 13]))
+        H2 = nx.MultiGraph(
+            G2.subgraph(
+                [
+                    mapped[2],
+                    mapped[3],
+                    mapped[8],
+                    mapped[9],
+                    mapped[10],
+                    mapped[11],
+                    mapped[12],
+                    mapped[13],
+                ]
+            )
+        )
+
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert not m
+
+        # Make them isomorphic
+        H2.remove_edges_from(
+            [(mapped[3], mapped[2]), (mapped[9], mapped[8]), (mapped[2], mapped[2])]
+        )
+        H2.add_edges_from([(mapped[9], mapped[9]), (mapped[2], mapped[8])])
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+        # Re-structure the disconnected sub-graph
+        H1.remove_node(12)
+        H2.remove_node(mapped[12])
+        H1.add_edge(13, 13)
+        H2.add_edge(mapped[13], mapped[13])
+
+        # Connect the two disconnected components, forming a single graph
+        H1.add_edges_from([(3, 13), (6, 11)])
+        H2.add_edges_from([(mapped[8], mapped[10]), (mapped[2], mapped[11])])
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+        # Change orientation of self-loops in one graph, maintaining the degree sequence
+        H1.remove_edges_from([(2, 2), (3, 6)])
+        H1.add_edges_from([(6, 6), (2, 3)])
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert not m
+
+    def test_custom_multigraph4_different_labels(self):
+        G1 = nx.MultiGraph()
+        edges1 = [
+            (1, 2),
+            (1, 2),
+            (2, 2),
+            (2, 3),
+            (3, 8),
+            (3, 8),
+            (3, 4),
+            (4, 5),
+            (4, 5),
+            (4, 5),
+            (4, 6),
+            (3, 6),
+            (3, 6),
+            (6, 6),
+            (8, 7),
+            (7, 7),
+            (8, 9),
+            (9, 9),
+            (8, 9),
+            (8, 9),
+            (5, 9),
+            (10, 11),
+            (11, 12),
+            (12, 13),
+            (11, 13),
+        ]
+
+        mapped = {
+            1: "n",
+            2: "m",
+            3: "l",
+            4: "j",
+            5: "k",
+            6: "i",
+            7: "g",
+            8: "h",
+            9: "f",
+            10: "b",
+            11: "a",
+            12: "d",
+            13: "e",
+        }
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label")
+        nx.set_node_attributes(
+            G2,
+            dict(zip([mapped[n] for n in G1], it.cycle(labels_many))),
+            "label",
+        )
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m == mapped
+
+        # Add extra but corresponding edges to both graphs
+        G1.add_edges_from([(2, 2), (2, 3), (2, 8), (3, 4)])
+        G2.add_edges_from([("m", "m"), ("m", "l"), ("m", "h"), ("l", "j")])
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m == mapped
+
+        # Obtain isomorphic subgraphs
+        H1 = nx.MultiGraph(G1.subgraph([2, 3, 4, 6]))
+        H2 = nx.MultiGraph(G2.subgraph(["m", "l", "j", "i"]))
+
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+        # Delete the 3-clique, keeping only the path-graph. Also, H1 mirrors H2
+        H1.remove_node(4)
+        H2.remove_node("j")
+        H1.remove_edges_from([(2, 2), (2, 3), (6, 6)])
+        H2.remove_edges_from([("l", "i"), ("m", "m"), ("m", "m")])
+
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert not m
+
+        # Assign the same labels so that mirroring means isomorphic
+        for n1, n2 in zip(H1.nodes(), H2.nodes()):
+            H1.nodes[n1]["label"] = "red"
+            H2.nodes[n2]["label"] = "red"
+
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+        # Leave only one node with self-loop
+        H1.remove_nodes_from([3, 6])
+        H2.remove_nodes_from(["m", "l"])
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+        # Remove one self-loop from H1
+        H1.remove_edge(2, 2)
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert not m
+
+        # Same for H2
+        H2.remove_edge("i", "i")
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+        # Compose H1 with the disconnected sub-graph of G1. Same for H2
+        S1 = nx.compose(H1, nx.MultiGraph(G1.subgraph([10, 11, 12, 13])))
+        S2 = nx.compose(H2, nx.MultiGraph(G2.subgraph(["a", "b", "d", "e"])))
+
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+        # Connect the two components
+        S1.add_edges_from([(13, 13), (13, 13), (2, 13)])
+        S2.add_edges_from([("a", "a"), ("a", "a"), ("i", "e")])
+        m = vf2pp_isomorphism(H1, H2, node_label="label")
+        assert m
+
+    def test_custom_multigraph5_same_labels(self):
+        G1 = nx.MultiGraph()
+
+        edges1 = [
+            (1, 5),
+            (1, 2),
+            (1, 4),
+            (2, 3),
+            (2, 6),
+            (3, 4),
+            (3, 7),
+            (4, 8),
+            (5, 8),
+            (5, 6),
+            (6, 7),
+            (7, 8),
+        ]
+        mapped = {1: "a", 2: "h", 3: "d", 4: "i", 5: "g", 6: "b", 7: "j", 8: "c"}
+
+        G1.add_edges_from(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label")
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Add multiple edges and self-loops, maintaining isomorphism
+        G1.add_edges_from(
+            [(1, 2), (1, 2), (3, 7), (8, 8), (8, 8), (7, 8), (2, 3), (5, 6)]
+        )
+        G2.add_edges_from(
+            [
+                ("a", "h"),
+                ("a", "h"),
+                ("d", "j"),
+                ("c", "c"),
+                ("c", "c"),
+                ("j", "c"),
+                ("d", "h"),
+                ("g", "b"),
+            ]
+        )
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Make G2 to be the rotated G1
+        G2.remove_edges_from(
+            [
+                ("a", "h"),
+                ("a", "h"),
+                ("d", "j"),
+                ("c", "c"),
+                ("c", "c"),
+                ("j", "c"),
+                ("d", "h"),
+                ("g", "b"),
+            ]
+        )
+        G2.add_edges_from(
+            [
+                ("d", "i"),
+                ("a", "h"),
+                ("g", "b"),
+                ("g", "b"),
+                ("i", "i"),
+                ("i", "i"),
+                ("b", "j"),
+                ("d", "j"),
+            ]
+        )
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+    def test_disconnected_multigraph_all_same_labels(self):
+        G1 = nx.MultiGraph()
+        G1.add_nodes_from(list(range(10)))
+        G1.add_edges_from([(i, i) for i in range(10)])
+
+        mapped = {0: 9, 1: 8, 2: 7, 3: 6, 4: 5, 5: 4, 6: 3, 7: 2, 8: 1, 9: 0}
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_same))), "label")
+        nx.set_node_attributes(G2, dict(zip(G2, it.cycle(labels_same))), "label")
+
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Add self-loops to non-mapped nodes. Should be the same, as the graph is disconnected.
+        G1.add_edges_from([(i, i) for i in range(5, 8)] * 3)
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Compensate in G2
+        G2.add_edges_from([(i, i) for i in range(3)] * 3)
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+        # Add one more self-loop in G2
+        G2.add_edges_from([(0, 0), (1, 1), (1, 1)])
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Compensate in G1
+        G1.add_edges_from([(5, 5), (7, 7), (7, 7)])
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+    def test_disconnected_multigraph_all_different_labels(self):
+        G1 = nx.MultiGraph()
+        G1.add_nodes_from(list(range(10)))
+        G1.add_edges_from([(i, i) for i in range(10)])
+
+        mapped = {0: 9, 1: 8, 2: 7, 3: 6, 4: 5, 5: 4, 6: 3, 7: 2, 8: 1, 9: 0}
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        nx.set_node_attributes(G1, dict(zip(G1, it.cycle(labels_many))), "label")
+        nx.set_node_attributes(
+            G2,
+            dict(zip([mapped[n] for n in G1], it.cycle(labels_many))),
+            "label",
+        )
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+        assert m == mapped
+
+        # Add self-loops to non-mapped nodes. Now it is not the same, as there are different labels
+        G1.add_edges_from([(i, i) for i in range(5, 8)] * 3)
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Add self-loops to non mapped nodes in G2 as well
+        G2.add_edges_from([(mapped[i], mapped[i]) for i in range(3)] * 7)
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Add self-loops to mapped nodes in G2
+        G2.add_edges_from([(mapped[i], mapped[i]) for i in range(5, 8)] * 3)
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert not m
+
+        # Add self-loops to G1 so that they are even in both graphs
+        G1.add_edges_from([(i, i) for i in range(3)] * 7)
+        m = vf2pp_isomorphism(G1, G2, node_label="label")
+        assert m
+
+
+class TestDiGraphISOVF2pp:
+    def test_wikipedia_graph(self):
+        edges1 = [
+            (1, 5),
+            (1, 2),
+            (1, 4),
+            (3, 2),
+            (6, 2),
+            (3, 4),
+            (7, 3),
+            (4, 8),
+            (5, 8),
+            (6, 5),
+            (6, 7),
+            (7, 8),
+        ]
+        mapped = {1: "a", 2: "h", 3: "d", 4: "i", 5: "g", 6: "b", 7: "j", 8: "c"}
+
+        G1 = nx.DiGraph(edges1)
+        G2 = nx.relabel_nodes(G1, mapped)
+
+        assert vf2pp_isomorphism(G1, G2) == mapped
+
+        # Change the direction of an edge
+        G1.remove_edge(1, 5)
+        G1.add_edge(5, 1)
+        assert vf2pp_isomorphism(G1, G2) is None
+
+    def test_non_isomorphic_same_degree_sequence(self):
+        r"""
+                G1                           G2
+        x--------------x              x--------------x
+        | \            |              | \            |
+        |  x-------x   |              |  x-------x   |
+        |  |       |   |              |  |       |   |
+        |  x-------x   |              |  x-------x   |
+        | /            |              |            \ |
+        x--------------x              x--------------x
+        """
+        edges1 = [
+            (1, 5),
+            (1, 2),
+            (4, 1),
+            (3, 2),
+            (3, 4),
+            (4, 8),
+            (5, 8),
+            (6, 5),
+            (6, 7),
+            (7, 8),
+        ]
+        edges2 = [
+            (1, 5),
+            (1, 2),
+            (4, 1),
+            (3, 2),
+            (4, 3),
+            (5, 8),
+            (6, 5),
+            (6, 7),
+            (3, 7),
+            (8, 7),
+        ]
+
+        G1 = nx.DiGraph(edges1)
+        G2 = nx.DiGraph(edges2)
+        assert vf2pp_isomorphism(G1, G2) is None

wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/tests/test_vf2userfunc.py

@@ -0,0 +1,200 @@
+"""
+Tests for VF2 isomorphism algorithm for weighted graphs.
+"""
+
+import math
+from operator import eq
+
+import networkx as nx
+import networkx.algorithms.isomorphism as iso
+
+
+def test_simple():
+    # 16 simple tests
+    w = "weight"
+    edges = [(0, 0, 1), (0, 0, 1.5), (0, 1, 2), (1, 0, 3)]
+    for g1 in [nx.Graph(), nx.DiGraph(), nx.MultiGraph(), nx.MultiDiGraph()]:
+        g1.add_weighted_edges_from(edges)
+        g2 = g1.subgraph(g1.nodes())
+        if g1.is_multigraph():
+            em = iso.numerical_multiedge_match("weight", 1)
+        else:
+            em = iso.numerical_edge_match("weight", 1)
+        assert nx.is_isomorphic(g1, g2, edge_match=em)
+
+        for mod1, mod2 in [(False, True), (True, False), (True, True)]:
+            # mod1 tests a regular edge
+            # mod2 tests a selfloop
+            if g2.is_multigraph():
+                if mod1:
+                    data1 = {0: {"weight": 10}}
+                if mod2:
+                    data2 = {0: {"weight": 1}, 1: {"weight": 2.5}}
+            else:
+                if mod1:
+                    data1 = {"weight": 10}
+                if mod2:
+                    data2 = {"weight": 2.5}
+
+            g2 = g1.subgraph(g1.nodes()).copy()
+            if mod1:
+                if not g1.is_directed():
+                    g2._adj[1][0] = data1
+                    g2._adj[0][1] = data1
+                else:
+                    g2._succ[1][0] = data1
+                    g2._pred[0][1] = data1
+            if mod2:
+                if not g1.is_directed():
+                    g2._adj[0][0] = data2
+                else:
+                    g2._succ[0][0] = data2
+                    g2._pred[0][0] = data2
+
+            assert not nx.is_isomorphic(g1, g2, edge_match=em)
+
+
+def test_weightkey():
+    g1 = nx.DiGraph()
+    g2 = nx.DiGraph()
+
+    g1.add_edge("A", "B", weight=1)
+    g2.add_edge("C", "D", weight=0)
+
+    assert nx.is_isomorphic(g1, g2)
+    em = iso.numerical_edge_match("nonexistent attribute", 1)
+    assert nx.is_isomorphic(g1, g2, edge_match=em)
+    em = iso.numerical_edge_match("weight", 1)
+    assert not nx.is_isomorphic(g1, g2, edge_match=em)
+
+    g2 = nx.DiGraph()
+    g2.add_edge("C", "D")
+    assert nx.is_isomorphic(g1, g2, edge_match=em)
+
+
+class TestNodeMatch_Graph:
+    def setup_method(self):
+        self.g1 = nx.Graph()
+        self.g2 = nx.Graph()
+        self.build()
+
+    def build(self):
+        self.nm = iso.categorical_node_match("color", "")
+        self.em = iso.numerical_edge_match("weight", 1)
+
+        self.g1.add_node("A", color="red")
+        self.g2.add_node("C", color="blue")
+
+        self.g1.add_edge("A", "B", weight=1)
+        self.g2.add_edge("C", "D", weight=1)
+
+    def test_noweight_nocolor(self):
+        assert nx.is_isomorphic(self.g1, self.g2)
+
+    def test_color1(self):
+        assert not nx.is_isomorphic(self.g1, self.g2, node_match=self.nm)
+
+    def test_color2(self):
+        self.g1.nodes["A"]["color"] = "blue"
+        assert nx.is_isomorphic(self.g1, self.g2, node_match=self.nm)
+
+    def test_weight1(self):
+        assert nx.is_isomorphic(self.g1, self.g2, edge_match=self.em)
+
+    def test_weight2(self):
+        self.g1.add_edge("A", "B", weight=2)
+        assert not nx.is_isomorphic(self.g1, self.g2, edge_match=self.em)
+
+    def test_colorsandweights1(self):
+        iso = nx.is_isomorphic(self.g1, self.g2, node_match=self.nm, edge_match=self.em)
+        assert not iso
+
+    def test_colorsandweights2(self):
+        self.g1.nodes["A"]["color"] = "blue"
+        iso = nx.is_isomorphic(self.g1, self.g2, node_match=self.nm, edge_match=self.em)
+        assert iso
+
+    def test_colorsandweights3(self):
+        # make the weights disagree
+        self.g1.add_edge("A", "B", weight=2)
+        assert not nx.is_isomorphic(
+            self.g1, self.g2, node_match=self.nm, edge_match=self.em
+        )
+
+
+class TestEdgeMatch_MultiGraph:
+    def setup_method(self):
+        self.g1 = nx.MultiGraph()
+        self.g2 = nx.MultiGraph()
+        self.GM = iso.MultiGraphMatcher
+        self.build()
+
+    def build(self):
+        g1 = self.g1
+        g2 = self.g2
+
+        # We will assume integer weights only.
+        g1.add_edge("A", "B", color="green", weight=0, size=0.5)
+        g1.add_edge("A", "B", color="red", weight=1, size=0.35)
+        g1.add_edge("A", "B", color="red", weight=2, size=0.65)
+
+        g2.add_edge("C", "D", color="green", weight=1, size=0.5)
+        g2.add_edge("C", "D", color="red", weight=0, size=0.45)
+        g2.add_edge("C", "D", color="red", weight=2, size=0.65)
+
+        if g1.is_multigraph():
+            self.em = iso.numerical_multiedge_match("weight", 1)
+            self.emc = iso.categorical_multiedge_match("color", "")
+            self.emcm = iso.categorical_multiedge_match(["color", "weight"], ["", 1])
+            self.emg1 = iso.generic_multiedge_match("color", "red", eq)
+            self.emg2 = iso.generic_multiedge_match(
+                ["color", "weight", "size"],
+                ["red", 1, 0.5],
+                [eq, eq, math.isclose],
+            )
+        else:
+            self.em = iso.numerical_edge_match("weight", 1)
+            self.emc = iso.categorical_edge_match("color", "")
+            self.emcm = iso.categorical_edge_match(["color", "weight"], ["", 1])
+            self.emg1 = iso.generic_multiedge_match("color", "red", eq)
+            self.emg2 = iso.generic_edge_match(
+                ["color", "weight", "size"],
+                ["red", 1, 0.5],
+                [eq, eq, math.isclose],
+            )
+
+    def test_weights_only(self):
+        assert nx.is_isomorphic(self.g1, self.g2, edge_match=self.em)
+
+    def test_colors_only(self):
+        gm = self.GM(self.g1, self.g2, edge_match=self.emc)
+        assert gm.is_isomorphic()
+
+    def test_colorsandweights(self):
+        gm = self.GM(self.g1, self.g2, edge_match=self.emcm)
+        assert not gm.is_isomorphic()
+
+    def test_generic1(self):
+        gm = self.GM(self.g1, self.g2, edge_match=self.emg1)
+        assert gm.is_isomorphic()
+
+    def test_generic2(self):
+        gm = self.GM(self.g1, self.g2, edge_match=self.emg2)
+        assert not gm.is_isomorphic()
+
+
+class TestEdgeMatch_DiGraph(TestNodeMatch_Graph):
+    def setup_method(self):
+        TestNodeMatch_Graph.setup_method(self)
+        self.g1 = nx.DiGraph()
+        self.g2 = nx.DiGraph()
+        self.build()
+
+
+class TestEdgeMatch_MultiDiGraph(TestEdgeMatch_MultiGraph):
+    def setup_method(self):
+        TestEdgeMatch_MultiGraph.setup_method(self)
+        self.g1 = nx.MultiDiGraph()
+        self.g2 = nx.MultiDiGraph()
+        self.GM = iso.MultiDiGraphMatcher
+        self.build()

wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/vf2pp.py

@@ -0,0 +1,1075 @@
+"""
+***************
+VF2++ Algorithm
+***************
+
+An implementation of the VF2++ algorithm [1]_ for Graph Isomorphism testing.
+
+The simplest interface to use this module is to call:
+
+`vf2pp_is_isomorphic`: to check whether two graphs are isomorphic.
+`vf2pp_isomorphism`: to obtain the node mapping between two graphs,
+in case they are isomorphic.
+`vf2pp_all_isomorphisms`: to generate all possible mappings between two graphs,
+if isomorphic.
+
+Introduction
+------------
+The VF2++ algorithm, follows a similar logic to that of VF2, while also
+introducing new easy-to-check cutting rules and determining the optimal access
+order of nodes. It is also implemented in a non-recursive manner, which saves
+both time and space, when compared to its previous counterpart.
+
+The optimal node ordering is obtained after taking into consideration both the
+degree but also the label rarity of each node.
+This way we place the nodes that are more likely to match, first in the order,
+thus examining the most promising branches in the beginning.
+The rules also consider node labels, making it easier to prune unfruitful
+branches early in the process.
+
+Examples
+--------
+
+Suppose G1 and G2 are Isomorphic Graphs. Verification is as follows:
+
+Without node labels:
+
+>>> import networkx as nx
+>>> G1 = nx.path_graph(4)
+>>> G2 = nx.path_graph(4)
+>>> nx.vf2pp_is_isomorphic(G1, G2, node_label=None)
+True
+>>> nx.vf2pp_isomorphism(G1, G2, node_label=None)
+{1: 1, 2: 2, 0: 0, 3: 3}
+
+With node labels:
+
+>>> G1 = nx.path_graph(4)
+>>> G2 = nx.path_graph(4)
+>>> mapped = {1: 1, 2: 2, 3: 3, 0: 0}
+>>> nx.set_node_attributes(
+...     G1, dict(zip(G1, ["blue", "red", "green", "yellow"])), "label"
+... )
+>>> nx.set_node_attributes(
+...     G2,
+...     dict(zip([mapped[u] for u in G1], ["blue", "red", "green", "yellow"])),
+...     "label",
+... )
+>>> nx.vf2pp_is_isomorphic(G1, G2, node_label="label")
+True
+>>> nx.vf2pp_isomorphism(G1, G2, node_label="label")
+{1: 1, 2: 2, 0: 0, 3: 3}
+
+References
+----------
+.. [1] Jüttner, Alpár & Madarasi, Péter. (2018). "VF2++—An improved subgraph
+   isomorphism algorithm". Discrete Applied Mathematics. 242.
+   https://doi.org/10.1016/j.dam.2018.02.018
+
+"""
+
+import collections
+
+import networkx as nx
+
+__all__ = ["vf2pp_isomorphism", "vf2pp_is_isomorphic", "vf2pp_all_isomorphisms"]
+
+_GraphParameters = collections.namedtuple(
+    "_GraphParameters",
+    [
+        "G1",
+        "G2",
+        "G1_labels",
+        "G2_labels",
+        "nodes_of_G1Labels",
+        "nodes_of_G2Labels",
+        "G2_nodes_of_degree",
+    ],
+)
+
+_StateParameters = collections.namedtuple(
+    "_StateParameters",
+    [
+        "mapping",
+        "reverse_mapping",
+        "T1",
+        "T1_in",
+        "T1_tilde",
+        "T1_tilde_in",
+        "T2",
+        "T2_in",
+        "T2_tilde",
+        "T2_tilde_in",
+    ],
+)
+
+
+@nx._dispatchable(graphs={"G1": 0, "G2": 1}, node_attrs={"node_label": "default_label"})
+def vf2pp_isomorphism(G1, G2, node_label=None, default_label=None):
+    """Return an isomorphic mapping between `G1` and `G2` if it exists.
+
+    Parameters
+    ----------
+    G1, G2 : NetworkX Graph or MultiGraph instances.
+        The two graphs to check for isomorphism.
+
+    node_label : str, optional
+        The name of the node attribute to be used when comparing nodes.
+        The default is `None`, meaning node attributes are not considered
+        in the comparison. Any node that doesn't have the `node_label`
+        attribute uses `default_label` instead.
+
+    default_label : scalar
+        Default value to use when a node doesn't have an attribute
+        named `node_label`. Default is `None`.
+
+    Returns
+    -------
+    dict or None
+        Node mapping if the two graphs are isomorphic. None otherwise.
+    """
+    try:
+        mapping = next(vf2pp_all_isomorphisms(G1, G2, node_label, default_label))
+        return mapping
+    except StopIteration:
+        return None
+
+
+@nx._dispatchable(graphs={"G1": 0, "G2": 1}, node_attrs={"node_label": "default_label"})
+def vf2pp_is_isomorphic(G1, G2, node_label=None, default_label=None):
+    """Examines whether G1 and G2 are isomorphic.
+
+    Parameters
+    ----------
+    G1, G2 : NetworkX Graph or MultiGraph instances.
+        The two graphs to check for isomorphism.
+
+    node_label : str, optional
+        The name of the node attribute to be used when comparing nodes.
+        The default is `None`, meaning node attributes are not considered
+        in the comparison. Any node that doesn't have the `node_label`
+        attribute uses `default_label` instead.
+
+    default_label : scalar
+        Default value to use when a node doesn't have an attribute
+        named `node_label`. Default is `None`.
+
+    Returns
+    -------
+    bool
+        True if the two graphs are isomorphic, False otherwise.
+    """
+    if vf2pp_isomorphism(G1, G2, node_label, default_label) is not None:
+        return True
+    return False
+
+
+@nx._dispatchable(graphs={"G1": 0, "G2": 1}, node_attrs={"node_label": "default_label"})
+def vf2pp_all_isomorphisms(G1, G2, node_label=None, default_label=None):
+    """Yields all the possible mappings between G1 and G2.
+
+    Parameters
+    ----------
+    G1, G2 : NetworkX Graph or MultiGraph instances.
+        The two graphs to check for isomorphism.
+
+    node_label : str, optional
+        The name of the node attribute to be used when comparing nodes.
+        The default is `None`, meaning node attributes are not considered
+        in the comparison. Any node that doesn't have the `node_label`
+        attribute uses `default_label` instead.
+
+    default_label : scalar
+        Default value to use when a node doesn't have an attribute
+        named `node_label`. Default is `None`.
+
+    Yields
+    ------
+    dict
+        Isomorphic mapping between the nodes in `G1` and `G2`.
+    """
+    if G1.number_of_nodes() == 0 or G2.number_of_nodes() == 0:
+        return False
+
+    # Create the degree dicts based on graph type
+    if G1.is_directed():
+        G1_degree = {
+            n: (in_degree, out_degree)
+            for (n, in_degree), (_, out_degree) in zip(G1.in_degree, G1.out_degree)
+        }
+        G2_degree = {
+            n: (in_degree, out_degree)
+            for (n, in_degree), (_, out_degree) in zip(G2.in_degree, G2.out_degree)
+        }
+    else:
+        G1_degree = dict(G1.degree)
+        G2_degree = dict(G2.degree)
+
+    if not G1.is_directed():
+        find_candidates = _find_candidates
+        restore_Tinout = _restore_Tinout
+    else:
+        find_candidates = _find_candidates_Di
+        restore_Tinout = _restore_Tinout_Di
+
+    # Check that both graphs have the same number of nodes and degree sequence
+    if G1.order() != G2.order():
+        return False
+    if sorted(G1_degree.values()) != sorted(G2_degree.values()):
+        return False
+
+    # Initialize parameters and cache necessary information about degree and labels
+    graph_params, state_params = _initialize_parameters(
+        G1, G2, G2_degree, node_label, default_label
+    )
+
+    # Check if G1 and G2 have the same labels, and that number of nodes per label is equal between the two graphs
+    if not _precheck_label_properties(graph_params):
+        return False
+
+    # Calculate the optimal node ordering
+    node_order = _matching_order(graph_params)
+
+    # Initialize the stack
+    stack = []
+    candidates = iter(
+        find_candidates(node_order[0], graph_params, state_params, G1_degree)
+    )
+    stack.append((node_order[0], candidates))
+
+    mapping = state_params.mapping
+    reverse_mapping = state_params.reverse_mapping
+
+    # Index of the node from the order, currently being examined
+    matching_node = 1
+
+    while stack:
+        current_node, candidate_nodes = stack[-1]
+
+        try:
+            candidate = next(candidate_nodes)
+        except StopIteration:
+            # If no remaining candidates, return to a previous state, and follow another branch
+            stack.pop()
+            matching_node -= 1
+            if stack:
+                # Pop the previously added u-v pair, and look for a different candidate _v for u
+                popped_node1, _ = stack[-1]
+                popped_node2 = mapping[popped_node1]
+                mapping.pop(popped_node1)
+                reverse_mapping.pop(popped_node2)
+                restore_Tinout(popped_node1, popped_node2, graph_params, state_params)
+            continue
+
+        if _feasibility(current_node, candidate, graph_params, state_params):
+            # Terminate if mapping is extended to its full
+            if len(mapping) == G2.number_of_nodes() - 1:
+                cp_mapping = mapping.copy()
+                cp_mapping[current_node] = candidate
+                yield cp_mapping
+                continue
+
+            # Feasibility rules pass, so extend the mapping and update the parameters
+            mapping[current_node] = candidate
+            reverse_mapping[candidate] = current_node
+            _update_Tinout(current_node, candidate, graph_params, state_params)
+            # Append the next node and its candidates to the stack
+            candidates = iter(
+                find_candidates(
+                    node_order[matching_node], graph_params, state_params, G1_degree
+                )
+            )
+            stack.append((node_order[matching_node], candidates))
+            matching_node += 1
+
+
+def _precheck_label_properties(graph_params):
+    G1, G2, G1_labels, G2_labels, nodes_of_G1Labels, nodes_of_G2Labels, _ = graph_params
+    if any(
+        label not in nodes_of_G1Labels or len(nodes_of_G1Labels[label]) != len(nodes)
+        for label, nodes in nodes_of_G2Labels.items()
+    ):
+        return False
+    return True
+
+
+def _initialize_parameters(G1, G2, G2_degree, node_label=None, default_label=-1):
+    """Initializes all the necessary parameters for VF2++
+
+    Parameters
+    ----------
+    G1,G2: NetworkX Graph or MultiGraph instances.
+        The two graphs to check for isomorphism or monomorphism
+
+    G1_labels,G2_labels: dict
+        The label of every node in G1 and G2 respectively
+
+    Returns
+    -------
+    graph_params: namedtuple
+        Contains all the Graph-related parameters:
+
+        G1,G2
+        G1_labels,G2_labels: dict
+
+    state_params: namedtuple
+        Contains all the State-related parameters:
+
+        mapping: dict
+            The mapping as extended so far. Maps nodes of G1 to nodes of G2
+
+        reverse_mapping: dict
+            The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed
+
+        T1, T2: set
+            Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are
+            neighbors of nodes that are.
+
+        T1_out, T2_out: set
+            Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti
+    """
+    G1_labels = dict(G1.nodes(data=node_label, default=default_label))
+    G2_labels = dict(G2.nodes(data=node_label, default=default_label))
+
+    graph_params = _GraphParameters(
+        G1,
+        G2,
+        G1_labels,
+        G2_labels,
+        nx.utils.groups(G1_labels),
+        nx.utils.groups(G2_labels),
+        nx.utils.groups(G2_degree),
+    )
+
+    T1, T1_in = set(), set()
+    T2, T2_in = set(), set()
+    if G1.is_directed():
+        T1_tilde, T1_tilde_in = (
+            set(G1.nodes()),
+            set(),
+        )  # todo: do we need Ti_tilde_in? What nodes does it have?
+        T2_tilde, T2_tilde_in = set(G2.nodes()), set()
+    else:
+        T1_tilde, T1_tilde_in = set(G1.nodes()), set()
+        T2_tilde, T2_tilde_in = set(G2.nodes()), set()
+
+    state_params = _StateParameters(
+        {},
+        {},
+        T1,
+        T1_in,
+        T1_tilde,
+        T1_tilde_in,
+        T2,
+        T2_in,
+        T2_tilde,
+        T2_tilde_in,
+    )
+
+    return graph_params, state_params
+
+
+def _matching_order(graph_params):
+    """The node ordering as introduced in VF2++.
+
+    Notes
+    -----
+    Taking into account the structure of the Graph and the node labeling, the nodes are placed in an order such that,
+    most of the unfruitful/infeasible branches of the search space can be pruned on high levels, significantly
+    decreasing the number of visited states. The premise is that, the algorithm will be able to recognize
+    inconsistencies early, proceeding to go deep into the search tree only if it's needed.
+
+    Parameters
+    ----------
+    graph_params: namedtuple
+        Contains:
+
+            G1,G2: NetworkX Graph or MultiGraph instances.
+                The two graphs to check for isomorphism or monomorphism.
+
+            G1_labels,G2_labels: dict
+                The label of every node in G1 and G2 respectively.
+
+    Returns
+    -------
+    node_order: list
+        The ordering of the nodes.
+    """
+    G1, G2, G1_labels, _, _, nodes_of_G2Labels, _ = graph_params
+    if not G1 and not G2:
+        return {}
+
+    if G1.is_directed():
+        G1 = G1.to_undirected(as_view=True)
+
+    V1_unordered = set(G1.nodes())
+    label_rarity = {label: len(nodes) for label, nodes in nodes_of_G2Labels.items()}
+    used_degrees = {node: 0 for node in G1}
+    node_order = []
+
+    while V1_unordered:
+        max_rarity = min(label_rarity[G1_labels[x]] for x in V1_unordered)
+        rarest_nodes = [
+            n for n in V1_unordered if label_rarity[G1_labels[n]] == max_rarity
+        ]
+        max_node = max(rarest_nodes, key=G1.degree)
+
+        for dlevel_nodes in nx.bfs_layers(G1, max_node):
+            nodes_to_add = dlevel_nodes.copy()
+            while nodes_to_add:
+                max_used_degree = max(used_degrees[n] for n in nodes_to_add)
+                max_used_degree_nodes = [
+                    n for n in nodes_to_add if used_degrees[n] == max_used_degree
+                ]
+                max_degree = max(G1.degree[n] for n in max_used_degree_nodes)
+                max_degree_nodes = [
+                    n for n in max_used_degree_nodes if G1.degree[n] == max_degree
+                ]
+                next_node = min(
+                    max_degree_nodes, key=lambda x: label_rarity[G1_labels[x]]
+                )
+
+                node_order.append(next_node)
+                for node in G1.neighbors(next_node):
+                    used_degrees[node] += 1
+
+                nodes_to_add.remove(next_node)
+                label_rarity[G1_labels[next_node]] -= 1
+                V1_unordered.discard(next_node)
+
+    return node_order
+
+
+def _find_candidates(
+    u, graph_params, state_params, G1_degree
+):  # todo: make the 4th argument the degree of u
+    """Given node u of G1, finds the candidates of u from G2.
+
+    Parameters
+    ----------
+    u: Graph node
+        The node from G1 for which to find the candidates from G2.
+
+    graph_params: namedtuple
+        Contains all the Graph-related parameters:
+
+        G1,G2: NetworkX Graph or MultiGraph instances.
+            The two graphs to check for isomorphism or monomorphism
+
+        G1_labels,G2_labels: dict
+            The label of every node in G1 and G2 respectively
+
+    state_params: namedtuple
+        Contains all the State-related parameters:
+
+        mapping: dict
+            The mapping as extended so far. Maps nodes of G1 to nodes of G2
+
+        reverse_mapping: dict
+            The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed
+
+        T1, T2: set
+            Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are
+            neighbors of nodes that are.
+
+        T1_tilde, T2_tilde: set
+            Ti_tilde contains all the nodes from Gi, that are neither in the mapping nor in Ti
+
+    Returns
+    -------
+    candidates: set
+        The nodes from G2 which are candidates for u.
+    """
+    G1, G2, G1_labels, _, _, nodes_of_G2Labels, G2_nodes_of_degree = graph_params
+    mapping, reverse_mapping, _, _, _, _, _, _, T2_tilde, _ = state_params
+
+    covered_nbrs = [nbr for nbr in G1[u] if nbr in mapping]
+    if not covered_nbrs:
+        candidates = set(nodes_of_G2Labels[G1_labels[u]])
+        candidates.intersection_update(G2_nodes_of_degree[G1_degree[u]])
+        candidates.intersection_update(T2_tilde)
+        candidates.difference_update(reverse_mapping)
+        if G1.is_multigraph():
+            candidates.difference_update(
+                {
+                    node
+                    for node in candidates
+                    if G1.number_of_edges(u, u) != G2.number_of_edges(node, node)
+                }
+            )
+        return candidates
+
+    nbr1 = covered_nbrs[0]
+    common_nodes = set(G2[mapping[nbr1]])
+
+    for nbr1 in covered_nbrs[1:]:
+        common_nodes.intersection_update(G2[mapping[nbr1]])
+
+    common_nodes.difference_update(reverse_mapping)
+    common_nodes.intersection_update(G2_nodes_of_degree[G1_degree[u]])
+    common_nodes.intersection_update(nodes_of_G2Labels[G1_labels[u]])
+    if G1.is_multigraph():
+        common_nodes.difference_update(
+            {
+                node
+                for node in common_nodes
+                if G1.number_of_edges(u, u) != G2.number_of_edges(node, node)
+            }
+        )
+    return common_nodes
+
+
+def _find_candidates_Di(u, graph_params, state_params, G1_degree):
+    G1, G2, G1_labels, _, _, nodes_of_G2Labels, G2_nodes_of_degree = graph_params
+    mapping, reverse_mapping, _, _, _, _, _, _, T2_tilde, _ = state_params
+
+    covered_successors = [succ for succ in G1[u] if succ in mapping]
+    covered_predecessors = [pred for pred in G1.pred[u] if pred in mapping]
+
+    if not (covered_successors or covered_predecessors):
+        candidates = set(nodes_of_G2Labels[G1_labels[u]])
+        candidates.intersection_update(G2_nodes_of_degree[G1_degree[u]])
+        candidates.intersection_update(T2_tilde)
+        candidates.difference_update(reverse_mapping)
+        if G1.is_multigraph():
+            candidates.difference_update(
+                {
+                    node
+                    for node in candidates
+                    if G1.number_of_edges(u, u) != G2.number_of_edges(node, node)
+                }
+            )
+        return candidates
+
+    if covered_successors:
+        succ1 = covered_successors[0]
+        common_nodes = set(G2.pred[mapping[succ1]])
+
+        for succ1 in covered_successors[1:]:
+            common_nodes.intersection_update(G2.pred[mapping[succ1]])
+    else:
+        pred1 = covered_predecessors.pop()
+        common_nodes = set(G2[mapping[pred1]])
+
+    for pred1 in covered_predecessors:
+        common_nodes.intersection_update(G2[mapping[pred1]])
+
+    common_nodes.difference_update(reverse_mapping)
+    common_nodes.intersection_update(G2_nodes_of_degree[G1_degree[u]])
+    common_nodes.intersection_update(nodes_of_G2Labels[G1_labels[u]])
+    if G1.is_multigraph():
+        common_nodes.difference_update(
+            {
+                node
+                for node in common_nodes
+                if G1.number_of_edges(u, u) != G2.number_of_edges(node, node)
+            }
+        )
+    return common_nodes
+
+
+def _feasibility(node1, node2, graph_params, state_params):
+    """Given a candidate pair of nodes u and v from G1 and G2 respectively, checks if it's feasible to extend the
+    mapping, i.e. if u and v can be matched.
+
+    Notes
+    -----
+    This function performs all the necessary checking by applying both consistency and cutting rules.
+
+    Parameters
+    ----------
+    node1, node2: Graph node
+        The candidate pair of nodes being checked for matching
+
+    graph_params: namedtuple
+        Contains all the Graph-related parameters:
+
+        G1,G2: NetworkX Graph or MultiGraph instances.
+            The two graphs to check for isomorphism or monomorphism
+
+        G1_labels,G2_labels: dict
+            The label of every node in G1 and G2 respectively
+
+    state_params: namedtuple
+        Contains all the State-related parameters:
+
+        mapping: dict
+            The mapping as extended so far. Maps nodes of G1 to nodes of G2
+
+        reverse_mapping: dict
+            The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed
+
+        T1, T2: set
+            Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are
+            neighbors of nodes that are.
+
+        T1_out, T2_out: set
+            Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti
+
+    Returns
+    -------
+    True if all checks are successful, False otherwise.
+    """
+    G1 = graph_params.G1
+
+    if _cut_PT(node1, node2, graph_params, state_params):
+        return False
+
+    if G1.is_multigraph():
+        if not _consistent_PT(node1, node2, graph_params, state_params):
+            return False
+
+    return True
+
+
+def _cut_PT(u, v, graph_params, state_params):
+    """Implements the cutting rules for the ISO problem.
+
+    Parameters
+    ----------
+    u, v: Graph node
+        The two candidate nodes being examined.
+
+    graph_params: namedtuple
+        Contains all the Graph-related parameters:
+
+        G1,G2: NetworkX Graph or MultiGraph instances.
+            The two graphs to check for isomorphism or monomorphism
+
+        G1_labels,G2_labels: dict
+            The label of every node in G1 and G2 respectively
+
+    state_params: namedtuple
+        Contains all the State-related parameters:
+
+        mapping: dict
+            The mapping as extended so far. Maps nodes of G1 to nodes of G2
+
+        reverse_mapping: dict
+            The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed
+
+        T1, T2: set
+            Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are
+            neighbors of nodes that are.
+
+        T1_tilde, T2_tilde: set
+            Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti
+
+    Returns
+    -------
+    True if we should prune this branch, i.e. the node pair failed the cutting checks. False otherwise.
+    """
+    G1, G2, G1_labels, G2_labels, _, _, _ = graph_params
+    (
+        _,
+        _,
+        T1,
+        T1_in,
+        T1_tilde,
+        _,
+        T2,
+        T2_in,
+        T2_tilde,
+        _,
+    ) = state_params
+
+    u_labels_predecessors, v_labels_predecessors = {}, {}
+    if G1.is_directed():
+        u_labels_predecessors = nx.utils.groups(
+            {n1: G1_labels[n1] for n1 in G1.pred[u]}
+        )
+        v_labels_predecessors = nx.utils.groups(
+            {n2: G2_labels[n2] for n2 in G2.pred[v]}
+        )
+
+        if set(u_labels_predecessors.keys()) != set(v_labels_predecessors.keys()):
+            return True
+
+    u_labels_successors = nx.utils.groups({n1: G1_labels[n1] for n1 in G1[u]})
+    v_labels_successors = nx.utils.groups({n2: G2_labels[n2] for n2 in G2[v]})
+
+    # if the neighbors of u, do not have the same labels as those of v, NOT feasible.
+    if set(u_labels_successors.keys()) != set(v_labels_successors.keys()):
+        return True
+
+    for label, G1_nbh in u_labels_successors.items():
+        G2_nbh = v_labels_successors[label]
+
+        if G1.is_multigraph():
+            # Check for every neighbor in the neighborhood, if u-nbr1 has same edges as v-nbr2
+            u_nbrs_edges = sorted(G1.number_of_edges(u, x) for x in G1_nbh)
+            v_nbrs_edges = sorted(G2.number_of_edges(v, x) for x in G2_nbh)
+            if any(
+                u_nbr_edges != v_nbr_edges
+                for u_nbr_edges, v_nbr_edges in zip(u_nbrs_edges, v_nbrs_edges)
+            ):
+                return True
+
+        if len(T1.intersection(G1_nbh)) != len(T2.intersection(G2_nbh)):
+            return True
+        if len(T1_tilde.intersection(G1_nbh)) != len(T2_tilde.intersection(G2_nbh)):
+            return True
+        if G1.is_directed() and len(T1_in.intersection(G1_nbh)) != len(
+            T2_in.intersection(G2_nbh)
+        ):
+            return True
+
+    if not G1.is_directed():
+        return False
+
+    for label, G1_pred in u_labels_predecessors.items():
+        G2_pred = v_labels_predecessors[label]
+
+        if G1.is_multigraph():
+            # Check for every neighbor in the neighborhood, if u-nbr1 has same edges as v-nbr2
+            u_pred_edges = sorted(G1.number_of_edges(u, x) for x in G1_pred)
+            v_pred_edges = sorted(G2.number_of_edges(v, x) for x in G2_pred)
+            if any(
+                u_nbr_edges != v_nbr_edges
+                for u_nbr_edges, v_nbr_edges in zip(u_pred_edges, v_pred_edges)
+            ):
+                return True
+
+        if len(T1.intersection(G1_pred)) != len(T2.intersection(G2_pred)):
+            return True
+        if len(T1_tilde.intersection(G1_pred)) != len(T2_tilde.intersection(G2_pred)):
+            return True
+        if len(T1_in.intersection(G1_pred)) != len(T2_in.intersection(G2_pred)):
+            return True
+
+    return False
+
+
+def _consistent_PT(u, v, graph_params, state_params):
+    """Checks the consistency of extending the mapping using the current node pair.
+
+    Parameters
+    ----------
+    u, v: Graph node
+        The two candidate nodes being examined.
+
+    graph_params: namedtuple
+        Contains all the Graph-related parameters:
+
+        G1,G2: NetworkX Graph or MultiGraph instances.
+            The two graphs to check for isomorphism or monomorphism
+
+        G1_labels,G2_labels: dict
+            The label of every node in G1 and G2 respectively
+
+    state_params: namedtuple
+        Contains all the State-related parameters:
+
+        mapping: dict
+            The mapping as extended so far. Maps nodes of G1 to nodes of G2
+
+        reverse_mapping: dict
+            The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed
+
+        T1, T2: set
+            Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are
+            neighbors of nodes that are.
+
+        T1_out, T2_out: set
+            Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti
+
+    Returns
+    -------
+    True if the pair passes all the consistency checks successfully. False otherwise.
+    """
+    G1, G2 = graph_params.G1, graph_params.G2
+    mapping, reverse_mapping = state_params.mapping, state_params.reverse_mapping
+
+    for neighbor in G1[u]:
+        if neighbor in mapping:
+            if G1.number_of_edges(u, neighbor) != G2.number_of_edges(
+                v, mapping[neighbor]
+            ):
+                return False
+
+    for neighbor in G2[v]:
+        if neighbor in reverse_mapping:
+            if G1.number_of_edges(u, reverse_mapping[neighbor]) != G2.number_of_edges(
+                v, neighbor
+            ):
+                return False
+
+    if not G1.is_directed():
+        return True
+
+    for predecessor in G1.pred[u]:
+        if predecessor in mapping:
+            if G1.number_of_edges(predecessor, u) != G2.number_of_edges(
+                mapping[predecessor], v
+            ):
+                return False
+
+    for predecessor in G2.pred[v]:
+        if predecessor in reverse_mapping:
+            if G1.number_of_edges(
+                reverse_mapping[predecessor], u
+            ) != G2.number_of_edges(predecessor, v):
+                return False
+
+    return True
+
+
+def _update_Tinout(new_node1, new_node2, graph_params, state_params):
+    """Updates the Ti/Ti_out (i=1,2) when a new node pair u-v is added to the mapping.
+
+    Notes
+    -----
+    This function should be called right after the feasibility checks are passed, and node1 is mapped to node2. The
+    purpose of this function is to avoid brute force computing of Ti/Ti_out by iterating over all nodes of the graph
+    and checking which nodes satisfy the necessary conditions. Instead, in every step of the algorithm we focus
+    exclusively on the two nodes that are being added to the mapping, incrementally updating Ti/Ti_out.
+
+    Parameters
+    ----------
+    new_node1, new_node2: Graph node
+        The two new nodes, added to the mapping.
+
+    graph_params: namedtuple
+        Contains all the Graph-related parameters:
+
+        G1,G2: NetworkX Graph or MultiGraph instances.
+            The two graphs to check for isomorphism or monomorphism
+
+        G1_labels,G2_labels: dict
+            The label of every node in G1 and G2 respectively
+
+    state_params: namedtuple
+        Contains all the State-related parameters:
+
+        mapping: dict
+            The mapping as extended so far. Maps nodes of G1 to nodes of G2
+
+        reverse_mapping: dict
+            The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed
+
+        T1, T2: set
+            Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are
+            neighbors of nodes that are.
+
+        T1_tilde, T2_tilde: set
+            Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti
+    """
+    G1, G2, _, _, _, _, _ = graph_params
+    (
+        mapping,
+        reverse_mapping,
+        T1,
+        T1_in,
+        T1_tilde,
+        T1_tilde_in,
+        T2,
+        T2_in,
+        T2_tilde,
+        T2_tilde_in,
+    ) = state_params
+
+    uncovered_successors_G1 = {succ for succ in G1[new_node1] if succ not in mapping}
+    uncovered_successors_G2 = {
+        succ for succ in G2[new_node2] if succ not in reverse_mapping
+    }
+
+    # Add the uncovered neighbors of node1 and node2 in T1 and T2 respectively
+    T1.update(uncovered_successors_G1)
+    T2.update(uncovered_successors_G2)
+    T1.discard(new_node1)
+    T2.discard(new_node2)
+
+    T1_tilde.difference_update(uncovered_successors_G1)
+    T2_tilde.difference_update(uncovered_successors_G2)
+    T1_tilde.discard(new_node1)
+    T2_tilde.discard(new_node2)
+
+    if not G1.is_directed():
+        return
+
+    uncovered_predecessors_G1 = {
+        pred for pred in G1.pred[new_node1] if pred not in mapping
+    }
+    uncovered_predecessors_G2 = {
+        pred for pred in G2.pred[new_node2] if pred not in reverse_mapping
+    }
+
+    T1_in.update(uncovered_predecessors_G1)
+    T2_in.update(uncovered_predecessors_G2)
+    T1_in.discard(new_node1)
+    T2_in.discard(new_node2)
+
+    T1_tilde.difference_update(uncovered_predecessors_G1)
+    T2_tilde.difference_update(uncovered_predecessors_G2)
+    T1_tilde.discard(new_node1)
+    T2_tilde.discard(new_node2)
+
+
+def _restore_Tinout(popped_node1, popped_node2, graph_params, state_params):
+    """Restores the previous version of Ti/Ti_out when a node pair is deleted from the mapping.
+
+    Parameters
+    ----------
+    popped_node1, popped_node2: Graph node
+        The two nodes deleted from the mapping.
+
+    graph_params: namedtuple
+        Contains all the Graph-related parameters:
+
+        G1,G2: NetworkX Graph or MultiGraph instances.
+            The two graphs to check for isomorphism or monomorphism
+
+        G1_labels,G2_labels: dict
+            The label of every node in G1 and G2 respectively
+
+    state_params: namedtuple
+        Contains all the State-related parameters:
+
+        mapping: dict
+            The mapping as extended so far. Maps nodes of G1 to nodes of G2
+
+        reverse_mapping: dict
+            The reverse mapping as extended so far. Maps nodes from G2 to nodes of G1. It's basically "mapping" reversed
+
+        T1, T2: set
+            Ti contains uncovered neighbors of covered nodes from Gi, i.e. nodes that are not in the mapping, but are
+            neighbors of nodes that are.
+
+        T1_tilde, T2_tilde: set
+            Ti_out contains all the nodes from Gi, that are neither in the mapping nor in Ti
+    """
+    # If the node we want to remove from the mapping, has at least one covered neighbor, add it to T1.
+    G1, G2, _, _, _, _, _ = graph_params
+    (
+        mapping,
+        reverse_mapping,
+        T1,
+        T1_in,
+        T1_tilde,
+        T1_tilde_in,
+        T2,
+        T2_in,
+        T2_tilde,
+        T2_tilde_in,
+    ) = state_params
+
+    is_added = False
+    for neighbor in G1[popped_node1]:
+        if neighbor in mapping:
+            # if a neighbor of the excluded node1 is in the mapping, keep node1 in T1
+            is_added = True
+            T1.add(popped_node1)
+        else:
+            # check if its neighbor has another connection with a covered node. If not, only then exclude it from T1
+            if any(nbr in mapping for nbr in G1[neighbor]):
+                continue
+            T1.discard(neighbor)
+            T1_tilde.add(neighbor)
+
+    # Case where the node is not present in neither the mapping nor T1. By definition, it should belong to T1_tilde
+    if not is_added:
+        T1_tilde.add(popped_node1)
+
+    is_added = False
+    for neighbor in G2[popped_node2]:
+        if neighbor in reverse_mapping:
+            is_added = True
+            T2.add(popped_node2)
+        else:
+            if any(nbr in reverse_mapping for nbr in G2[neighbor]):
+                continue
+            T2.discard(neighbor)
+            T2_tilde.add(neighbor)
+
+    if not is_added:
+        T2_tilde.add(popped_node2)
+
+
+def _restore_Tinout_Di(popped_node1, popped_node2, graph_params, state_params):
+    # If the node we want to remove from the mapping, has at least one covered neighbor, add it to T1.
+    G1, G2, _, _, _, _, _ = graph_params
+    (
+        mapping,
+        reverse_mapping,
+        T1,
+        T1_in,
+        T1_tilde,
+        T1_tilde_in,
+        T2,
+        T2_in,
+        T2_tilde,
+        T2_tilde_in,
+    ) = state_params
+
+    is_added = False
+    for successor in G1[popped_node1]:
+        if successor in mapping:
+            # if a neighbor of the excluded node1 is in the mapping, keep node1 in T1
+            is_added = True
+            T1_in.add(popped_node1)
+        else:
+            # check if its neighbor has another connection with a covered node. If not, only then exclude it from T1
+            if not any(pred in mapping for pred in G1.pred[successor]):
+                T1.discard(successor)
+
+            if not any(succ in mapping for succ in G1[successor]):
+                T1_in.discard(successor)
+
+            if successor not in T1:
+                if successor not in T1_in:
+                    T1_tilde.add(successor)
+
+    for predecessor in G1.pred[popped_node1]:
+        if predecessor in mapping:
+            # if a neighbor of the excluded node1 is in the mapping, keep node1 in T1
+            is_added = True
+            T1.add(popped_node1)
+        else:
+            # check if its neighbor has another connection with a covered node. If not, only then exclude it from T1
+            if not any(pred in mapping for pred in G1.pred[predecessor]):
+                T1.discard(predecessor)
+
+            if not any(succ in mapping for succ in G1[predecessor]):
+                T1_in.discard(predecessor)
+
+            if not (predecessor in T1 or predecessor in T1_in):
+                T1_tilde.add(predecessor)
+
+    # Case where the node is not present in neither the mapping nor T1. By definition it should belong to T1_tilde
+    if not is_added:
+        T1_tilde.add(popped_node1)
+
+    is_added = False
+    for successor in G2[popped_node2]:
+        if successor in reverse_mapping:
+            is_added = True
+            T2_in.add(popped_node2)
+        else:
+            if not any(pred in reverse_mapping for pred in G2.pred[successor]):
+                T2.discard(successor)
+
+            if not any(succ in reverse_mapping for succ in G2[successor]):
+                T2_in.discard(successor)
+
+            if successor not in T2:
+                if successor not in T2_in:
+                    T2_tilde.add(successor)
+
+    for predecessor in G2.pred[popped_node2]:
+        if predecessor in reverse_mapping:
+            # if a neighbor of the excluded node1 is in the mapping, keep node1 in T1
+            is_added = True
+            T2.add(popped_node2)
+        else:
+            # check if its neighbor has another connection with a covered node. If not, only then exclude it from T1
+            if not any(pred in reverse_mapping for pred in G2.pred[predecessor]):
+                T2.discard(predecessor)
+
+            if not any(succ in reverse_mapping for succ in G2[predecessor]):
+                T2_in.discard(predecessor)
+
+            if not (predecessor in T2 or predecessor in T2_in):
+                T2_tilde.add(predecessor)
+
+    if not is_added:
+        T2_tilde.add(popped_node2)

wemm/lib/python3.10/site-packages/networkx/algorithms/isomorphism/vf2userfunc.py

@@ -0,0 +1,192 @@
+"""
+Module to simplify the specification of user-defined equality functions for
+node and edge attributes during isomorphism checks.
+
+During the construction of an isomorphism, the algorithm considers two
+candidate nodes n1 in G1 and n2 in G2.  The graphs G1 and G2 are then
+compared with respect to properties involving n1 and n2, and if the outcome
+is good, then the candidate nodes are considered isomorphic. NetworkX
+provides a simple mechanism for users to extend the comparisons to include
+node and edge attributes.
+
+Node attributes are handled by the node_match keyword. When considering
+n1 and n2, the algorithm passes their node attribute dictionaries to
+node_match, and if it returns False, then n1 and n2 cannot be
+considered to be isomorphic.
+
+Edge attributes are handled by the edge_match keyword. When considering
+n1 and n2, the algorithm must verify that outgoing edges from n1 are
+commensurate with the outgoing edges for n2. If the graph is directed,
+then a similar check is also performed for incoming edges.
+
+Focusing only on outgoing edges, we consider pairs of nodes (n1, v1) from
+G1 and (n2, v2) from G2. For graphs and digraphs, there is only one edge
+between (n1, v1) and only one edge between (n2, v2). Those edge attribute
+dictionaries are passed to edge_match, and if it returns False, then
+n1 and n2 cannot be considered isomorphic. For multigraphs and
+multidigraphs, there can be multiple edges between (n1, v1) and also
+multiple edges between (n2, v2).  Now, there must exist an isomorphism
+from "all the edges between (n1, v1)" to "all the edges between (n2, v2)".
+So, all of the edge attribute dictionaries are passed to edge_match, and
+it must determine if there is an isomorphism between the two sets of edges.
+"""
+
+from . import isomorphvf2 as vf2
+
+__all__ = ["GraphMatcher", "DiGraphMatcher", "MultiGraphMatcher", "MultiDiGraphMatcher"]
+
+
+def _semantic_feasibility(self, G1_node, G2_node):
+    """Returns True if mapping G1_node to G2_node is semantically feasible."""
+    # Make sure the nodes match
+    if self.node_match is not None:
+        nm = self.node_match(self.G1.nodes[G1_node], self.G2.nodes[G2_node])
+        if not nm:
+            return False
+
+    # Make sure the edges match
+    if self.edge_match is not None:
+        # Cached lookups
+        G1nbrs = self.G1_adj[G1_node]
+        G2nbrs = self.G2_adj[G2_node]
+        core_1 = self.core_1
+        edge_match = self.edge_match
+
+        for neighbor in G1nbrs:
+            # G1_node is not in core_1, so we must handle R_self separately
+            if neighbor == G1_node:
+                if G2_node in G2nbrs and not edge_match(
+                    G1nbrs[G1_node], G2nbrs[G2_node]
+                ):
+                    return False
+            elif neighbor in core_1:
+                G2_nbr = core_1[neighbor]
+                if G2_nbr in G2nbrs and not edge_match(
+                    G1nbrs[neighbor], G2nbrs[G2_nbr]
+                ):
+                    return False
+        # syntactic check has already verified that neighbors are symmetric
+
+    return True
+
+
+class GraphMatcher(vf2.GraphMatcher):
+    """VF2 isomorphism checker for undirected graphs."""
+
+    def __init__(self, G1, G2, node_match=None, edge_match=None):
+        """Initialize graph matcher.
+
+        Parameters
+        ----------
+        G1, G2: graph
+            The graphs to be tested.
+
+        node_match: callable
+            A function that returns True iff node n1 in G1 and n2 in G2
+            should be considered equal during the isomorphism test. The
+            function will be called like::
+
+               node_match(G1.nodes[n1], G2.nodes[n2])
+
+            That is, the function will receive the node attribute dictionaries
+            of the nodes under consideration. If None, then no attributes are
+            considered when testing for an isomorphism.
+
+        edge_match: callable
+            A function that returns True iff the edge attribute dictionary for
+            the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be
+            considered equal during the isomorphism test. The function will be
+            called like::
+
+               edge_match(G1[u1][v1], G2[u2][v2])
+
+            That is, the function will receive the edge attribute dictionaries
+            of the edges under consideration. If None, then no attributes are
+            considered when testing for an isomorphism.
+
+        """
+        vf2.GraphMatcher.__init__(self, G1, G2)
+
+        self.node_match = node_match
+        self.edge_match = edge_match
+
+        # These will be modified during checks to minimize code repeat.
+        self.G1_adj = self.G1.adj
+        self.G2_adj = self.G2.adj
+
+    semantic_feasibility = _semantic_feasibility
+
+
+class DiGraphMatcher(vf2.DiGraphMatcher):
+    """VF2 isomorphism checker for directed graphs."""
+
+    def __init__(self, G1, G2, node_match=None, edge_match=None):
+        """Initialize graph matcher.
+
+        Parameters
+        ----------
+        G1, G2 : graph
+            The graphs to be tested.
+
+        node_match : callable
+            A function that returns True iff node n1 in G1 and n2 in G2
+            should be considered equal during the isomorphism test. The
+            function will be called like::
+
+               node_match(G1.nodes[n1], G2.nodes[n2])
+
+            That is, the function will receive the node attribute dictionaries
+            of the nodes under consideration. If None, then no attributes are
+            considered when testing for an isomorphism.
+
+        edge_match : callable
+            A function that returns True iff the edge attribute dictionary for
+            the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be
+            considered equal during the isomorphism test. The function will be
+            called like::
+
+               edge_match(G1[u1][v1], G2[u2][v2])
+
+            That is, the function will receive the edge attribute dictionaries
+            of the edges under consideration. If None, then no attributes are
+            considered when testing for an isomorphism.
+
+        """
+        vf2.DiGraphMatcher.__init__(self, G1, G2)
+
+        self.node_match = node_match
+        self.edge_match = edge_match
+
+        # These will be modified during checks to minimize code repeat.
+        self.G1_adj = self.G1.adj
+        self.G2_adj = self.G2.adj
+
+    def semantic_feasibility(self, G1_node, G2_node):
+        """Returns True if mapping G1_node to G2_node is semantically feasible."""
+
+        # Test node_match and also test edge_match on successors
+        feasible = _semantic_feasibility(self, G1_node, G2_node)
+        if not feasible:
+            return False
+
+        # Test edge_match on predecessors
+        self.G1_adj = self.G1.pred
+        self.G2_adj = self.G2.pred
+        feasible = _semantic_feasibility(self, G1_node, G2_node)
+        self.G1_adj = self.G1.adj
+        self.G2_adj = self.G2.adj
+
+        return feasible
+
+
+# The "semantics" of edge_match are different for multi(di)graphs, but
+# the implementation is the same.  So, technically we do not need to
+# provide "multi" versions, but we do so to match NetworkX's base classes.
+
+
+class MultiGraphMatcher(GraphMatcher):
+    """VF2 isomorphism checker for undirected multigraphs."""
+
+
+class MultiDiGraphMatcher(DiGraphMatcher):
+    """VF2 isomorphism checker for directed multigraphs."""