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wemm/lib/python3.10/site-packages/botocore/data/cloudwatch/2010-08-01/paginators-1.json

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+{
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+      "input_token": "NextToken",
+      "output_token": "NextToken",
+      "limit_key": "MaxRecords",
+      "result_key": "AlarmHistoryItems"
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+      "result_key": [
+        "MetricAlarms",
+        "CompositeAlarms"
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+    "ListDashboards": {
+      "input_token": "NextToken",
+      "output_token": "NextToken",
+      "result_key": "DashboardEntries"
+    },
+    "ListMetrics": {
+      "input_token": "NextToken",
+      "output_token": "NextToken",
+      "result_key": [
+        "Metrics",
+        "OwningAccounts"
+      ]
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+    "GetMetricData": {
+      "input_token": "NextToken",
+      "limit_key": "MaxDatapoints",
+      "output_token": "NextToken",
+      "result_key": [
+        "MetricDataResults",
+        "Messages"
+      ]
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+      "output_token": "NextToken",
+      "result_key": "AnomalyDetectors"
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+  }
+}

wemm/lib/python3.10/site-packages/botocore/data/dataexchange/2017-07-25/paginators-1.json

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+{
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+      "input_token": "NextToken",
+      "output_token": "NextToken",
+      "limit_key": "MaxResults",
+      "result_key": "Revisions"
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+      "input_token": "NextToken",
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+      "limit_key": "MaxResults",
+      "result_key": "EventActions"
+    }
+  }
+}

wemm/lib/python3.10/site-packages/botocore/data/iot1click-projects/2018-05-14/endpoint-rule-set-1.json.gz

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+version https://git-lfs.github.com/spec/v1
+oid sha256:ad9329e1001844795dcced93fdd36961b09643c69bdac478e81a0a6f6ac21632
+size 1154

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

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+"""
+==========================
+Bipartite Graph Algorithms
+==========================
+"""
+
+import networkx as nx
+from networkx.algorithms.components import connected_components
+from networkx.exception import AmbiguousSolution
+
+__all__ = [
+    "is_bipartite",
+    "is_bipartite_node_set",
+    "color",
+    "sets",
+    "density",
+    "degrees",
+]
+
+
+@nx._dispatchable
+def color(G):
+    """Returns a two-coloring of the graph.
+
+    Raises an exception if the graph is not bipartite.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    Returns
+    -------
+    color : dictionary
+        A dictionary keyed by node with a 1 or 0 as data for each node color.
+
+    Raises
+    ------
+    NetworkXError
+        If the graph is not two-colorable.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)
+    >>> c = bipartite.color(G)
+    >>> print(c)
+    {0: 1, 1: 0, 2: 1, 3: 0}
+
+    You can use this to set a node attribute indicating the bipartite set:
+
+    >>> nx.set_node_attributes(G, c, "bipartite")
+    >>> print(G.nodes[0]["bipartite"])
+    1
+    >>> print(G.nodes[1]["bipartite"])
+    0
+    """
+    if G.is_directed():
+        import itertools
+
+        def neighbors(v):
+            return itertools.chain.from_iterable([G.predecessors(v), G.successors(v)])
+
+    else:
+        neighbors = G.neighbors
+
+    color = {}
+    for n in G:  # handle disconnected graphs
+        if n in color or len(G[n]) == 0:  # skip isolates
+            continue
+        queue = [n]
+        color[n] = 1  # nodes seen with color (1 or 0)
+        while queue:
+            v = queue.pop()
+            c = 1 - color[v]  # opposite color of node v
+            for w in neighbors(v):
+                if w in color:
+                    if color[w] == color[v]:
+                        raise nx.NetworkXError("Graph is not bipartite.")
+                else:
+                    color[w] = c
+                    queue.append(w)
+    # color isolates with 0
+    color.update(dict.fromkeys(nx.isolates(G), 0))
+    return color
+
+
+@nx._dispatchable
+def is_bipartite(G):
+    """Returns True if graph G is bipartite, False if not.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)
+    >>> print(bipartite.is_bipartite(G))
+    True
+
+    See Also
+    --------
+    color, is_bipartite_node_set
+    """
+    try:
+        color(G)
+        return True
+    except nx.NetworkXError:
+        return False
+
+
+@nx._dispatchable
+def is_bipartite_node_set(G, nodes):
+    """Returns True if nodes and G/nodes are a bipartition of G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    nodes: list or container
+      Check if nodes are a one of a bipartite set.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)
+    >>> X = set([1, 3])
+    >>> bipartite.is_bipartite_node_set(G, X)
+    True
+
+    Notes
+    -----
+    An exception is raised if the input nodes are not distinct, because in this
+    case some bipartite algorithms will yield incorrect results.
+    For connected graphs the bipartite sets are unique.  This function handles
+    disconnected graphs.
+    """
+    S = set(nodes)
+
+    if len(S) < len(nodes):
+        # this should maybe just return False?
+        raise AmbiguousSolution(
+            "The input node set contains duplicates.\n"
+            "This may lead to incorrect results when using it in bipartite algorithms.\n"
+            "Consider using set(nodes) as the input"
+        )
+
+    for CC in (G.subgraph(c).copy() for c in connected_components(G)):
+        X, Y = sets(CC)
+        if not (
+            (X.issubset(S) and Y.isdisjoint(S)) or (Y.issubset(S) and X.isdisjoint(S))
+        ):
+            return False
+    return True
+
+
+@nx._dispatchable
+def sets(G, top_nodes=None):
+    """Returns bipartite node sets of graph G.
+
+    Raises an exception if the graph is not bipartite or if the input
+    graph is disconnected and thus more than one valid solution exists.
+    See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
+    for further details on how bipartite graphs are handled in NetworkX.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    top_nodes : container, optional
+      Container with all nodes in one bipartite node set. If not supplied
+      it will be computed. But if more than one solution exists an exception
+      will be raised.
+
+    Returns
+    -------
+    X : set
+      Nodes from one side of the bipartite graph.
+    Y : set
+      Nodes from the other side.
+
+    Raises
+    ------
+    AmbiguousSolution
+      Raised if the input bipartite graph is disconnected and no container
+      with all nodes in one bipartite set is provided. When determining
+      the nodes in each bipartite set more than one valid solution is
+      possible if the input graph is disconnected.
+    NetworkXError
+      Raised if the input graph is not bipartite.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)
+    >>> X, Y = bipartite.sets(G)
+    >>> list(X)
+    [0, 2]
+    >>> list(Y)
+    [1, 3]
+
+    See Also
+    --------
+    color
+
+    """
+    if G.is_directed():
+        is_connected = nx.is_weakly_connected
+    else:
+        is_connected = nx.is_connected
+    if top_nodes is not None:
+        X = set(top_nodes)
+        Y = set(G) - X
+    else:
+        if not is_connected(G):
+            msg = "Disconnected graph: Ambiguous solution for bipartite sets."
+            raise nx.AmbiguousSolution(msg)
+        c = color(G)
+        X = {n for n, is_top in c.items() if is_top}
+        Y = {n for n, is_top in c.items() if not is_top}
+    return (X, Y)
+
+
+@nx._dispatchable(graphs="B")
+def density(B, nodes):
+    """Returns density of bipartite graph B.
+
+    Parameters
+    ----------
+    B : NetworkX graph
+
+    nodes: list or container
+      Nodes in one node set of the bipartite graph.
+
+    Returns
+    -------
+    d : float
+       The bipartite density
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.complete_bipartite_graph(3, 2)
+    >>> X = set([0, 1, 2])
+    >>> bipartite.density(G, X)
+    1.0
+    >>> Y = set([3, 4])
+    >>> bipartite.density(G, Y)
+    1.0
+
+    Notes
+    -----
+    The container of nodes passed as argument must contain all nodes
+    in one of the two bipartite node sets to avoid ambiguity in the
+    case of disconnected graphs.
+    See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
+    for further details on how bipartite graphs are handled in NetworkX.
+
+    See Also
+    --------
+    color
+    """
+    n = len(B)
+    m = nx.number_of_edges(B)
+    nb = len(nodes)
+    nt = n - nb
+    if m == 0:  # includes cases n==0 and n==1
+        d = 0.0
+    else:
+        if B.is_directed():
+            d = m / (2 * nb * nt)
+        else:
+            d = m / (nb * nt)
+    return d
+
+
+@nx._dispatchable(graphs="B", edge_attrs="weight")
+def degrees(B, nodes, weight=None):
+    """Returns the degrees of the two node sets in the bipartite graph B.
+
+    Parameters
+    ----------
+    B : NetworkX graph
+
+    nodes: list or container
+      Nodes in one node set of the bipartite graph.
+
+    weight : string or None, optional (default=None)
+       The edge attribute that holds the numerical value used as a weight.
+       If None, then each edge has weight 1.
+       The degree is the sum of the edge weights adjacent to the node.
+
+    Returns
+    -------
+    (degX,degY) : tuple of dictionaries
+       The degrees of the two bipartite sets as dictionaries keyed by node.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.complete_bipartite_graph(3, 2)
+    >>> Y = set([3, 4])
+    >>> degX, degY = bipartite.degrees(G, Y)
+    >>> dict(degX)
+    {0: 2, 1: 2, 2: 2}
+
+    Notes
+    -----
+    The container of nodes passed as argument must contain all nodes
+    in one of the two bipartite node sets to avoid ambiguity in the
+    case of disconnected graphs.
+    See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
+    for further details on how bipartite graphs are handled in NetworkX.
+
+    See Also
+    --------
+    color, density
+    """
+    bottom = set(nodes)
+    top = set(B) - bottom
+    return (B.degree(top, weight), B.degree(bottom, weight))

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

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+"""Functions for computing clustering of pairs"""
+
+import itertools
+
+import networkx as nx
+
+__all__ = [
+    "clustering",
+    "average_clustering",
+    "latapy_clustering",
+    "robins_alexander_clustering",
+]
+
+
+def cc_dot(nu, nv):
+    return len(nu & nv) / len(nu | nv)
+
+
+def cc_max(nu, nv):
+    return len(nu & nv) / max(len(nu), len(nv))
+
+
+def cc_min(nu, nv):
+    return len(nu & nv) / min(len(nu), len(nv))
+
+
+modes = {"dot": cc_dot, "min": cc_min, "max": cc_max}
+
+
+@nx._dispatchable
+def latapy_clustering(G, nodes=None, mode="dot"):
+    r"""Compute a bipartite clustering coefficient for nodes.
+
+    The bipartite clustering coefficient is a measure of local density
+    of connections defined as [1]_:
+
+    .. math::
+
+       c_u = \frac{\sum_{v \in N(N(u))} c_{uv} }{|N(N(u))|}
+
+    where `N(N(u))` are the second order neighbors of `u` in `G` excluding `u`,
+    and `c_{uv}` is the pairwise clustering coefficient between nodes
+    `u` and `v`.
+
+    The mode selects the function for `c_{uv}` which can be:
+
+    `dot`:
+
+    .. math::
+
+       c_{uv}=\frac{|N(u)\cap N(v)|}{|N(u) \cup N(v)|}
+
+    `min`:
+
+    .. math::
+
+       c_{uv}=\frac{|N(u)\cap N(v)|}{min(|N(u)|,|N(v)|)}
+
+    `max`:
+
+    .. math::
+
+       c_{uv}=\frac{|N(u)\cap N(v)|}{max(|N(u)|,|N(v)|)}
+
+
+    Parameters
+    ----------
+    G : graph
+        A bipartite graph
+
+    nodes : list or iterable (optional)
+        Compute bipartite clustering for these nodes. The default
+        is all nodes in G.
+
+    mode : string
+        The pairwise bipartite clustering method to be used in the computation.
+        It must be "dot", "max", or "min".
+
+    Returns
+    -------
+    clustering : dictionary
+        A dictionary keyed by node with the clustering coefficient value.
+
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)  # path graphs are bipartite
+    >>> c = bipartite.clustering(G)
+    >>> c[0]
+    0.5
+    >>> c = bipartite.clustering(G, mode="min")
+    >>> c[0]
+    1.0
+
+    See Also
+    --------
+    robins_alexander_clustering
+    average_clustering
+    networkx.algorithms.cluster.square_clustering
+
+    References
+    ----------
+    .. [1] Latapy, Matthieu, Clémence Magnien, and Nathalie Del Vecchio (2008).
+       Basic notions for the analysis of large two-mode networks.
+       Social Networks 30(1), 31--48.
+    """
+    if not nx.algorithms.bipartite.is_bipartite(G):
+        raise nx.NetworkXError("Graph is not bipartite")
+
+    try:
+        cc_func = modes[mode]
+    except KeyError as err:
+        raise nx.NetworkXError(
+            "Mode for bipartite clustering must be: dot, min or max"
+        ) from err
+
+    if nodes is None:
+        nodes = G
+    ccs = {}
+    for v in nodes:
+        cc = 0.0
+        nbrs2 = {u for nbr in G[v] for u in G[nbr]} - {v}
+        for u in nbrs2:
+            cc += cc_func(set(G[u]), set(G[v]))
+        if cc > 0.0:  # len(nbrs2)>0
+            cc /= len(nbrs2)
+        ccs[v] = cc
+    return ccs
+
+
+clustering = latapy_clustering
+
+
+@nx._dispatchable(name="bipartite_average_clustering")
+def average_clustering(G, nodes=None, mode="dot"):
+    r"""Compute the average bipartite clustering coefficient.
+
+    A clustering coefficient for the whole graph is the average,
+
+    .. math::
+
+       C = \frac{1}{n}\sum_{v \in G} c_v,
+
+    where `n` is the number of nodes in `G`.
+
+    Similar measures for the two bipartite sets can be defined [1]_
+
+    .. math::
+
+       C_X = \frac{1}{|X|}\sum_{v \in X} c_v,
+
+    where `X` is a bipartite set of `G`.
+
+    Parameters
+    ----------
+    G : graph
+        a bipartite graph
+
+    nodes : list or iterable, optional
+        A container of nodes to use in computing the average.
+        The nodes should be either the entire graph (the default) or one of the
+        bipartite sets.
+
+    mode : string
+        The pairwise bipartite clustering method.
+        It must be "dot", "max", or "min"
+
+    Returns
+    -------
+    clustering : float
+       The average bipartite clustering for the given set of nodes or the
+       entire graph if no nodes are specified.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.star_graph(3)  # star graphs are bipartite
+    >>> bipartite.average_clustering(G)
+    0.75
+    >>> X, Y = bipartite.sets(G)
+    >>> bipartite.average_clustering(G, X)
+    0.0
+    >>> bipartite.average_clustering(G, Y)
+    1.0
+
+    See Also
+    --------
+    clustering
+
+    Notes
+    -----
+    The container of nodes passed to this function must contain all of the nodes
+    in one of the bipartite sets ("top" or "bottom") in order to compute
+    the correct average bipartite clustering coefficients.
+    See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
+    for further details on how bipartite graphs are handled in NetworkX.
+
+
+    References
+    ----------
+    .. [1] Latapy, Matthieu, Clémence Magnien, and Nathalie Del Vecchio (2008).
+        Basic notions for the analysis of large two-mode networks.
+        Social Networks 30(1), 31--48.
+    """
+    if nodes is None:
+        nodes = G
+    ccs = latapy_clustering(G, nodes=nodes, mode=mode)
+    return sum(ccs[v] for v in nodes) / len(nodes)
+
+
+@nx._dispatchable
+def robins_alexander_clustering(G):
+    r"""Compute the bipartite clustering of G.
+
+    Robins and Alexander [1]_ defined bipartite clustering coefficient as
+    four times the number of four cycles `C_4` divided by the number of
+    three paths `L_3` in a bipartite graph:
+
+    .. math::
+
+       CC_4 = \frac{4 * C_4}{L_3}
+
+    Parameters
+    ----------
+    G : graph
+        a bipartite graph
+
+    Returns
+    -------
+    clustering : float
+       The Robins and Alexander bipartite clustering for the input graph.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.davis_southern_women_graph()
+    >>> print(round(bipartite.robins_alexander_clustering(G), 3))
+    0.468
+
+    See Also
+    --------
+    latapy_clustering
+    networkx.algorithms.cluster.square_clustering
+
+    References
+    ----------
+    .. [1] Robins, G. and M. Alexander (2004). Small worlds among interlocking
+           directors: Network structure and distance in bipartite graphs.
+           Computational & Mathematical Organization Theory 10(1), 69–94.
+
+    """
+    if G.order() < 4 or G.size() < 3:
+        return 0
+    L_3 = _threepaths(G)
+    if L_3 == 0:
+        return 0
+    C_4 = _four_cycles(G)
+    return (4.0 * C_4) / L_3
+
+
+def _four_cycles(G):
+    cycles = 0
+    for v in G:
+        for u, w in itertools.combinations(G[v], 2):
+            cycles += len((set(G[u]) & set(G[w])) - {v})
+    return cycles / 4
+
+
+def _threepaths(G):
+    paths = 0
+    for v in G:
+        for u in G[v]:
+            for w in set(G[u]) - {v}:
+                paths += len(set(G[w]) - {v, u})
+    # Divide by two because we count each three path twice
+    # one for each possible starting point
+    return paths / 2

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

@@ -0,0 +1,105 @@
+"""Provides a function for computing the extendability of a graph which is
+undirected, simple, connected and bipartite and contains at least one perfect matching."""
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["maximal_extendability"]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def maximal_extendability(G):
+    """Computes the extendability of a graph.
+
+    The extendability of a graph is defined as the maximum $k$ for which `G`
+    is $k$-extendable. Graph `G` is $k$-extendable if and only if `G` has a
+    perfect matching and every set of $k$ independent edges can be extended
+    to a perfect matching in `G`.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        A fully-connected bipartite graph without self-loops
+
+    Returns
+    -------
+    extendability : int
+
+    Raises
+    ------
+    NetworkXError
+       If the graph `G` is disconnected.
+       If the graph `G` is not bipartite.
+       If the graph `G` does not contain a perfect matching.
+       If the residual graph of `G` is not strongly connected.
+
+    Notes
+    -----
+    Definition:
+    Let `G` be a simple, connected, undirected and bipartite graph with a perfect
+    matching M and bipartition (U,V). The residual graph of `G`, denoted by $G_M$,
+    is the graph obtained from G by directing the edges of M from V to U and the
+    edges that do not belong to M from U to V.
+
+    Lemma [1]_ :
+    Let M be a perfect matching of `G`. `G` is $k$-extendable if and only if its residual
+    graph $G_M$ is strongly connected and there are $k$ vertex-disjoint directed
+    paths between every vertex of U and every vertex of V.
+
+    Assuming that input graph `G` is undirected, simple, connected, bipartite and contains
+    a perfect matching M, this function constructs the residual graph $G_M$ of G and
+    returns the minimum value among the maximum vertex-disjoint directed paths between
+    every vertex of U and every vertex of V in $G_M$. By combining the definitions
+    and the lemma, this value represents the extendability of the graph `G`.
+
+    Time complexity O($n^3$ $m^2$)) where $n$ is the number of vertices
+    and $m$ is the number of edges.
+
+    References
+    ----------
+    .. [1] "A polynomial algorithm for the extendability problem in bipartite graphs",
+          J. Lakhal, L. Litzler, Information Processing Letters, 1998.
+    .. [2] "On n-extendible graphs", M. D. Plummer, Discrete Mathematics, 31:201–210, 1980
+          https://doi.org/10.1016/0012-365X(80)90037-0
+
+    """
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("Graph G is not connected")
+
+    if not nx.bipartite.is_bipartite(G):
+        raise nx.NetworkXError("Graph G is not bipartite")
+
+    U, V = nx.bipartite.sets(G)
+
+    maximum_matching = nx.bipartite.hopcroft_karp_matching(G)
+
+    if not nx.is_perfect_matching(G, maximum_matching):
+        raise nx.NetworkXError("Graph G does not contain a perfect matching")
+
+    # list of edges in perfect matching, directed from V to U
+    pm = [(node, maximum_matching[node]) for node in V & maximum_matching.keys()]
+
+    # Direct all the edges of G, from V to U if in matching, else from U to V
+    directed_edges = [
+        (x, y) if (x in V and (x, y) in pm) or (x in U and (y, x) not in pm) else (y, x)
+        for x, y in G.edges
+    ]
+
+    # Construct the residual graph of G
+    residual_G = nx.DiGraph()
+    residual_G.add_nodes_from(G)
+    residual_G.add_edges_from(directed_edges)
+
+    if not nx.is_strongly_connected(residual_G):
+        raise nx.NetworkXError("The residual graph of G is not strongly connected")
+
+    # For node-pairs between V & U, keep min of max number of node-disjoint paths
+    # Variable $k$ stands for the extendability of graph G
+    k = float("inf")
+    for u in U:
+        for v in V:
+            num_paths = sum(1 for _ in nx.node_disjoint_paths(residual_G, u, v))
+            k = k if k < num_paths else num_paths
+    return k

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

@@ -0,0 +1,604 @@
+"""
+Generators and functions for bipartite graphs.
+"""
+
+import math
+import numbers
+from functools import reduce
+
+import networkx as nx
+from networkx.utils import nodes_or_number, py_random_state
+
+__all__ = [
+    "configuration_model",
+    "havel_hakimi_graph",
+    "reverse_havel_hakimi_graph",
+    "alternating_havel_hakimi_graph",
+    "preferential_attachment_graph",
+    "random_graph",
+    "gnmk_random_graph",
+    "complete_bipartite_graph",
+]
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number([0, 1])
+def complete_bipartite_graph(n1, n2, create_using=None):
+    """Returns the complete bipartite graph `K_{n_1,n_2}`.
+
+    The graph is composed of two partitions with nodes 0 to (n1 - 1)
+    in the first and nodes n1 to (n1 + n2 - 1) in the second.
+    Each node in the first is connected to each node in the second.
+
+    Parameters
+    ----------
+    n1, n2 : integer or iterable container of nodes
+        If integers, nodes are from `range(n1)` and `range(n1, n1 + n2)`.
+        If a container, the elements are the nodes.
+    create_using : NetworkX graph instance, (default: nx.Graph)
+       Return graph of this type.
+
+    Notes
+    -----
+    Nodes are the integers 0 to `n1 + n2 - 1` unless either n1 or n2 are
+    containers of nodes. If only one of n1 or n2 are integers, that
+    integer is replaced by `range` of that integer.
+
+    The nodes are assigned the attribute 'bipartite' with the value 0 or 1
+    to indicate which bipartite set the node belongs to.
+
+    This function is not imported in the main namespace.
+    To use it use nx.bipartite.complete_bipartite_graph
+    """
+    G = nx.empty_graph(0, create_using)
+    if G.is_directed():
+        raise nx.NetworkXError("Directed Graph not supported")
+
+    n1, top = n1
+    n2, bottom = n2
+    if isinstance(n1, numbers.Integral) and isinstance(n2, numbers.Integral):
+        bottom = [n1 + i for i in bottom]
+    G.add_nodes_from(top, bipartite=0)
+    G.add_nodes_from(bottom, bipartite=1)
+    if len(G) != len(top) + len(bottom):
+        raise nx.NetworkXError("Inputs n1 and n2 must contain distinct nodes")
+    G.add_edges_from((u, v) for u in top for v in bottom)
+    G.graph["name"] = f"complete_bipartite_graph({len(top)}, {len(bottom)})"
+    return G
+
+
+@py_random_state(3)
+@nx._dispatchable(name="bipartite_configuration_model", graphs=None, returns_graph=True)
+def configuration_model(aseq, bseq, create_using=None, seed=None):
+    """Returns a random bipartite graph from two given degree sequences.
+
+    Parameters
+    ----------
+    aseq : list
+       Degree sequence for node set A.
+    bseq : list
+       Degree sequence for node set B.
+    create_using : NetworkX graph instance, optional
+       Return graph of this type.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    The graph is composed of two partitions. Set A has nodes 0 to
+    (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1).
+    Nodes from set A are connected to nodes in set B by choosing
+    randomly from the possible free stubs, one in A and one in B.
+
+    Notes
+    -----
+    The sum of the two sequences must be equal: sum(aseq)=sum(bseq)
+    If no graph type is specified use MultiGraph with parallel edges.
+    If you want a graph with no parallel edges use create_using=Graph()
+    but then the resulting degree sequences might not be exact.
+
+    The nodes are assigned the attribute 'bipartite' with the value 0 or 1
+    to indicate which bipartite set the node belongs to.
+
+    This function is not imported in the main namespace.
+    To use it use nx.bipartite.configuration_model
+    """
+    G = nx.empty_graph(0, create_using, default=nx.MultiGraph)
+    if G.is_directed():
+        raise nx.NetworkXError("Directed Graph not supported")
+
+    # length and sum of each sequence
+    lena = len(aseq)
+    lenb = len(bseq)
+    suma = sum(aseq)
+    sumb = sum(bseq)
+
+    if not suma == sumb:
+        raise nx.NetworkXError(
+            f"invalid degree sequences, sum(aseq)!=sum(bseq),{suma},{sumb}"
+        )
+
+    G = _add_nodes_with_bipartite_label(G, lena, lenb)
+
+    if len(aseq) == 0 or max(aseq) == 0:
+        return G  # done if no edges
+
+    # build lists of degree-repeated vertex numbers
+    stubs = [[v] * aseq[v] for v in range(lena)]
+    astubs = [x for subseq in stubs for x in subseq]
+
+    stubs = [[v] * bseq[v - lena] for v in range(lena, lena + lenb)]
+    bstubs = [x for subseq in stubs for x in subseq]
+
+    # shuffle lists
+    seed.shuffle(astubs)
+    seed.shuffle(bstubs)
+
+    G.add_edges_from([astubs[i], bstubs[i]] for i in range(suma))
+
+    G.name = "bipartite_configuration_model"
+    return G
+
+
+@nx._dispatchable(name="bipartite_havel_hakimi_graph", graphs=None, returns_graph=True)
+def havel_hakimi_graph(aseq, bseq, create_using=None):
+    """Returns a bipartite graph from two given degree sequences using a
+    Havel-Hakimi style construction.
+
+    The graph is composed of two partitions. Set A has nodes 0 to
+    (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1).
+    Nodes from the set A are connected to nodes in the set B by
+    connecting the highest degree nodes in set A to the highest degree
+    nodes in set B until all stubs are connected.
+
+    Parameters
+    ----------
+    aseq : list
+       Degree sequence for node set A.
+    bseq : list
+       Degree sequence for node set B.
+    create_using : NetworkX graph instance, optional
+       Return graph of this type.
+
+    Notes
+    -----
+    The sum of the two sequences must be equal: sum(aseq)=sum(bseq)
+    If no graph type is specified use MultiGraph with parallel edges.
+    If you want a graph with no parallel edges use create_using=Graph()
+    but then the resulting degree sequences might not be exact.
+
+    The nodes are assigned the attribute 'bipartite' with the value 0 or 1
+    to indicate which bipartite set the node belongs to.
+
+    This function is not imported in the main namespace.
+    To use it use nx.bipartite.havel_hakimi_graph
+    """
+    G = nx.empty_graph(0, create_using, default=nx.MultiGraph)
+    if G.is_directed():
+        raise nx.NetworkXError("Directed Graph not supported")
+
+    # length of the each sequence
+    naseq = len(aseq)
+    nbseq = len(bseq)
+
+    suma = sum(aseq)
+    sumb = sum(bseq)
+
+    if not suma == sumb:
+        raise nx.NetworkXError(
+            f"invalid degree sequences, sum(aseq)!=sum(bseq),{suma},{sumb}"
+        )
+
+    G = _add_nodes_with_bipartite_label(G, naseq, nbseq)
+
+    if len(aseq) == 0 or max(aseq) == 0:
+        return G  # done if no edges
+
+    # build list of degree-repeated vertex numbers
+    astubs = [[aseq[v], v] for v in range(naseq)]
+    bstubs = [[bseq[v - naseq], v] for v in range(naseq, naseq + nbseq)]
+    astubs.sort()
+    while astubs:
+        (degree, u) = astubs.pop()  # take of largest degree node in the a set
+        if degree == 0:
+            break  # done, all are zero
+        # connect the source to largest degree nodes in the b set
+        bstubs.sort()
+        for target in bstubs[-degree:]:
+            v = target[1]
+            G.add_edge(u, v)
+            target[0] -= 1  # note this updates bstubs too.
+            if target[0] == 0:
+                bstubs.remove(target)
+
+    G.name = "bipartite_havel_hakimi_graph"
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def reverse_havel_hakimi_graph(aseq, bseq, create_using=None):
+    """Returns a bipartite graph from two given degree sequences using a
+    Havel-Hakimi style construction.
+
+    The graph is composed of two partitions. Set A has nodes 0 to
+    (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1).
+    Nodes from set A are connected to nodes in the set B by connecting
+    the highest degree nodes in set A to the lowest degree nodes in
+    set B until all stubs are connected.
+
+    Parameters
+    ----------
+    aseq : list
+       Degree sequence for node set A.
+    bseq : list
+       Degree sequence for node set B.
+    create_using : NetworkX graph instance, optional
+       Return graph of this type.
+
+    Notes
+    -----
+    The sum of the two sequences must be equal: sum(aseq)=sum(bseq)
+    If no graph type is specified use MultiGraph with parallel edges.
+    If you want a graph with no parallel edges use create_using=Graph()
+    but then the resulting degree sequences might not be exact.
+
+    The nodes are assigned the attribute 'bipartite' with the value 0 or 1
+    to indicate which bipartite set the node belongs to.
+
+    This function is not imported in the main namespace.
+    To use it use nx.bipartite.reverse_havel_hakimi_graph
+    """
+    G = nx.empty_graph(0, create_using, default=nx.MultiGraph)
+    if G.is_directed():
+        raise nx.NetworkXError("Directed Graph not supported")
+
+    # length of the each sequence
+    lena = len(aseq)
+    lenb = len(bseq)
+    suma = sum(aseq)
+    sumb = sum(bseq)
+
+    if not suma == sumb:
+        raise nx.NetworkXError(
+            f"invalid degree sequences, sum(aseq)!=sum(bseq),{suma},{sumb}"
+        )
+
+    G = _add_nodes_with_bipartite_label(G, lena, lenb)
+
+    if len(aseq) == 0 or max(aseq) == 0:
+        return G  # done if no edges
+
+    # build list of degree-repeated vertex numbers
+    astubs = [[aseq[v], v] for v in range(lena)]
+    bstubs = [[bseq[v - lena], v] for v in range(lena, lena + lenb)]
+    astubs.sort()
+    bstubs.sort()
+    while astubs:
+        (degree, u) = astubs.pop()  # take of largest degree node in the a set
+        if degree == 0:
+            break  # done, all are zero
+        # connect the source to the smallest degree nodes in the b set
+        for target in bstubs[0:degree]:
+            v = target[1]
+            G.add_edge(u, v)
+            target[0] -= 1  # note this updates bstubs too.
+            if target[0] == 0:
+                bstubs.remove(target)
+
+    G.name = "bipartite_reverse_havel_hakimi_graph"
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def alternating_havel_hakimi_graph(aseq, bseq, create_using=None):
+    """Returns a bipartite graph from two given degree sequences using
+    an alternating Havel-Hakimi style construction.
+
+    The graph is composed of two partitions. Set A has nodes 0 to
+    (len(aseq) - 1) and set B has nodes len(aseq) to (len(bseq) - 1).
+    Nodes from the set A are connected to nodes in the set B by
+    connecting the highest degree nodes in set A to alternatively the
+    highest and the lowest degree nodes in set B until all stubs are
+    connected.
+
+    Parameters
+    ----------
+    aseq : list
+       Degree sequence for node set A.
+    bseq : list
+       Degree sequence for node set B.
+    create_using : NetworkX graph instance, optional
+       Return graph of this type.
+
+    Notes
+    -----
+    The sum of the two sequences must be equal: sum(aseq)=sum(bseq)
+    If no graph type is specified use MultiGraph with parallel edges.
+    If you want a graph with no parallel edges use create_using=Graph()
+    but then the resulting degree sequences might not be exact.
+
+    The nodes are assigned the attribute 'bipartite' with the value 0 or 1
+    to indicate which bipartite set the node belongs to.
+
+    This function is not imported in the main namespace.
+    To use it use nx.bipartite.alternating_havel_hakimi_graph
+    """
+    G = nx.empty_graph(0, create_using, default=nx.MultiGraph)
+    if G.is_directed():
+        raise nx.NetworkXError("Directed Graph not supported")
+
+    # length of the each sequence
+    naseq = len(aseq)
+    nbseq = len(bseq)
+    suma = sum(aseq)
+    sumb = sum(bseq)
+
+    if not suma == sumb:
+        raise nx.NetworkXError(
+            f"invalid degree sequences, sum(aseq)!=sum(bseq),{suma},{sumb}"
+        )
+
+    G = _add_nodes_with_bipartite_label(G, naseq, nbseq)
+
+    if len(aseq) == 0 or max(aseq) == 0:
+        return G  # done if no edges
+    # build list of degree-repeated vertex numbers
+    astubs = [[aseq[v], v] for v in range(naseq)]
+    bstubs = [[bseq[v - naseq], v] for v in range(naseq, naseq + nbseq)]
+    while astubs:
+        astubs.sort()
+        (degree, u) = astubs.pop()  # take of largest degree node in the a set
+        if degree == 0:
+            break  # done, all are zero
+        bstubs.sort()
+        small = bstubs[0 : degree // 2]  # add these low degree targets
+        large = bstubs[(-degree + degree // 2) :]  # now high degree targets
+        stubs = [x for z in zip(large, small) for x in z]  # combine, sorry
+        if len(stubs) < len(small) + len(large):  # check for zip truncation
+            stubs.append(large.pop())
+        for target in stubs:
+            v = target[1]
+            G.add_edge(u, v)
+            target[0] -= 1  # note this updates bstubs too.
+            if target[0] == 0:
+                bstubs.remove(target)
+
+    G.name = "bipartite_alternating_havel_hakimi_graph"
+    return G
+
+
+@py_random_state(3)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def preferential_attachment_graph(aseq, p, create_using=None, seed=None):
+    """Create a bipartite graph with a preferential attachment model from
+    a given single degree sequence.
+
+    The graph is composed of two partitions. Set A has nodes 0 to
+    (len(aseq) - 1) and set B has nodes starting with node len(aseq).
+    The number of nodes in set B is random.
+
+    Parameters
+    ----------
+    aseq : list
+       Degree sequence for node set A.
+    p :  float
+       Probability that a new bottom node is added.
+    create_using : NetworkX graph instance, optional
+       Return graph of this type.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    References
+    ----------
+    .. [1] Guillaume, J.L. and Latapy, M.,
+       Bipartite graphs as models of complex networks.
+       Physica A: Statistical Mechanics and its Applications,
+       2006, 371(2), pp.795-813.
+    .. [2] Jean-Loup Guillaume and Matthieu Latapy,
+       Bipartite structure of all complex networks,
+       Inf. Process. Lett. 90, 2004, pg. 215-221
+       https://doi.org/10.1016/j.ipl.2004.03.007
+
+    Notes
+    -----
+    The nodes are assigned the attribute 'bipartite' with the value 0 or 1
+    to indicate which bipartite set the node belongs to.
+
+    This function is not imported in the main namespace.
+    To use it use nx.bipartite.preferential_attachment_graph
+    """
+    G = nx.empty_graph(0, create_using, default=nx.MultiGraph)
+    if G.is_directed():
+        raise nx.NetworkXError("Directed Graph not supported")
+
+    if p > 1:
+        raise nx.NetworkXError(f"probability {p} > 1")
+
+    naseq = len(aseq)
+    G = _add_nodes_with_bipartite_label(G, naseq, 0)
+    vv = [[v] * aseq[v] for v in range(naseq)]
+    while vv:
+        while vv[0]:
+            source = vv[0][0]
+            vv[0].remove(source)
+            if seed.random() < p or len(G) == naseq:
+                target = len(G)
+                G.add_node(target, bipartite=1)
+                G.add_edge(source, target)
+            else:
+                bb = [[b] * G.degree(b) for b in range(naseq, len(G))]
+                # flatten the list of lists into a list.
+                bbstubs = reduce(lambda x, y: x + y, bb)
+                # choose preferentially a bottom node.
+                target = seed.choice(bbstubs)
+                G.add_node(target, bipartite=1)
+                G.add_edge(source, target)
+        vv.remove(vv[0])
+    G.name = "bipartite_preferential_attachment_model"
+    return G
+
+
+@py_random_state(3)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def random_graph(n, m, p, seed=None, directed=False):
+    """Returns a bipartite random graph.
+
+    This is a bipartite version of the binomial (Erdős-Rényi) graph.
+    The graph is composed of two partitions. Set A has nodes 0 to
+    (n - 1) and set B has nodes n to (n + m - 1).
+
+    Parameters
+    ----------
+    n : int
+        The number of nodes in the first bipartite set.
+    m : int
+        The number of nodes in the second bipartite set.
+    p : float
+        Probability for edge creation.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+    directed : bool, optional (default=False)
+        If True return a directed graph
+
+    Notes
+    -----
+    The bipartite random graph algorithm chooses each of the n*m (undirected)
+    or 2*nm (directed) possible edges with probability p.
+
+    This algorithm is $O(n+m)$ where $m$ is the expected number of edges.
+
+    The nodes are assigned the attribute 'bipartite' with the value 0 or 1
+    to indicate which bipartite set the node belongs to.
+
+    This function is not imported in the main namespace.
+    To use it use nx.bipartite.random_graph
+
+    See Also
+    --------
+    gnp_random_graph, configuration_model
+
+    References
+    ----------
+    .. [1] Vladimir Batagelj and Ulrik Brandes,
+       "Efficient generation of large random networks",
+       Phys. Rev. E, 71, 036113, 2005.
+    """
+    G = nx.Graph()
+    G = _add_nodes_with_bipartite_label(G, n, m)
+    if directed:
+        G = nx.DiGraph(G)
+    G.name = f"fast_gnp_random_graph({n},{m},{p})"
+
+    if p <= 0:
+        return G
+    if p >= 1:
+        return nx.complete_bipartite_graph(n, m)
+
+    lp = math.log(1.0 - p)
+
+    v = 0
+    w = -1
+    while v < n:
+        lr = math.log(1.0 - seed.random())
+        w = w + 1 + int(lr / lp)
+        while w >= m and v < n:
+            w = w - m
+            v = v + 1
+        if v < n:
+            G.add_edge(v, n + w)
+
+    if directed:
+        # use the same algorithm to
+        # add edges from the "m" to "n" set
+        v = 0
+        w = -1
+        while v < n:
+            lr = math.log(1.0 - seed.random())
+            w = w + 1 + int(lr / lp)
+            while w >= m and v < n:
+                w = w - m
+                v = v + 1
+            if v < n:
+                G.add_edge(n + w, v)
+
+    return G
+
+
+@py_random_state(3)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def gnmk_random_graph(n, m, k, seed=None, directed=False):
+    """Returns a random bipartite graph G_{n,m,k}.
+
+    Produces a bipartite graph chosen randomly out of the set of all graphs
+    with n top nodes, m bottom nodes, and k edges.
+    The graph is composed of two sets of nodes.
+    Set A has nodes 0 to (n - 1) and set B has nodes n to (n + m - 1).
+
+    Parameters
+    ----------
+    n : int
+        The number of nodes in the first bipartite set.
+    m : int
+        The number of nodes in the second bipartite set.
+    k : int
+        The number of edges
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+    directed : bool, optional (default=False)
+        If True return a directed graph
+
+    Examples
+    --------
+    from nx.algorithms import bipartite
+    G = bipartite.gnmk_random_graph(10,20,50)
+
+    See Also
+    --------
+    gnm_random_graph
+
+    Notes
+    -----
+    If k > m * n then a complete bipartite graph is returned.
+
+    This graph is a bipartite version of the `G_{nm}` random graph model.
+
+    The nodes are assigned the attribute 'bipartite' with the value 0 or 1
+    to indicate which bipartite set the node belongs to.
+
+    This function is not imported in the main namespace.
+    To use it use nx.bipartite.gnmk_random_graph
+    """
+    G = nx.Graph()
+    G = _add_nodes_with_bipartite_label(G, n, m)
+    if directed:
+        G = nx.DiGraph(G)
+    G.name = f"bipartite_gnm_random_graph({n},{m},{k})"
+    if n == 1 or m == 1:
+        return G
+    max_edges = n * m  # max_edges for bipartite networks
+    if k >= max_edges:  # Maybe we should raise an exception here
+        return nx.complete_bipartite_graph(n, m, create_using=G)
+
+    top = [n for n, d in G.nodes(data=True) if d["bipartite"] == 0]
+    bottom = list(set(G) - set(top))
+    edge_count = 0
+    while edge_count < k:
+        # generate random edge,u,v
+        u = seed.choice(top)
+        v = seed.choice(bottom)
+        if v in G[u]:
+            continue
+        else:
+            G.add_edge(u, v)
+            edge_count += 1
+    return G
+
+
+def _add_nodes_with_bipartite_label(G, lena, lenb):
+    G.add_nodes_from(range(lena + lenb))
+    b = dict(zip(range(lena), [0] * lena))
+    b.update(dict(zip(range(lena, lena + lenb), [1] * lenb)))
+    nx.set_node_attributes(G, b, "bipartite")
+    return G

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

@@ -0,0 +1,192 @@
+import pytest
+
+import networkx as nx
+from networkx.algorithms import bipartite
+
+
+class TestBipartiteCentrality:
+    @classmethod
+    def setup_class(cls):
+        cls.P4 = nx.path_graph(4)
+        cls.K3 = nx.complete_bipartite_graph(3, 3)
+        cls.C4 = nx.cycle_graph(4)
+        cls.davis = nx.davis_southern_women_graph()
+        cls.top_nodes = [
+            n for n, d in cls.davis.nodes(data=True) if d["bipartite"] == 0
+        ]
+
+    def test_degree_centrality(self):
+        d = bipartite.degree_centrality(self.P4, [1, 3])
+        answer = {0: 0.5, 1: 1.0, 2: 1.0, 3: 0.5}
+        assert d == answer
+        d = bipartite.degree_centrality(self.K3, [0, 1, 2])
+        answer = {0: 1.0, 1: 1.0, 2: 1.0, 3: 1.0, 4: 1.0, 5: 1.0}
+        assert d == answer
+        d = bipartite.degree_centrality(self.C4, [0, 2])
+        answer = {0: 1.0, 1: 1.0, 2: 1.0, 3: 1.0}
+        assert d == answer
+
+    def test_betweenness_centrality(self):
+        c = bipartite.betweenness_centrality(self.P4, [1, 3])
+        answer = {0: 0.0, 1: 1.0, 2: 1.0, 3: 0.0}
+        assert c == answer
+        c = bipartite.betweenness_centrality(self.K3, [0, 1, 2])
+        answer = {0: 0.125, 1: 0.125, 2: 0.125, 3: 0.125, 4: 0.125, 5: 0.125}
+        assert c == answer
+        c = bipartite.betweenness_centrality(self.C4, [0, 2])
+        answer = {0: 0.25, 1: 0.25, 2: 0.25, 3: 0.25}
+        assert c == answer
+
+    def test_closeness_centrality(self):
+        c = bipartite.closeness_centrality(self.P4, [1, 3])
+        answer = {0: 2.0 / 3, 1: 1.0, 2: 1.0, 3: 2.0 / 3}
+        assert c == answer
+        c = bipartite.closeness_centrality(self.K3, [0, 1, 2])
+        answer = {0: 1.0, 1: 1.0, 2: 1.0, 3: 1.0, 4: 1.0, 5: 1.0}
+        assert c == answer
+        c = bipartite.closeness_centrality(self.C4, [0, 2])
+        answer = {0: 1.0, 1: 1.0, 2: 1.0, 3: 1.0}
+        assert c == answer
+        G = nx.Graph()
+        G.add_node(0)
+        G.add_node(1)
+        c = bipartite.closeness_centrality(G, [0])
+        assert c == {0: 0.0, 1: 0.0}
+        c = bipartite.closeness_centrality(G, [1])
+        assert c == {0: 0.0, 1: 0.0}
+
+    def test_bipartite_closeness_centrality_unconnected(self):
+        G = nx.complete_bipartite_graph(3, 3)
+        G.add_edge(6, 7)
+        c = bipartite.closeness_centrality(G, [0, 2, 4, 6], normalized=False)
+        answer = {
+            0: 10.0 / 7,
+            2: 10.0 / 7,
+            4: 10.0 / 7,
+            6: 10.0,
+            1: 10.0 / 7,
+            3: 10.0 / 7,
+            5: 10.0 / 7,
+            7: 10.0,
+        }
+        assert c == answer
+
+    def test_davis_degree_centrality(self):
+        G = self.davis
+        deg = bipartite.degree_centrality(G, self.top_nodes)
+        answer = {
+            "E8": 0.78,
+            "E9": 0.67,
+            "E7": 0.56,
+            "Nora Fayette": 0.57,
+            "Evelyn Jefferson": 0.57,
+            "Theresa Anderson": 0.57,
+            "E6": 0.44,
+            "Sylvia Avondale": 0.50,
+            "Laura Mandeville": 0.50,
+            "Brenda Rogers": 0.50,
+            "Katherina Rogers": 0.43,
+            "E5": 0.44,
+            "Helen Lloyd": 0.36,
+            "E3": 0.33,
+            "Ruth DeSand": 0.29,
+            "Verne Sanderson": 0.29,
+            "E12": 0.33,
+            "Myra Liddel": 0.29,
+            "E11": 0.22,
+            "Eleanor Nye": 0.29,
+            "Frances Anderson": 0.29,
+            "Pearl Oglethorpe": 0.21,
+            "E4": 0.22,
+            "Charlotte McDowd": 0.29,
+            "E10": 0.28,
+            "Olivia Carleton": 0.14,
+            "Flora Price": 0.14,
+            "E2": 0.17,
+            "E1": 0.17,
+            "Dorothy Murchison": 0.14,
+            "E13": 0.17,
+            "E14": 0.17,
+        }
+        for node, value in answer.items():
+            assert value == pytest.approx(deg[node], abs=1e-2)
+
+    def test_davis_betweenness_centrality(self):
+        G = self.davis
+        bet = bipartite.betweenness_centrality(G, self.top_nodes)
+        answer = {
+            "E8": 0.24,
+            "E9": 0.23,
+            "E7": 0.13,
+            "Nora Fayette": 0.11,
+            "Evelyn Jefferson": 0.10,
+            "Theresa Anderson": 0.09,
+            "E6": 0.07,
+            "Sylvia Avondale": 0.07,
+            "Laura Mandeville": 0.05,
+            "Brenda Rogers": 0.05,
+            "Katherina Rogers": 0.05,
+            "E5": 0.04,
+            "Helen Lloyd": 0.04,
+            "E3": 0.02,
+            "Ruth DeSand": 0.02,
+            "Verne Sanderson": 0.02,
+            "E12": 0.02,
+            "Myra Liddel": 0.02,
+            "E11": 0.02,
+            "Eleanor Nye": 0.01,
+            "Frances Anderson": 0.01,
+            "Pearl Oglethorpe": 0.01,
+            "E4": 0.01,
+            "Charlotte McDowd": 0.01,
+            "E10": 0.01,
+            "Olivia Carleton": 0.01,
+            "Flora Price": 0.01,
+            "E2": 0.00,
+            "E1": 0.00,
+            "Dorothy Murchison": 0.00,
+            "E13": 0.00,
+            "E14": 0.00,
+        }
+        for node, value in answer.items():
+            assert value == pytest.approx(bet[node], abs=1e-2)
+
+    def test_davis_closeness_centrality(self):
+        G = self.davis
+        clos = bipartite.closeness_centrality(G, self.top_nodes)
+        answer = {
+            "E8": 0.85,
+            "E9": 0.79,
+            "E7": 0.73,
+            "Nora Fayette": 0.80,
+            "Evelyn Jefferson": 0.80,
+            "Theresa Anderson": 0.80,
+            "E6": 0.69,
+            "Sylvia Avondale": 0.77,
+            "Laura Mandeville": 0.73,
+            "Brenda Rogers": 0.73,
+            "Katherina Rogers": 0.73,
+            "E5": 0.59,
+            "Helen Lloyd": 0.73,
+            "E3": 0.56,
+            "Ruth DeSand": 0.71,
+            "Verne Sanderson": 0.71,
+            "E12": 0.56,
+            "Myra Liddel": 0.69,
+            "E11": 0.54,
+            "Eleanor Nye": 0.67,
+            "Frances Anderson": 0.67,
+            "Pearl Oglethorpe": 0.67,
+            "E4": 0.54,
+            "Charlotte McDowd": 0.60,
+            "E10": 0.55,
+            "Olivia Carleton": 0.59,
+            "Flora Price": 0.59,
+            "E2": 0.52,
+            "E1": 0.52,
+            "Dorothy Murchison": 0.65,
+            "E13": 0.52,
+            "E14": 0.52,
+        }
+        for node, value in answer.items():
+            assert value == pytest.approx(clos[node], abs=1e-2)

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

@@ -0,0 +1,84 @@
+import pytest
+
+import networkx as nx
+from networkx.algorithms import bipartite
+from networkx.algorithms.bipartite.cluster import cc_dot, cc_max, cc_min
+
+
+def test_pairwise_bipartite_cc_functions():
+    # Test functions for different kinds of bipartite clustering coefficients
+    # between pairs of nodes using 3 example graphs from figure 5 p. 40
+    # Latapy et al (2008)
+    G1 = nx.Graph([(0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (1, 5), (1, 6), (1, 7)])
+    G2 = nx.Graph([(0, 2), (0, 3), (0, 4), (1, 3), (1, 4), (1, 5)])
+    G3 = nx.Graph(
+        [(0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9)]
+    )
+    result = {
+        0: [1 / 3.0, 2 / 3.0, 2 / 5.0],
+        1: [1 / 2.0, 2 / 3.0, 2 / 3.0],
+        2: [2 / 8.0, 2 / 5.0, 2 / 5.0],
+    }
+    for i, G in enumerate([G1, G2, G3]):
+        assert bipartite.is_bipartite(G)
+        assert cc_dot(set(G[0]), set(G[1])) == result[i][0]
+        assert cc_min(set(G[0]), set(G[1])) == result[i][1]
+        assert cc_max(set(G[0]), set(G[1])) == result[i][2]
+
+
+def test_star_graph():
+    G = nx.star_graph(3)
+    # all modes are the same
+    answer = {0: 0, 1: 1, 2: 1, 3: 1}
+    assert bipartite.clustering(G, mode="dot") == answer
+    assert bipartite.clustering(G, mode="min") == answer
+    assert bipartite.clustering(G, mode="max") == answer
+
+
+def test_not_bipartite():
+    with pytest.raises(nx.NetworkXError):
+        bipartite.clustering(nx.complete_graph(4))
+
+
+def test_bad_mode():
+    with pytest.raises(nx.NetworkXError):
+        bipartite.clustering(nx.path_graph(4), mode="foo")
+
+
+def test_path_graph():
+    G = nx.path_graph(4)
+    answer = {0: 0.5, 1: 0.5, 2: 0.5, 3: 0.5}
+    assert bipartite.clustering(G, mode="dot") == answer
+    assert bipartite.clustering(G, mode="max") == answer
+    answer = {0: 1, 1: 1, 2: 1, 3: 1}
+    assert bipartite.clustering(G, mode="min") == answer
+
+
+def test_average_path_graph():
+    G = nx.path_graph(4)
+    assert bipartite.average_clustering(G, mode="dot") == 0.5
+    assert bipartite.average_clustering(G, mode="max") == 0.5
+    assert bipartite.average_clustering(G, mode="min") == 1
+
+
+def test_ra_clustering_davis():
+    G = nx.davis_southern_women_graph()
+    cc4 = round(bipartite.robins_alexander_clustering(G), 3)
+    assert cc4 == 0.468
+
+
+def test_ra_clustering_square():
+    G = nx.path_graph(4)
+    G.add_edge(0, 3)
+    assert bipartite.robins_alexander_clustering(G) == 1.0
+
+
+def test_ra_clustering_zero():
+    G = nx.Graph()
+    assert bipartite.robins_alexander_clustering(G) == 0
+    G.add_nodes_from(range(4))
+    assert bipartite.robins_alexander_clustering(G) == 0
+    G.add_edges_from([(0, 1), (2, 3), (3, 4)])
+    assert bipartite.robins_alexander_clustering(G) == 0
+    G.add_edge(1, 2)
+    assert bipartite.robins_alexander_clustering(G) == 0

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

@@ -0,0 +1,409 @@
+import numbers
+
+import pytest
+
+import networkx as nx
+
+from ..generators import (
+    alternating_havel_hakimi_graph,
+    complete_bipartite_graph,
+    configuration_model,
+    gnmk_random_graph,
+    havel_hakimi_graph,
+    preferential_attachment_graph,
+    random_graph,
+    reverse_havel_hakimi_graph,
+)
+
+"""
+Generators - Bipartite
+----------------------
+"""
+
+
+class TestGeneratorsBipartite:
+    def test_complete_bipartite_graph(self):
+        G = complete_bipartite_graph(0, 0)
+        assert nx.is_isomorphic(G, nx.null_graph())
+
+        for i in [1, 5]:
+            G = complete_bipartite_graph(i, 0)
+            assert nx.is_isomorphic(G, nx.empty_graph(i))
+            G = complete_bipartite_graph(0, i)
+            assert nx.is_isomorphic(G, nx.empty_graph(i))
+
+        G = complete_bipartite_graph(2, 2)
+        assert nx.is_isomorphic(G, nx.cycle_graph(4))
+
+        G = complete_bipartite_graph(1, 5)
+        assert nx.is_isomorphic(G, nx.star_graph(5))
+
+        G = complete_bipartite_graph(5, 1)
+        assert nx.is_isomorphic(G, nx.star_graph(5))
+
+        # complete_bipartite_graph(m1,m2) is a connected graph with
+        # m1+m2 nodes and  m1*m2 edges
+        for m1, m2 in [(5, 11), (7, 3)]:
+            G = complete_bipartite_graph(m1, m2)
+            assert nx.number_of_nodes(G) == m1 + m2
+            assert nx.number_of_edges(G) == m1 * m2
+
+        with pytest.raises(nx.NetworkXError):
+            complete_bipartite_graph(7, 3, create_using=nx.DiGraph)
+        with pytest.raises(nx.NetworkXError):
+            complete_bipartite_graph(7, 3, create_using=nx.MultiDiGraph)
+
+        mG = complete_bipartite_graph(7, 3, create_using=nx.MultiGraph)
+        assert mG.is_multigraph()
+        assert sorted(mG.edges()) == sorted(G.edges())
+
+        mG = complete_bipartite_graph(7, 3, create_using=nx.MultiGraph)
+        assert mG.is_multigraph()
+        assert sorted(mG.edges()) == sorted(G.edges())
+
+        mG = complete_bipartite_graph(7, 3)  # default to Graph
+        assert sorted(mG.edges()) == sorted(G.edges())
+        assert not mG.is_multigraph()
+        assert not mG.is_directed()
+
+        # specify nodes rather than number of nodes
+        for n1, n2 in [([1, 2], "ab"), (3, 2), (3, "ab"), ("ab", 3)]:
+            G = complete_bipartite_graph(n1, n2)
+            if isinstance(n1, numbers.Integral):
+                if isinstance(n2, numbers.Integral):
+                    n2 = range(n1, n1 + n2)
+                n1 = range(n1)
+            elif isinstance(n2, numbers.Integral):
+                n2 = range(n2)
+            edges = {(u, v) for u in n1 for v in n2}
+            assert edges == set(G.edges)
+            assert G.size() == len(edges)
+
+        # raise when node sets are not distinct
+        for n1, n2 in [([1, 2], 3), (3, [1, 2]), ("abc", "bcd")]:
+            pytest.raises(nx.NetworkXError, complete_bipartite_graph, n1, n2)
+
+    def test_configuration_model(self):
+        aseq = []
+        bseq = []
+        G = configuration_model(aseq, bseq)
+        assert len(G) == 0
+
+        aseq = [0, 0]
+        bseq = [0, 0]
+        G = configuration_model(aseq, bseq)
+        assert len(G) == 4
+        assert G.number_of_edges() == 0
+
+        aseq = [3, 3, 3, 3]
+        bseq = [2, 2, 2, 2, 2]
+        pytest.raises(nx.NetworkXError, configuration_model, aseq, bseq)
+
+        aseq = [3, 3, 3, 3]
+        bseq = [2, 2, 2, 2, 2, 2]
+        G = configuration_model(aseq, bseq)
+        assert sorted(d for n, d in G.degree()) == [2, 2, 2, 2, 2, 2, 3, 3, 3, 3]
+
+        aseq = [2, 2, 2, 2, 2, 2]
+        bseq = [3, 3, 3, 3]
+        G = configuration_model(aseq, bseq)
+        assert sorted(d for n, d in G.degree()) == [2, 2, 2, 2, 2, 2, 3, 3, 3, 3]
+
+        aseq = [2, 2, 2, 1, 1, 1]
+        bseq = [3, 3, 3]
+        G = configuration_model(aseq, bseq)
+        assert G.is_multigraph()
+        assert not G.is_directed()
+        assert sorted(d for n, d in G.degree()) == [1, 1, 1, 2, 2, 2, 3, 3, 3]
+
+        GU = nx.projected_graph(nx.Graph(G), range(len(aseq)))
+        assert GU.number_of_nodes() == 6
+
+        GD = nx.projected_graph(nx.Graph(G), range(len(aseq), len(aseq) + len(bseq)))
+        assert GD.number_of_nodes() == 3
+
+        G = reverse_havel_hakimi_graph(aseq, bseq, create_using=nx.Graph)
+        assert not G.is_multigraph()
+        assert not G.is_directed()
+
+        pytest.raises(
+            nx.NetworkXError, configuration_model, aseq, bseq, create_using=nx.DiGraph()
+        )
+        pytest.raises(
+            nx.NetworkXError, configuration_model, aseq, bseq, create_using=nx.DiGraph
+        )
+        pytest.raises(
+            nx.NetworkXError,
+            configuration_model,
+            aseq,
+            bseq,
+            create_using=nx.MultiDiGraph,
+        )
+
+    def test_havel_hakimi_graph(self):
+        aseq = []
+        bseq = []
+        G = havel_hakimi_graph(aseq, bseq)
+        assert len(G) == 0
+
+        aseq = [0, 0]
+        bseq = [0, 0]
+        G = havel_hakimi_graph(aseq, bseq)
+        assert len(G) == 4
+        assert G.number_of_edges() == 0
+
+        aseq = [3, 3, 3, 3]
+        bseq = [2, 2, 2, 2, 2]
+        pytest.raises(nx.NetworkXError, havel_hakimi_graph, aseq, bseq)
+
+        bseq = [2, 2, 2, 2, 2, 2]
+        G = havel_hakimi_graph(aseq, bseq)
+        assert sorted(d for n, d in G.degree()) == [2, 2, 2, 2, 2, 2, 3, 3, 3, 3]
+
+        aseq = [2, 2, 2, 2, 2, 2]
+        bseq = [3, 3, 3, 3]
+        G = havel_hakimi_graph(aseq, bseq)
+        assert G.is_multigraph()
+        assert not G.is_directed()
+        assert sorted(d for n, d in G.degree()) == [2, 2, 2, 2, 2, 2, 3, 3, 3, 3]
+
+        GU = nx.projected_graph(nx.Graph(G), range(len(aseq)))
+        assert GU.number_of_nodes() == 6
+
+        GD = nx.projected_graph(nx.Graph(G), range(len(aseq), len(aseq) + len(bseq)))
+        assert GD.number_of_nodes() == 4
+
+        G = reverse_havel_hakimi_graph(aseq, bseq, create_using=nx.Graph)
+        assert not G.is_multigraph()
+        assert not G.is_directed()
+
+        pytest.raises(
+            nx.NetworkXError, havel_hakimi_graph, aseq, bseq, create_using=nx.DiGraph
+        )
+        pytest.raises(
+            nx.NetworkXError, havel_hakimi_graph, aseq, bseq, create_using=nx.DiGraph
+        )
+        pytest.raises(
+            nx.NetworkXError,
+            havel_hakimi_graph,
+            aseq,
+            bseq,
+            create_using=nx.MultiDiGraph,
+        )
+
+    def test_reverse_havel_hakimi_graph(self):
+        aseq = []
+        bseq = []
+        G = reverse_havel_hakimi_graph(aseq, bseq)
+        assert len(G) == 0
+
+        aseq = [0, 0]
+        bseq = [0, 0]
+        G = reverse_havel_hakimi_graph(aseq, bseq)
+        assert len(G) == 4
+        assert G.number_of_edges() == 0
+
+        aseq = [3, 3, 3, 3]
+        bseq = [2, 2, 2, 2, 2]
+        pytest.raises(nx.NetworkXError, reverse_havel_hakimi_graph, aseq, bseq)
+
+        bseq = [2, 2, 2, 2, 2, 2]
+        G = reverse_havel_hakimi_graph(aseq, bseq)
+        assert sorted(d for n, d in G.degree()) == [2, 2, 2, 2, 2, 2, 3, 3, 3, 3]
+
+        aseq = [2, 2, 2, 2, 2, 2]
+        bseq = [3, 3, 3, 3]
+        G = reverse_havel_hakimi_graph(aseq, bseq)
+        assert sorted(d for n, d in G.degree()) == [2, 2, 2, 2, 2, 2, 3, 3, 3, 3]
+
+        aseq = [2, 2, 2, 1, 1, 1]
+        bseq = [3, 3, 3]
+        G = reverse_havel_hakimi_graph(aseq, bseq)
+        assert G.is_multigraph()
+        assert not G.is_directed()
+        assert sorted(d for n, d in G.degree()) == [1, 1, 1, 2, 2, 2, 3, 3, 3]
+
+        GU = nx.projected_graph(nx.Graph(G), range(len(aseq)))
+        assert GU.number_of_nodes() == 6
+
+        GD = nx.projected_graph(nx.Graph(G), range(len(aseq), len(aseq) + len(bseq)))
+        assert GD.number_of_nodes() == 3
+
+        G = reverse_havel_hakimi_graph(aseq, bseq, create_using=nx.Graph)
+        assert not G.is_multigraph()
+        assert not G.is_directed()
+
+        pytest.raises(
+            nx.NetworkXError,
+            reverse_havel_hakimi_graph,
+            aseq,
+            bseq,
+            create_using=nx.DiGraph,
+        )
+        pytest.raises(
+            nx.NetworkXError,
+            reverse_havel_hakimi_graph,
+            aseq,
+            bseq,
+            create_using=nx.DiGraph,
+        )
+        pytest.raises(
+            nx.NetworkXError,
+            reverse_havel_hakimi_graph,
+            aseq,
+            bseq,
+            create_using=nx.MultiDiGraph,
+        )
+
+    def test_alternating_havel_hakimi_graph(self):
+        aseq = []
+        bseq = []
+        G = alternating_havel_hakimi_graph(aseq, bseq)
+        assert len(G) == 0
+
+        aseq = [0, 0]
+        bseq = [0, 0]
+        G = alternating_havel_hakimi_graph(aseq, bseq)
+        assert len(G) == 4
+        assert G.number_of_edges() == 0
+
+        aseq = [3, 3, 3, 3]
+        bseq = [2, 2, 2, 2, 2]
+        pytest.raises(nx.NetworkXError, alternating_havel_hakimi_graph, aseq, bseq)
+
+        bseq = [2, 2, 2, 2, 2, 2]
+        G = alternating_havel_hakimi_graph(aseq, bseq)
+        assert sorted(d for n, d in G.degree()) == [2, 2, 2, 2, 2, 2, 3, 3, 3, 3]
+
+        aseq = [2, 2, 2, 2, 2, 2]
+        bseq = [3, 3, 3, 3]
+        G = alternating_havel_hakimi_graph(aseq, bseq)
+        assert sorted(d for n, d in G.degree()) == [2, 2, 2, 2, 2, 2, 3, 3, 3, 3]
+
+        aseq = [2, 2, 2, 1, 1, 1]
+        bseq = [3, 3, 3]
+        G = alternating_havel_hakimi_graph(aseq, bseq)
+        assert G.is_multigraph()
+        assert not G.is_directed()
+        assert sorted(d for n, d in G.degree()) == [1, 1, 1, 2, 2, 2, 3, 3, 3]
+
+        GU = nx.projected_graph(nx.Graph(G), range(len(aseq)))
+        assert GU.number_of_nodes() == 6
+
+        GD = nx.projected_graph(nx.Graph(G), range(len(aseq), len(aseq) + len(bseq)))
+        assert GD.number_of_nodes() == 3
+
+        G = reverse_havel_hakimi_graph(aseq, bseq, create_using=nx.Graph)
+        assert not G.is_multigraph()
+        assert not G.is_directed()
+
+        pytest.raises(
+            nx.NetworkXError,
+            alternating_havel_hakimi_graph,
+            aseq,
+            bseq,
+            create_using=nx.DiGraph,
+        )
+        pytest.raises(
+            nx.NetworkXError,
+            alternating_havel_hakimi_graph,
+            aseq,
+            bseq,
+            create_using=nx.DiGraph,
+        )
+        pytest.raises(
+            nx.NetworkXError,
+            alternating_havel_hakimi_graph,
+            aseq,
+            bseq,
+            create_using=nx.MultiDiGraph,
+        )
+
+    def test_preferential_attachment(self):
+        aseq = [3, 2, 1, 1]
+        G = preferential_attachment_graph(aseq, 0.5)
+        assert G.is_multigraph()
+        assert not G.is_directed()
+
+        G = preferential_attachment_graph(aseq, 0.5, create_using=nx.Graph)
+        assert not G.is_multigraph()
+        assert not G.is_directed()
+
+        pytest.raises(
+            nx.NetworkXError,
+            preferential_attachment_graph,
+            aseq,
+            0.5,
+            create_using=nx.DiGraph(),
+        )
+        pytest.raises(
+            nx.NetworkXError,
+            preferential_attachment_graph,
+            aseq,
+            0.5,
+            create_using=nx.DiGraph(),
+        )
+        pytest.raises(
+            nx.NetworkXError,
+            preferential_attachment_graph,
+            aseq,
+            0.5,
+            create_using=nx.DiGraph(),
+        )
+
+    def test_random_graph(self):
+        n = 10
+        m = 20
+        G = random_graph(n, m, 0.9)
+        assert len(G) == 30
+        assert nx.is_bipartite(G)
+        X, Y = nx.algorithms.bipartite.sets(G)
+        assert set(range(n)) == X
+        assert set(range(n, n + m)) == Y
+
+    def test_random_digraph(self):
+        n = 10
+        m = 20
+        G = random_graph(n, m, 0.9, directed=True)
+        assert len(G) == 30
+        assert nx.is_bipartite(G)
+        X, Y = nx.algorithms.bipartite.sets(G)
+        assert set(range(n)) == X
+        assert set(range(n, n + m)) == Y
+
+    def test_gnmk_random_graph(self):
+        n = 10
+        m = 20
+        edges = 100
+        # set seed because sometimes it is not connected
+        # which raises an error in bipartite.sets(G) below.
+        G = gnmk_random_graph(n, m, edges, seed=1234)
+        assert len(G) == n + m
+        assert nx.is_bipartite(G)
+        X, Y = nx.algorithms.bipartite.sets(G)
+        # print(X)
+        assert set(range(n)) == X
+        assert set(range(n, n + m)) == Y
+        assert edges == len(list(G.edges()))
+
+    def test_gnmk_random_graph_complete(self):
+        n = 10
+        m = 20
+        edges = 200
+        G = gnmk_random_graph(n, m, edges)
+        assert len(G) == n + m
+        assert nx.is_bipartite(G)
+        X, Y = nx.algorithms.bipartite.sets(G)
+        # print(X)
+        assert set(range(n)) == X
+        assert set(range(n, n + m)) == Y
+        assert edges == len(list(G.edges()))
+
+    @pytest.mark.parametrize("n", (4, range(4), {0, 1, 2, 3}))
+    @pytest.mark.parametrize("m", (range(4, 7), {4, 5, 6}))
+    def test_complete_bipartite_graph_str(self, n, m):
+        """Ensure G.name is consistent for all inputs accepted by nodes_or_number.
+        See gh-7396"""
+        G = nx.complete_bipartite_graph(n, m)
+        ans = "Graph named 'complete_bipartite_graph(4, 3)' with 7 nodes and 12 edges"
+        assert str(G) == ans

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

@@ -0,0 +1,407 @@
+import pytest
+
+import networkx as nx
+from networkx.algorithms import bipartite
+from networkx.utils import edges_equal, nodes_equal
+
+
+class TestBipartiteProject:
+    def test_path_projected_graph(self):
+        G = nx.path_graph(4)
+        P = bipartite.projected_graph(G, [1, 3])
+        assert nodes_equal(list(P), [1, 3])
+        assert edges_equal(list(P.edges()), [(1, 3)])
+        P = bipartite.projected_graph(G, [0, 2])
+        assert nodes_equal(list(P), [0, 2])
+        assert edges_equal(list(P.edges()), [(0, 2)])
+        G = nx.MultiGraph([(0, 1)])
+        with pytest.raises(nx.NetworkXError, match="not defined for multigraphs"):
+            bipartite.projected_graph(G, [0])
+
+    def test_path_projected_properties_graph(self):
+        G = nx.path_graph(4)
+        G.add_node(1, name="one")
+        G.add_node(2, name="two")
+        P = bipartite.projected_graph(G, [1, 3])
+        assert nodes_equal(list(P), [1, 3])
+        assert edges_equal(list(P.edges()), [(1, 3)])
+        assert P.nodes[1]["name"] == G.nodes[1]["name"]
+        P = bipartite.projected_graph(G, [0, 2])
+        assert nodes_equal(list(P), [0, 2])
+        assert edges_equal(list(P.edges()), [(0, 2)])
+        assert P.nodes[2]["name"] == G.nodes[2]["name"]
+
+    def test_path_collaboration_projected_graph(self):
+        G = nx.path_graph(4)
+        P = bipartite.collaboration_weighted_projected_graph(G, [1, 3])
+        assert nodes_equal(list(P), [1, 3])
+        assert edges_equal(list(P.edges()), [(1, 3)])
+        P[1][3]["weight"] = 1
+        P = bipartite.collaboration_weighted_projected_graph(G, [0, 2])
+        assert nodes_equal(list(P), [0, 2])
+        assert edges_equal(list(P.edges()), [(0, 2)])
+        P[0][2]["weight"] = 1
+
+    def test_directed_path_collaboration_projected_graph(self):
+        G = nx.DiGraph()
+        nx.add_path(G, range(4))
+        P = bipartite.collaboration_weighted_projected_graph(G, [1, 3])
+        assert nodes_equal(list(P), [1, 3])
+        assert edges_equal(list(P.edges()), [(1, 3)])
+        P[1][3]["weight"] = 1
+        P = bipartite.collaboration_weighted_projected_graph(G, [0, 2])
+        assert nodes_equal(list(P), [0, 2])
+        assert edges_equal(list(P.edges()), [(0, 2)])
+        P[0][2]["weight"] = 1
+
+    def test_path_weighted_projected_graph(self):
+        G = nx.path_graph(4)
+
+        with pytest.raises(nx.NetworkXAlgorithmError):
+            bipartite.weighted_projected_graph(G, [1, 2, 3, 3])
+
+        P = bipartite.weighted_projected_graph(G, [1, 3])
+        assert nodes_equal(list(P), [1, 3])
+        assert edges_equal(list(P.edges()), [(1, 3)])
+        P[1][3]["weight"] = 1
+        P = bipartite.weighted_projected_graph(G, [0, 2])
+        assert nodes_equal(list(P), [0, 2])
+        assert edges_equal(list(P.edges()), [(0, 2)])
+        P[0][2]["weight"] = 1
+
+    def test_digraph_weighted_projection(self):
+        G = nx.DiGraph([(0, 1), (1, 2), (2, 3), (3, 4)])
+        P = bipartite.overlap_weighted_projected_graph(G, [1, 3])
+        assert nx.get_edge_attributes(P, "weight") == {(1, 3): 1.0}
+        assert len(P) == 2
+
+    def test_path_weighted_projected_directed_graph(self):
+        G = nx.DiGraph()
+        nx.add_path(G, range(4))
+        P = bipartite.weighted_projected_graph(G, [1, 3])
+        assert nodes_equal(list(P), [1, 3])
+        assert edges_equal(list(P.edges()), [(1, 3)])
+        P[1][3]["weight"] = 1
+        P = bipartite.weighted_projected_graph(G, [0, 2])
+        assert nodes_equal(list(P), [0, 2])
+        assert edges_equal(list(P.edges()), [(0, 2)])
+        P[0][2]["weight"] = 1
+
+    def test_star_projected_graph(self):
+        G = nx.star_graph(3)
+        P = bipartite.projected_graph(G, [1, 2, 3])
+        assert nodes_equal(list(P), [1, 2, 3])
+        assert edges_equal(list(P.edges()), [(1, 2), (1, 3), (2, 3)])
+        P = bipartite.weighted_projected_graph(G, [1, 2, 3])
+        assert nodes_equal(list(P), [1, 2, 3])
+        assert edges_equal(list(P.edges()), [(1, 2), (1, 3), (2, 3)])
+
+        P = bipartite.projected_graph(G, [0])
+        assert nodes_equal(list(P), [0])
+        assert edges_equal(list(P.edges()), [])
+
+    def test_project_multigraph(self):
+        G = nx.Graph()
+        G.add_edge("a", 1)
+        G.add_edge("b", 1)
+        G.add_edge("a", 2)
+        G.add_edge("b", 2)
+        P = bipartite.projected_graph(G, "ab")
+        assert edges_equal(list(P.edges()), [("a", "b")])
+        P = bipartite.weighted_projected_graph(G, "ab")
+        assert edges_equal(list(P.edges()), [("a", "b")])
+        P = bipartite.projected_graph(G, "ab", multigraph=True)
+        assert edges_equal(list(P.edges()), [("a", "b"), ("a", "b")])
+
+    def test_project_collaboration(self):
+        G = nx.Graph()
+        G.add_edge("a", 1)
+        G.add_edge("b", 1)
+        G.add_edge("b", 2)
+        G.add_edge("c", 2)
+        G.add_edge("c", 3)
+        G.add_edge("c", 4)
+        G.add_edge("b", 4)
+        P = bipartite.collaboration_weighted_projected_graph(G, "abc")
+        assert P["a"]["b"]["weight"] == 1
+        assert P["b"]["c"]["weight"] == 2
+
+    def test_directed_projection(self):
+        G = nx.DiGraph()
+        G.add_edge("A", 1)
+        G.add_edge(1, "B")
+        G.add_edge("A", 2)
+        G.add_edge("B", 2)
+        P = bipartite.projected_graph(G, "AB")
+        assert edges_equal(list(P.edges()), [("A", "B")])
+        P = bipartite.weighted_projected_graph(G, "AB")
+        assert edges_equal(list(P.edges()), [("A", "B")])
+        assert P["A"]["B"]["weight"] == 1
+
+        P = bipartite.projected_graph(G, "AB", multigraph=True)
+        assert edges_equal(list(P.edges()), [("A", "B")])
+
+        G = nx.DiGraph()
+        G.add_edge("A", 1)
+        G.add_edge(1, "B")
+        G.add_edge("A", 2)
+        G.add_edge(2, "B")
+        P = bipartite.projected_graph(G, "AB")
+        assert edges_equal(list(P.edges()), [("A", "B")])
+        P = bipartite.weighted_projected_graph(G, "AB")
+        assert edges_equal(list(P.edges()), [("A", "B")])
+        assert P["A"]["B"]["weight"] == 2
+
+        P = bipartite.projected_graph(G, "AB", multigraph=True)
+        assert edges_equal(list(P.edges()), [("A", "B"), ("A", "B")])
+
+
+class TestBipartiteWeightedProjection:
+    @classmethod
+    def setup_class(cls):
+        # Tore Opsahl's example
+        # http://toreopsahl.com/2009/05/01/projecting-two-mode-networks-onto-weighted-one-mode-networks/
+        cls.G = nx.Graph()
+        cls.G.add_edge("A", 1)
+        cls.G.add_edge("A", 2)
+        cls.G.add_edge("B", 1)
+        cls.G.add_edge("B", 2)
+        cls.G.add_edge("B", 3)
+        cls.G.add_edge("B", 4)
+        cls.G.add_edge("B", 5)
+        cls.G.add_edge("C", 1)
+        cls.G.add_edge("D", 3)
+        cls.G.add_edge("E", 4)
+        cls.G.add_edge("E", 5)
+        cls.G.add_edge("E", 6)
+        cls.G.add_edge("F", 6)
+        # Graph based on figure 6 from Newman (2001)
+        cls.N = nx.Graph()
+        cls.N.add_edge("A", 1)
+        cls.N.add_edge("A", 2)
+        cls.N.add_edge("A", 3)
+        cls.N.add_edge("B", 1)
+        cls.N.add_edge("B", 2)
+        cls.N.add_edge("B", 3)
+        cls.N.add_edge("C", 1)
+        cls.N.add_edge("D", 1)
+        cls.N.add_edge("E", 3)
+
+    def test_project_weighted_shared(self):
+        edges = [
+            ("A", "B", 2),
+            ("A", "C", 1),
+            ("B", "C", 1),
+            ("B", "D", 1),
+            ("B", "E", 2),
+            ("E", "F", 1),
+        ]
+        Panswer = nx.Graph()
+        Panswer.add_weighted_edges_from(edges)
+        P = bipartite.weighted_projected_graph(self.G, "ABCDEF")
+        assert edges_equal(list(P.edges()), Panswer.edges())
+        for u, v in list(P.edges()):
+            assert P[u][v]["weight"] == Panswer[u][v]["weight"]
+
+        edges = [
+            ("A", "B", 3),
+            ("A", "E", 1),
+            ("A", "C", 1),
+            ("A", "D", 1),
+            ("B", "E", 1),
+            ("B", "C", 1),
+            ("B", "D", 1),
+            ("C", "D", 1),
+        ]
+        Panswer = nx.Graph()
+        Panswer.add_weighted_edges_from(edges)
+        P = bipartite.weighted_projected_graph(self.N, "ABCDE")
+        assert edges_equal(list(P.edges()), Panswer.edges())
+        for u, v in list(P.edges()):
+            assert P[u][v]["weight"] == Panswer[u][v]["weight"]
+
+    def test_project_weighted_newman(self):
+        edges = [
+            ("A", "B", 1.5),
+            ("A", "C", 0.5),
+            ("B", "C", 0.5),
+            ("B", "D", 1),
+            ("B", "E", 2),
+            ("E", "F", 1),
+        ]
+        Panswer = nx.Graph()
+        Panswer.add_weighted_edges_from(edges)
+        P = bipartite.collaboration_weighted_projected_graph(self.G, "ABCDEF")
+        assert edges_equal(list(P.edges()), Panswer.edges())
+        for u, v in list(P.edges()):
+            assert P[u][v]["weight"] == Panswer[u][v]["weight"]
+
+        edges = [
+            ("A", "B", 11 / 6.0),
+            ("A", "E", 1 / 2.0),
+            ("A", "C", 1 / 3.0),
+            ("A", "D", 1 / 3.0),
+            ("B", "E", 1 / 2.0),
+            ("B", "C", 1 / 3.0),
+            ("B", "D", 1 / 3.0),
+            ("C", "D", 1 / 3.0),
+        ]
+        Panswer = nx.Graph()
+        Panswer.add_weighted_edges_from(edges)
+        P = bipartite.collaboration_weighted_projected_graph(self.N, "ABCDE")
+        assert edges_equal(list(P.edges()), Panswer.edges())
+        for u, v in list(P.edges()):
+            assert P[u][v]["weight"] == Panswer[u][v]["weight"]
+
+    def test_project_weighted_ratio(self):
+        edges = [
+            ("A", "B", 2 / 6.0),
+            ("A", "C", 1 / 6.0),
+            ("B", "C", 1 / 6.0),
+            ("B", "D", 1 / 6.0),
+            ("B", "E", 2 / 6.0),
+            ("E", "F", 1 / 6.0),
+        ]
+        Panswer = nx.Graph()
+        Panswer.add_weighted_edges_from(edges)
+        P = bipartite.weighted_projected_graph(self.G, "ABCDEF", ratio=True)
+        assert edges_equal(list(P.edges()), Panswer.edges())
+        for u, v in list(P.edges()):
+            assert P[u][v]["weight"] == Panswer[u][v]["weight"]
+
+        edges = [
+            ("A", "B", 3 / 3.0),
+            ("A", "E", 1 / 3.0),
+            ("A", "C", 1 / 3.0),
+            ("A", "D", 1 / 3.0),
+            ("B", "E", 1 / 3.0),
+            ("B", "C", 1 / 3.0),
+            ("B", "D", 1 / 3.0),
+            ("C", "D", 1 / 3.0),
+        ]
+        Panswer = nx.Graph()
+        Panswer.add_weighted_edges_from(edges)
+        P = bipartite.weighted_projected_graph(self.N, "ABCDE", ratio=True)
+        assert edges_equal(list(P.edges()), Panswer.edges())
+        for u, v in list(P.edges()):
+            assert P[u][v]["weight"] == Panswer[u][v]["weight"]
+
+    def test_project_weighted_overlap(self):
+        edges = [
+            ("A", "B", 2 / 2.0),
+            ("A", "C", 1 / 1.0),
+            ("B", "C", 1 / 1.0),
+            ("B", "D", 1 / 1.0),
+            ("B", "E", 2 / 3.0),
+            ("E", "F", 1 / 1.0),
+        ]
+        Panswer = nx.Graph()
+        Panswer.add_weighted_edges_from(edges)
+        P = bipartite.overlap_weighted_projected_graph(self.G, "ABCDEF", jaccard=False)
+        assert edges_equal(list(P.edges()), Panswer.edges())
+        for u, v in list(P.edges()):
+            assert P[u][v]["weight"] == Panswer[u][v]["weight"]
+
+        edges = [
+            ("A", "B", 3 / 3.0),
+            ("A", "E", 1 / 1.0),
+            ("A", "C", 1 / 1.0),
+            ("A", "D", 1 / 1.0),
+            ("B", "E", 1 / 1.0),
+            ("B", "C", 1 / 1.0),
+            ("B", "D", 1 / 1.0),
+            ("C", "D", 1 / 1.0),
+        ]
+        Panswer = nx.Graph()
+        Panswer.add_weighted_edges_from(edges)
+        P = bipartite.overlap_weighted_projected_graph(self.N, "ABCDE", jaccard=False)
+        assert edges_equal(list(P.edges()), Panswer.edges())
+        for u, v in list(P.edges()):
+            assert P[u][v]["weight"] == Panswer[u][v]["weight"]
+
+    def test_project_weighted_jaccard(self):
+        edges = [
+            ("A", "B", 2 / 5.0),
+            ("A", "C", 1 / 2.0),
+            ("B", "C", 1 / 5.0),
+            ("B", "D", 1 / 5.0),
+            ("B", "E", 2 / 6.0),
+            ("E", "F", 1 / 3.0),
+        ]
+        Panswer = nx.Graph()
+        Panswer.add_weighted_edges_from(edges)
+        P = bipartite.overlap_weighted_projected_graph(self.G, "ABCDEF")
+        assert edges_equal(list(P.edges()), Panswer.edges())
+        for u, v in list(P.edges()):
+            assert P[u][v]["weight"] == Panswer[u][v]["weight"]
+
+        edges = [
+            ("A", "B", 3 / 3.0),
+            ("A", "E", 1 / 3.0),
+            ("A", "C", 1 / 3.0),
+            ("A", "D", 1 / 3.0),
+            ("B", "E", 1 / 3.0),
+            ("B", "C", 1 / 3.0),
+            ("B", "D", 1 / 3.0),
+            ("C", "D", 1 / 1.0),
+        ]
+        Panswer = nx.Graph()
+        Panswer.add_weighted_edges_from(edges)
+        P = bipartite.overlap_weighted_projected_graph(self.N, "ABCDE")
+        assert edges_equal(list(P.edges()), Panswer.edges())
+        for u, v in P.edges():
+            assert P[u][v]["weight"] == Panswer[u][v]["weight"]
+
+    def test_generic_weighted_projected_graph_simple(self):
+        def shared(G, u, v):
+            return len(set(G[u]) & set(G[v]))
+
+        B = nx.path_graph(5)
+        G = bipartite.generic_weighted_projected_graph(
+            B, [0, 2, 4], weight_function=shared
+        )
+        assert nodes_equal(list(G), [0, 2, 4])
+        assert edges_equal(
+            list(G.edges(data=True)),
+            [(0, 2, {"weight": 1}), (2, 4, {"weight": 1})],
+        )
+
+        G = bipartite.generic_weighted_projected_graph(B, [0, 2, 4])
+        assert nodes_equal(list(G), [0, 2, 4])
+        assert edges_equal(
+            list(G.edges(data=True)),
+            [(0, 2, {"weight": 1}), (2, 4, {"weight": 1})],
+        )
+        B = nx.DiGraph()
+        nx.add_path(B, range(5))
+        G = bipartite.generic_weighted_projected_graph(B, [0, 2, 4])
+        assert nodes_equal(list(G), [0, 2, 4])
+        assert edges_equal(
+            list(G.edges(data=True)), [(0, 2, {"weight": 1}), (2, 4, {"weight": 1})]
+        )
+
+    def test_generic_weighted_projected_graph_custom(self):
+        def jaccard(G, u, v):
+            unbrs = set(G[u])
+            vnbrs = set(G[v])
+            return 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.edges[u, nbr].get(weight, 1) + G.edges[v, nbr].get(weight, 1)
+            return w
+
+        B = nx.bipartite.complete_bipartite_graph(2, 2)
+        for i, (u, v) in enumerate(B.edges()):
+            B.edges[u, v]["weight"] = i + 1
+        G = bipartite.generic_weighted_projected_graph(
+            B, [0, 1], weight_function=jaccard
+        )
+        assert edges_equal(list(G.edges(data=True)), [(0, 1, {"weight": 1.0})])
+        G = bipartite.generic_weighted_projected_graph(
+            B, [0, 1], weight_function=my_weight
+        )
+        assert edges_equal(list(G.edges(data=True)), [(0, 1, {"weight": 10})])
+        G = bipartite.generic_weighted_projected_graph(B, [0, 1])
+        assert edges_equal(list(G.edges(data=True)), [(0, 1, {"weight": 2})])

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

@@ -0,0 +1,35 @@
+"""Unit tests for the :mod:`networkx.algorithms.bipartite.redundancy` module."""
+
+import pytest
+
+from networkx import NetworkXError, cycle_graph
+from networkx.algorithms.bipartite import complete_bipartite_graph, node_redundancy
+
+
+def test_no_redundant_nodes():
+    G = complete_bipartite_graph(2, 2)
+
+    # when nodes is None
+    rc = node_redundancy(G)
+    assert all(redundancy == 1 for redundancy in rc.values())
+
+    # when set of nodes is specified
+    rc = node_redundancy(G, (2, 3))
+    assert rc == {2: 1.0, 3: 1.0}
+
+
+def test_redundant_nodes():
+    G = cycle_graph(6)
+    edge = {0, 3}
+    G.add_edge(*edge)
+    redundancy = node_redundancy(G)
+    for v in edge:
+        assert redundancy[v] == 2 / 3
+    for v in set(G) - edge:
+        assert redundancy[v] == 1
+
+
+def test_not_enough_neighbors():
+    with pytest.raises(NetworkXError):
+        G = complete_bipartite_graph(1, 2)
+        node_redundancy(G)

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

@@ -0,0 +1,20 @@
+from .betweenness import *
+from .betweenness_subset import *
+from .closeness import *
+from .current_flow_betweenness import *
+from .current_flow_betweenness_subset import *
+from .current_flow_closeness import *
+from .degree_alg import *
+from .dispersion import *
+from .eigenvector import *
+from .group import *
+from .harmonic import *
+from .katz import *
+from .load import *
+from .percolation import *
+from .reaching import *
+from .second_order import *
+from .subgraph_alg import *
+from .trophic import *
+from .voterank_alg import *
+from .laplacian import *

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

@@ -0,0 +1,436 @@
+"""Betweenness centrality measures."""
+
+from collections import deque
+from heapq import heappop, heappush
+from itertools import count
+
+import networkx as nx
+from networkx.algorithms.shortest_paths.weighted import _weight_function
+from networkx.utils import py_random_state
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = ["betweenness_centrality", "edge_betweenness_centrality"]
+
+
+@py_random_state(5)
+@nx._dispatchable(edge_attrs="weight")
+def betweenness_centrality(
+    G, k=None, normalized=True, weight=None, endpoints=False, seed=None
+):
+    r"""Compute the shortest-path betweenness centrality for nodes.
+
+    Betweenness centrality of a node $v$ is the sum of the
+    fraction of all-pairs shortest paths that pass through $v$
+
+    .. math::
+
+       c_B(v) =\sum_{s,t \in V} \frac{\sigma(s, t|v)}{\sigma(s, t)}
+
+    where $V$ is the set of nodes, $\sigma(s, t)$ is the number of
+    shortest $(s, t)$-paths,  and $\sigma(s, t|v)$ is the number of
+    those paths  passing through some  node $v$ other than $s, t$.
+    If $s = t$, $\sigma(s, t) = 1$, and if $v \in {s, t}$,
+    $\sigma(s, t|v) = 0$ [2]_.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph.
+
+    k : int, optional (default=None)
+      If k is not None use k node samples to estimate betweenness.
+      The value of k <= n where n is the number of nodes in the graph.
+      Higher values give better approximation.
+
+    normalized : bool, optional
+      If True the betweenness values are normalized by `2/((n-1)(n-2))`
+      for graphs, and `1/((n-1)(n-2))` for directed graphs where `n`
+      is the number of nodes in G.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      Weights are used to calculate weighted shortest paths, so they are
+      interpreted as distances.
+
+    endpoints : bool, optional
+      If True include the endpoints in the shortest path counts.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+        Note that this is only used if k is not None.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with betweenness centrality as the value.
+
+    See Also
+    --------
+    edge_betweenness_centrality
+    load_centrality
+
+    Notes
+    -----
+    The algorithm is from Ulrik Brandes [1]_.
+    See [4]_ for the original first published version and [2]_ for details on
+    algorithms for variations and related metrics.
+
+    For approximate betweenness calculations set k=#samples to use
+    k nodes ("pivots") to estimate the betweenness values. For an estimate
+    of the number of pivots needed see [3]_.
+
+    For weighted graphs the edge weights must be greater than zero.
+    Zero edge weights can produce an infinite number of equal length
+    paths between pairs of nodes.
+
+    The total number of paths between source and target is counted
+    differently for directed and undirected graphs. Directed paths
+    are easy to count. Undirected paths are tricky: should a path
+    from "u" to "v" count as 1 undirected path or as 2 directed paths?
+
+    For betweenness_centrality we report the number of undirected
+    paths when G is undirected.
+
+    For betweenness_centrality_subset the reporting is different.
+    If the source and target subsets are the same, then we want
+    to count undirected paths. But if the source and target subsets
+    differ -- for example, if sources is {0} and targets is {1},
+    then we are only counting the paths in one direction. They are
+    undirected paths but we are counting them in a directed way.
+    To count them as undirected paths, each should count as half a path.
+
+    This algorithm is not guaranteed to be correct if edge weights
+    are floating point numbers. As a workaround you can use integer
+    numbers by multiplying the relevant edge attributes by a convenient
+    constant factor (eg 100) and converting to integers.
+
+    References
+    ----------
+    .. [1] Ulrik Brandes:
+       A Faster Algorithm for Betweenness Centrality.
+       Journal of Mathematical Sociology 25(2):163-177, 2001.
+       https://doi.org/10.1080/0022250X.2001.9990249
+    .. [2] Ulrik Brandes:
+       On Variants of Shortest-Path Betweenness
+       Centrality and their Generic Computation.
+       Social Networks 30(2):136-145, 2008.
+       https://doi.org/10.1016/j.socnet.2007.11.001
+    .. [3] Ulrik Brandes and Christian Pich:
+       Centrality Estimation in Large Networks.
+       International Journal of Bifurcation and Chaos 17(7):2303-2318, 2007.
+       https://dx.doi.org/10.1142/S0218127407018403
+    .. [4] Linton C. Freeman:
+       A set of measures of centrality based on betweenness.
+       Sociometry 40: 35–41, 1977
+       https://doi.org/10.2307/3033543
+    """
+    betweenness = dict.fromkeys(G, 0.0)  # b[v]=0 for v in G
+    if k is None:
+        nodes = G
+    else:
+        nodes = seed.sample(list(G.nodes()), k)
+    for s in nodes:
+        # single source shortest paths
+        if weight is None:  # use BFS
+            S, P, sigma, _ = _single_source_shortest_path_basic(G, s)
+        else:  # use Dijkstra's algorithm
+            S, P, sigma, _ = _single_source_dijkstra_path_basic(G, s, weight)
+        # accumulation
+        if endpoints:
+            betweenness, _ = _accumulate_endpoints(betweenness, S, P, sigma, s)
+        else:
+            betweenness, _ = _accumulate_basic(betweenness, S, P, sigma, s)
+    # rescaling
+    betweenness = _rescale(
+        betweenness,
+        len(G),
+        normalized=normalized,
+        directed=G.is_directed(),
+        k=k,
+        endpoints=endpoints,
+    )
+    return betweenness
+
+
+@py_random_state(4)
+@nx._dispatchable(edge_attrs="weight")
+def edge_betweenness_centrality(G, k=None, normalized=True, weight=None, seed=None):
+    r"""Compute betweenness centrality for edges.
+
+    Betweenness centrality of an edge $e$ is the sum of the
+    fraction of all-pairs shortest paths that pass through $e$
+
+    .. math::
+
+       c_B(e) =\sum_{s,t \in V} \frac{\sigma(s, t|e)}{\sigma(s, t)}
+
+    where $V$ is the set of nodes, $\sigma(s, t)$ is the number of
+    shortest $(s, t)$-paths, and $\sigma(s, t|e)$ is the number of
+    those paths passing through edge $e$ [2]_.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph.
+
+    k : int, optional (default=None)
+      If k is not None use k node samples to estimate betweenness.
+      The value of k <= n where n is the number of nodes in the graph.
+      Higher values give better approximation.
+
+    normalized : bool, optional
+      If True the betweenness values are normalized by $2/(n(n-1))$
+      for graphs, and $1/(n(n-1))$ for directed graphs where $n$
+      is the number of nodes in G.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      Weights are used to calculate weighted shortest paths, so they are
+      interpreted as distances.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+        Note that this is only used if k is not None.
+
+    Returns
+    -------
+    edges : dictionary
+       Dictionary of edges with betweenness centrality as the value.
+
+    See Also
+    --------
+    betweenness_centrality
+    edge_load
+
+    Notes
+    -----
+    The algorithm is from Ulrik Brandes [1]_.
+
+    For weighted graphs the edge weights must be greater than zero.
+    Zero edge weights can produce an infinite number of equal length
+    paths between pairs of nodes.
+
+    References
+    ----------
+    .. [1]  A Faster Algorithm for Betweenness Centrality. Ulrik Brandes,
+       Journal of Mathematical Sociology 25(2):163-177, 2001.
+       https://doi.org/10.1080/0022250X.2001.9990249
+    .. [2] Ulrik Brandes: On Variants of Shortest-Path Betweenness
+       Centrality and their Generic Computation.
+       Social Networks 30(2):136-145, 2008.
+       https://doi.org/10.1016/j.socnet.2007.11.001
+    """
+    betweenness = dict.fromkeys(G, 0.0)  # b[v]=0 for v in G
+    # b[e]=0 for e in G.edges()
+    betweenness.update(dict.fromkeys(G.edges(), 0.0))
+    if k is None:
+        nodes = G
+    else:
+        nodes = seed.sample(list(G.nodes()), k)
+    for s in nodes:
+        # single source shortest paths
+        if weight is None:  # use BFS
+            S, P, sigma, _ = _single_source_shortest_path_basic(G, s)
+        else:  # use Dijkstra's algorithm
+            S, P, sigma, _ = _single_source_dijkstra_path_basic(G, s, weight)
+        # accumulation
+        betweenness = _accumulate_edges(betweenness, S, P, sigma, s)
+    # rescaling
+    for n in G:  # remove nodes to only return edges
+        del betweenness[n]
+    betweenness = _rescale_e(
+        betweenness, len(G), normalized=normalized, directed=G.is_directed()
+    )
+    if G.is_multigraph():
+        betweenness = _add_edge_keys(G, betweenness, weight=weight)
+    return betweenness
+
+
+# helpers for betweenness centrality
+
+
+def _single_source_shortest_path_basic(G, s):
+    S = []
+    P = {}
+    for v in G:
+        P[v] = []
+    sigma = dict.fromkeys(G, 0.0)  # sigma[v]=0 for v in G
+    D = {}
+    sigma[s] = 1.0
+    D[s] = 0
+    Q = deque([s])
+    while Q:  # use BFS to find shortest paths
+        v = Q.popleft()
+        S.append(v)
+        Dv = D[v]
+        sigmav = sigma[v]
+        for w in G[v]:
+            if w not in D:
+                Q.append(w)
+                D[w] = Dv + 1
+            if D[w] == Dv + 1:  # this is a shortest path, count paths
+                sigma[w] += sigmav
+                P[w].append(v)  # predecessors
+    return S, P, sigma, D
+
+
+def _single_source_dijkstra_path_basic(G, s, weight):
+    weight = _weight_function(G, weight)
+    # modified from Eppstein
+    S = []
+    P = {}
+    for v in G:
+        P[v] = []
+    sigma = dict.fromkeys(G, 0.0)  # sigma[v]=0 for v in G
+    D = {}
+    sigma[s] = 1.0
+    push = heappush
+    pop = heappop
+    seen = {s: 0}
+    c = count()
+    Q = []  # use Q as heap with (distance,node id) tuples
+    push(Q, (0, next(c), s, s))
+    while Q:
+        (dist, _, pred, v) = pop(Q)
+        if v in D:
+            continue  # already searched this node.
+        sigma[v] += sigma[pred]  # count paths
+        S.append(v)
+        D[v] = dist
+        for w, edgedata in G[v].items():
+            vw_dist = dist + weight(v, w, edgedata)
+            if w not in D and (w not in seen or vw_dist < seen[w]):
+                seen[w] = vw_dist
+                push(Q, (vw_dist, next(c), v, w))
+                sigma[w] = 0.0
+                P[w] = [v]
+            elif vw_dist == seen[w]:  # handle equal paths
+                sigma[w] += sigma[v]
+                P[w].append(v)
+    return S, P, sigma, D
+
+
+def _accumulate_basic(betweenness, S, P, sigma, s):
+    delta = dict.fromkeys(S, 0)
+    while S:
+        w = S.pop()
+        coeff = (1 + delta[w]) / sigma[w]
+        for v in P[w]:
+            delta[v] += sigma[v] * coeff
+        if w != s:
+            betweenness[w] += delta[w]
+    return betweenness, delta
+
+
+def _accumulate_endpoints(betweenness, S, P, sigma, s):
+    betweenness[s] += len(S) - 1
+    delta = dict.fromkeys(S, 0)
+    while S:
+        w = S.pop()
+        coeff = (1 + delta[w]) / sigma[w]
+        for v in P[w]:
+            delta[v] += sigma[v] * coeff
+        if w != s:
+            betweenness[w] += delta[w] + 1
+    return betweenness, delta
+
+
+def _accumulate_edges(betweenness, S, P, sigma, s):
+    delta = dict.fromkeys(S, 0)
+    while S:
+        w = S.pop()
+        coeff = (1 + delta[w]) / sigma[w]
+        for v in P[w]:
+            c = sigma[v] * coeff
+            if (v, w) not in betweenness:
+                betweenness[(w, v)] += c
+            else:
+                betweenness[(v, w)] += c
+            delta[v] += c
+        if w != s:
+            betweenness[w] += delta[w]
+    return betweenness
+
+
+def _rescale(betweenness, n, normalized, directed=False, k=None, endpoints=False):
+    if normalized:
+        if endpoints:
+            if n < 2:
+                scale = None  # no normalization
+            else:
+                # Scale factor should include endpoint nodes
+                scale = 1 / (n * (n - 1))
+        elif n <= 2:
+            scale = None  # no normalization b=0 for all nodes
+        else:
+            scale = 1 / ((n - 1) * (n - 2))
+    else:  # rescale by 2 for undirected graphs
+        if not directed:
+            scale = 0.5
+        else:
+            scale = None
+    if scale is not None:
+        if k is not None:
+            scale = scale * n / k
+        for v in betweenness:
+            betweenness[v] *= scale
+    return betweenness
+
+
+def _rescale_e(betweenness, n, normalized, directed=False, k=None):
+    if normalized:
+        if n <= 1:
+            scale = None  # no normalization b=0 for all nodes
+        else:
+            scale = 1 / (n * (n - 1))
+    else:  # rescale by 2 for undirected graphs
+        if not directed:
+            scale = 0.5
+        else:
+            scale = None
+    if scale is not None:
+        if k is not None:
+            scale = scale * n / k
+        for v in betweenness:
+            betweenness[v] *= scale
+    return betweenness
+
+
+@not_implemented_for("graph")
+def _add_edge_keys(G, betweenness, weight=None):
+    r"""Adds the corrected betweenness centrality (BC) values for multigraphs.
+
+    Parameters
+    ----------
+    G : NetworkX graph.
+
+    betweenness : dictionary
+        Dictionary mapping adjacent node tuples to betweenness centrality values.
+
+    weight : string or function
+        See `_weight_function` for details. Defaults to `None`.
+
+    Returns
+    -------
+    edges : dictionary
+        The parameter `betweenness` including edges with keys and their
+        betweenness centrality values.
+
+    The BC value is divided among edges of equal weight.
+    """
+    _weight = _weight_function(G, weight)
+
+    edge_bc = dict.fromkeys(G.edges, 0.0)
+    for u, v in betweenness:
+        d = G[u][v]
+        wt = _weight(u, v, d)
+        keys = [k for k in d if _weight(u, v, {k: d[k]}) == wt]
+        bc = betweenness[(u, v)] / len(keys)
+        for k in keys:
+            edge_bc[(u, v, k)] = bc
+
+    return edge_bc

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

@@ -0,0 +1,275 @@
+"""Betweenness centrality measures for subsets of nodes."""
+
+import networkx as nx
+from networkx.algorithms.centrality.betweenness import (
+    _add_edge_keys,
+)
+from networkx.algorithms.centrality.betweenness import (
+    _single_source_dijkstra_path_basic as dijkstra,
+)
+from networkx.algorithms.centrality.betweenness import (
+    _single_source_shortest_path_basic as shortest_path,
+)
+
+__all__ = [
+    "betweenness_centrality_subset",
+    "edge_betweenness_centrality_subset",
+]
+
+
+@nx._dispatchable(edge_attrs="weight")
+def betweenness_centrality_subset(G, sources, targets, normalized=False, weight=None):
+    r"""Compute betweenness centrality for a subset of nodes.
+
+    .. math::
+
+       c_B(v) =\sum_{s\in S, t \in T} \frac{\sigma(s, t|v)}{\sigma(s, t)}
+
+    where $S$ is the set of sources, $T$ is the set of targets,
+    $\sigma(s, t)$ is the number of shortest $(s, t)$-paths,
+    and $\sigma(s, t|v)$ is the number of those paths
+    passing through some  node $v$ other than $s, t$.
+    If $s = t$, $\sigma(s, t) = 1$,
+    and if $v \in {s, t}$, $\sigma(s, t|v) = 0$ [2]_.
+
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph.
+
+    sources: list of nodes
+      Nodes to use as sources for shortest paths in betweenness
+
+    targets: list of nodes
+      Nodes to use as targets for shortest paths in betweenness
+
+    normalized : bool, optional
+      If True the betweenness values are normalized by $2/((n-1)(n-2))$
+      for graphs, and $1/((n-1)(n-2))$ for directed graphs where $n$
+      is the number of nodes in G.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      Weights are used to calculate weighted shortest paths, so they are
+      interpreted as distances.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with betweenness centrality as the value.
+
+    See Also
+    --------
+    edge_betweenness_centrality
+    load_centrality
+
+    Notes
+    -----
+    The basic algorithm is from [1]_.
+
+    For weighted graphs the edge weights must be greater than zero.
+    Zero edge weights can produce an infinite number of equal length
+    paths between pairs of nodes.
+
+    The normalization might seem a little strange but it is
+    designed to make betweenness_centrality(G) be the same as
+    betweenness_centrality_subset(G,sources=G.nodes(),targets=G.nodes()).
+
+    The total number of paths between source and target is counted
+    differently for directed and undirected graphs. Directed paths
+    are easy to count. Undirected paths are tricky: should a path
+    from "u" to "v" count as 1 undirected path or as 2 directed paths?
+
+    For betweenness_centrality we report the number of undirected
+    paths when G is undirected.
+
+    For betweenness_centrality_subset the reporting is different.
+    If the source and target subsets are the same, then we want
+    to count undirected paths. But if the source and target subsets
+    differ -- for example, if sources is {0} and targets is {1},
+    then we are only counting the paths in one direction. They are
+    undirected paths but we are counting them in a directed way.
+    To count them as undirected paths, each should count as half a path.
+
+    References
+    ----------
+    .. [1] Ulrik Brandes, A Faster Algorithm for Betweenness Centrality.
+       Journal of Mathematical Sociology 25(2):163-177, 2001.
+       https://doi.org/10.1080/0022250X.2001.9990249
+    .. [2] Ulrik Brandes: On Variants of Shortest-Path Betweenness
+       Centrality and their Generic Computation.
+       Social Networks 30(2):136-145, 2008.
+       https://doi.org/10.1016/j.socnet.2007.11.001
+    """
+    b = dict.fromkeys(G, 0.0)  # b[v]=0 for v in G
+    for s in sources:
+        # single source shortest paths
+        if weight is None:  # use BFS
+            S, P, sigma, _ = shortest_path(G, s)
+        else:  # use Dijkstra's algorithm
+            S, P, sigma, _ = dijkstra(G, s, weight)
+        b = _accumulate_subset(b, S, P, sigma, s, targets)
+    b = _rescale(b, len(G), normalized=normalized, directed=G.is_directed())
+    return b
+
+
+@nx._dispatchable(edge_attrs="weight")
+def edge_betweenness_centrality_subset(
+    G, sources, targets, normalized=False, weight=None
+):
+    r"""Compute betweenness centrality for edges for a subset of nodes.
+
+    .. math::
+
+       c_B(v) =\sum_{s\in S,t \in T} \frac{\sigma(s, t|e)}{\sigma(s, t)}
+
+    where $S$ is the set of sources, $T$ is the set of targets,
+    $\sigma(s, t)$ is the number of shortest $(s, t)$-paths,
+    and $\sigma(s, t|e)$ is the number of those paths
+    passing through edge $e$ [2]_.
+
+    Parameters
+    ----------
+    G : graph
+      A networkx graph.
+
+    sources: list of nodes
+      Nodes to use as sources for shortest paths in betweenness
+
+    targets: list of nodes
+      Nodes to use as targets for shortest paths in betweenness
+
+    normalized : bool, optional
+      If True the betweenness values are normalized by `2/(n(n-1))`
+      for graphs, and `1/(n(n-1))` for directed graphs where `n`
+      is the number of nodes in G.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      Weights are used to calculate weighted shortest paths, so they are
+      interpreted as distances.
+
+    Returns
+    -------
+    edges : dictionary
+       Dictionary of edges with Betweenness centrality as the value.
+
+    See Also
+    --------
+    betweenness_centrality
+    edge_load
+
+    Notes
+    -----
+    The basic algorithm is from [1]_.
+
+    For weighted graphs the edge weights must be greater than zero.
+    Zero edge weights can produce an infinite number of equal length
+    paths between pairs of nodes.
+
+    The normalization might seem a little strange but it is the same
+    as in edge_betweenness_centrality() and is designed to make
+    edge_betweenness_centrality(G) be the same as
+    edge_betweenness_centrality_subset(G,sources=G.nodes(),targets=G.nodes()).
+
+    References
+    ----------
+    .. [1] Ulrik Brandes, A Faster Algorithm for Betweenness Centrality.
+       Journal of Mathematical Sociology 25(2):163-177, 2001.
+       https://doi.org/10.1080/0022250X.2001.9990249
+    .. [2] Ulrik Brandes: On Variants of Shortest-Path Betweenness
+       Centrality and their Generic Computation.
+       Social Networks 30(2):136-145, 2008.
+       https://doi.org/10.1016/j.socnet.2007.11.001
+    """
+    b = dict.fromkeys(G, 0.0)  # b[v]=0 for v in G
+    b.update(dict.fromkeys(G.edges(), 0.0))  # b[e] for e in G.edges()
+    for s in sources:
+        # single source shortest paths
+        if weight is None:  # use BFS
+            S, P, sigma, _ = shortest_path(G, s)
+        else:  # use Dijkstra's algorithm
+            S, P, sigma, _ = dijkstra(G, s, weight)
+        b = _accumulate_edges_subset(b, S, P, sigma, s, targets)
+    for n in G:  # remove nodes to only return edges
+        del b[n]
+    b = _rescale_e(b, len(G), normalized=normalized, directed=G.is_directed())
+    if G.is_multigraph():
+        b = _add_edge_keys(G, b, weight=weight)
+    return b
+
+
+def _accumulate_subset(betweenness, S, P, sigma, s, targets):
+    delta = dict.fromkeys(S, 0.0)
+    target_set = set(targets) - {s}
+    while S:
+        w = S.pop()
+        if w in target_set:
+            coeff = (delta[w] + 1.0) / sigma[w]
+        else:
+            coeff = delta[w] / sigma[w]
+        for v in P[w]:
+            delta[v] += sigma[v] * coeff
+        if w != s:
+            betweenness[w] += delta[w]
+    return betweenness
+
+
+def _accumulate_edges_subset(betweenness, S, P, sigma, s, targets):
+    """edge_betweenness_centrality_subset helper."""
+    delta = dict.fromkeys(S, 0)
+    target_set = set(targets)
+    while S:
+        w = S.pop()
+        for v in P[w]:
+            if w in target_set:
+                c = (sigma[v] / sigma[w]) * (1.0 + delta[w])
+            else:
+                c = delta[w] / len(P[w])
+            if (v, w) not in betweenness:
+                betweenness[(w, v)] += c
+            else:
+                betweenness[(v, w)] += c
+            delta[v] += c
+        if w != s:
+            betweenness[w] += delta[w]
+    return betweenness
+
+
+def _rescale(betweenness, n, normalized, directed=False):
+    """betweenness_centrality_subset helper."""
+    if normalized:
+        if n <= 2:
+            scale = None  # no normalization b=0 for all nodes
+        else:
+            scale = 1.0 / ((n - 1) * (n - 2))
+    else:  # rescale by 2 for undirected graphs
+        if not directed:
+            scale = 0.5
+        else:
+            scale = None
+    if scale is not None:
+        for v in betweenness:
+            betweenness[v] *= scale
+    return betweenness
+
+
+def _rescale_e(betweenness, n, normalized, directed=False):
+    """edge_betweenness_centrality_subset helper."""
+    if normalized:
+        if n <= 1:
+            scale = None  # no normalization b=0 for all nodes
+        else:
+            scale = 1.0 / (n * (n - 1))
+    else:  # rescale by 2 for undirected graphs
+        if not directed:
+            scale = 0.5
+        else:
+            scale = None
+    if scale is not None:
+        for v in betweenness:
+            betweenness[v] *= scale
+    return betweenness

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

@@ -0,0 +1,282 @@
+"""
+Closeness centrality measures.
+"""
+
+import functools
+
+import networkx as nx
+from networkx.exception import NetworkXError
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = ["closeness_centrality", "incremental_closeness_centrality"]
+
+
+@nx._dispatchable(edge_attrs="distance")
+def closeness_centrality(G, u=None, distance=None, wf_improved=True):
+    r"""Compute closeness centrality for nodes.
+
+    Closeness centrality [1]_ of a node `u` is the reciprocal of the
+    average shortest path distance to `u` over all `n-1` reachable nodes.
+
+    .. math::
+
+        C(u) = \frac{n - 1}{\sum_{v=1}^{n-1} d(v, u)},
+
+    where `d(v, u)` is the shortest-path distance between `v` and `u`,
+    and `n-1` is the number of nodes reachable from `u`. Notice that the
+    closeness distance function computes the incoming distance to `u`
+    for directed graphs. To use outward distance, act on `G.reverse()`.
+
+    Notice that higher values of closeness indicate higher centrality.
+
+    Wasserman and Faust propose an improved formula for graphs with
+    more than one connected component. The result is "a ratio of the
+    fraction of actors in the group who are reachable, to the average
+    distance" from the reachable actors [2]_. You might think this
+    scale factor is inverted but it is not. As is, nodes from small
+    components receive a smaller closeness value. Letting `N` denote
+    the number of nodes in the graph,
+
+    .. math::
+
+        C_{WF}(u) = \frac{n-1}{N-1} \frac{n - 1}{\sum_{v=1}^{n-1} d(v, u)},
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    u : node, optional
+      Return only the value for node u
+
+    distance : edge attribute key, optional (default=None)
+      Use the specified edge attribute as the edge distance in shortest
+      path calculations.  If `None` (the default) all edges have a distance of 1.
+      Absent edge attributes are assigned a distance of 1. Note that no check
+      is performed to ensure that edges have the provided attribute.
+
+    wf_improved : bool, optional (default=True)
+      If True, scale by the fraction of nodes reachable. This gives the
+      Wasserman and Faust improved formula. For single component graphs
+      it is the same as the original formula.
+
+    Returns
+    -------
+    nodes : dictionary
+      Dictionary of nodes with closeness centrality as the value.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
+    >>> nx.closeness_centrality(G)
+    {0: 1.0, 1: 1.0, 2: 0.75, 3: 0.75}
+
+    See Also
+    --------
+    betweenness_centrality, load_centrality, eigenvector_centrality,
+    degree_centrality, incremental_closeness_centrality
+
+    Notes
+    -----
+    The closeness centrality is normalized to `(n-1)/(|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 scaled by that parts size.
+
+    If the 'distance' keyword is set to an edge attribute key then the
+    shortest-path length will be computed using Dijkstra's algorithm with
+    that edge attribute as the edge weight.
+
+    The closeness centrality uses *inward* distance to a node, not outward.
+    If you want to use outword distances apply the function to `G.reverse()`
+
+    In NetworkX 2.2 and earlier a bug caused Dijkstra's algorithm to use the
+    outward distance rather than the inward distance. If you use a 'distance'
+    keyword and a DiGraph, your results will change between v2.2 and v2.3.
+
+    References
+    ----------
+    .. [1] Linton C. Freeman: Centrality in networks: I.
+       Conceptual clarification. Social Networks 1:215-239, 1979.
+       https://doi.org/10.1016/0378-8733(78)90021-7
+    .. [2] pg. 201 of Wasserman, S. and Faust, K.,
+       Social Network Analysis: Methods and Applications, 1994,
+       Cambridge University Press.
+    """
+    if G.is_directed():
+        G = G.reverse()  # create a reversed graph view
+
+    if distance is not None:
+        # use Dijkstra's algorithm with specified attribute as edge weight
+        path_length = functools.partial(
+            nx.single_source_dijkstra_path_length, weight=distance
+        )
+    else:
+        path_length = nx.single_source_shortest_path_length
+
+    if u is None:
+        nodes = G.nodes
+    else:
+        nodes = [u]
+    closeness_dict = {}
+    for n in nodes:
+        sp = path_length(G, n)
+        totsp = sum(sp.values())
+        len_G = len(G)
+        _closeness_centrality = 0.0
+        if totsp > 0.0 and len_G > 1:
+            _closeness_centrality = (len(sp) - 1.0) / totsp
+            # normalize to number of nodes-1 in connected part
+            if wf_improved:
+                s = (len(sp) - 1.0) / (len_G - 1)
+                _closeness_centrality *= s
+        closeness_dict[n] = _closeness_centrality
+    if u is not None:
+        return closeness_dict[u]
+    return closeness_dict
+
+
+@not_implemented_for("directed")
+@nx._dispatchable(mutates_input=True)
+def incremental_closeness_centrality(
+    G, edge, prev_cc=None, insertion=True, wf_improved=True
+):
+    r"""Incremental closeness centrality for nodes.
+
+    Compute closeness centrality for nodes using level-based work filtering
+    as described in Incremental Algorithms for Closeness Centrality by Sariyuce et al.
+
+    Level-based work filtering detects unnecessary updates to the closeness
+    centrality and filters them out.
+
+    ---
+    From "Incremental Algorithms for Closeness Centrality":
+
+    Theorem 1: Let :math:`G = (V, E)` be a graph and u and v be two vertices in V
+    such that there is no edge (u, v) in E. Let :math:`G' = (V, E \cup uv)`
+    Then :math:`cc[s] = cc'[s]` if and only if :math:`\left|dG(s, u) - dG(s, v)\right| \leq 1`.
+
+    Where :math:`dG(u, v)` denotes the length of the shortest path between
+    two vertices u, v in a graph G, cc[s] is the closeness centrality for a
+    vertex s in V, and cc'[s] is the closeness centrality for a
+    vertex s in V, with the (u, v) edge added.
+    ---
+
+    We use Theorem 1 to filter out updates when adding or removing an edge.
+    When adding an edge (u, v), we compute the shortest path lengths from all
+    other nodes to u and to v before the node is added. When removing an edge,
+    we compute the shortest path lengths after the edge is removed. Then we
+    apply Theorem 1 to use previously computed closeness centrality for nodes
+    where :math:`\left|dG(s, u) - dG(s, v)\right| \leq 1`. This works only for
+    undirected, unweighted graphs; the distance argument is not supported.
+
+    Closeness centrality [1]_ of a node `u` is the reciprocal of the
+    sum of the shortest path distances from `u` to all `n-1` other nodes.
+    Since the sum of distances depends on the number of nodes in the
+    graph, closeness is normalized by the sum of minimum possible
+    distances `n-1`.
+
+    .. math::
+
+        C(u) = \frac{n - 1}{\sum_{v=1}^{n-1} d(v, u)},
+
+    where `d(v, u)` is the shortest-path distance between `v` and `u`,
+    and `n` is the number of nodes in the graph.
+
+    Notice that higher values of closeness indicate higher centrality.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    edge : tuple
+      The modified edge (u, v) in the graph.
+
+    prev_cc : dictionary
+      The previous closeness centrality for all nodes in the graph.
+
+    insertion : bool, optional
+      If True (default) the edge was inserted, otherwise it was deleted from the graph.
+
+    wf_improved : bool, optional (default=True)
+      If True, scale by the fraction of nodes reachable. This gives the
+      Wasserman and Faust improved formula. For single component graphs
+      it is the same as the original formula.
+
+    Returns
+    -------
+    nodes : dictionary
+      Dictionary of nodes with closeness centrality as the value.
+
+    See Also
+    --------
+    betweenness_centrality, load_centrality, eigenvector_centrality,
+    degree_centrality, closeness_centrality
+
+    Notes
+    -----
+    The closeness centrality is normalized to `(n-1)/(|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] Freeman, L.C., 1979. Centrality in networks: I.
+       Conceptual clarification.  Social Networks 1, 215--239.
+       https://doi.org/10.1016/0378-8733(78)90021-7
+    .. [2] Sariyuce, A.E. ; Kaya, K. ; Saule, E. ; Catalyiirek, U.V. Incremental
+       Algorithms for Closeness Centrality. 2013 IEEE International Conference on Big Data
+       http://sariyuce.com/papers/bigdata13.pdf
+    """
+    if prev_cc is not None and set(prev_cc.keys()) != set(G.nodes()):
+        raise NetworkXError("prev_cc and G do not have the same nodes")
+
+    # Unpack edge
+    (u, v) = edge
+    path_length = nx.single_source_shortest_path_length
+
+    if insertion:
+        # For edge insertion, we want shortest paths before the edge is inserted
+        du = path_length(G, u)
+        dv = path_length(G, v)
+
+        G.add_edge(u, v)
+    else:
+        G.remove_edge(u, v)
+
+        # For edge removal, we want shortest paths after the edge is removed
+        du = path_length(G, u)
+        dv = path_length(G, v)
+
+    if prev_cc is None:
+        return nx.closeness_centrality(G)
+
+    nodes = G.nodes()
+    closeness_dict = {}
+    for n in nodes:
+        if n in du and n in dv and abs(du[n] - dv[n]) <= 1:
+            closeness_dict[n] = prev_cc[n]
+        else:
+            sp = path_length(G, n)
+            totsp = sum(sp.values())
+            len_G = len(G)
+            _closeness_centrality = 0.0
+            if totsp > 0.0 and len_G > 1:
+                _closeness_centrality = (len(sp) - 1.0) / totsp
+                # normalize to number of nodes-1 in connected part
+                if wf_improved:
+                    s = (len(sp) - 1.0) / (len_G - 1)
+                    _closeness_centrality *= s
+            closeness_dict[n] = _closeness_centrality
+
+    # Leave the graph as we found it
+    if insertion:
+        G.remove_edge(u, v)
+    else:
+        G.add_edge(u, v)
+
+    return closeness_dict

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

@@ -0,0 +1,227 @@
+"""Current-flow betweenness centrality measures for subsets of nodes."""
+
+import networkx as nx
+from networkx.algorithms.centrality.flow_matrix import flow_matrix_row
+from networkx.utils import not_implemented_for, reverse_cuthill_mckee_ordering
+
+__all__ = [
+    "current_flow_betweenness_centrality_subset",
+    "edge_current_flow_betweenness_centrality_subset",
+]
+
+
+@not_implemented_for("directed")
+@nx._dispatchable(edge_attrs="weight")
+def current_flow_betweenness_centrality_subset(
+    G, sources, targets, normalized=True, weight=None, dtype=float, solver="lu"
+):
+    r"""Compute current-flow betweenness centrality for subsets of nodes.
+
+    Current-flow betweenness centrality uses an electrical current
+    model for information spreading in contrast to betweenness
+    centrality which uses shortest paths.
+
+    Current-flow betweenness centrality is also known as
+    random-walk betweenness centrality [2]_.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    sources: list of nodes
+      Nodes to use as sources for current
+
+    targets: list of nodes
+      Nodes to use as sinks for current
+
+    normalized : bool, optional (default=True)
+      If True the betweenness values are normalized by b=b/(n-1)(n-2) where
+      n is the number of nodes in G.
+
+    weight : string or None, optional (default=None)
+      Key for edge data used as the edge weight.
+      If None, then use 1 as each edge weight.
+      The weight reflects the capacity or the strength of the
+      edge.
+
+    dtype: data type (float)
+      Default data type for internal matrices.
+      Set to np.float32 for lower memory consumption.
+
+    solver: string (default='lu')
+       Type of linear solver to use for computing the flow matrix.
+       Options are "full" (uses most memory), "lu" (recommended), and
+       "cg" (uses least memory).
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with betweenness centrality as the value.
+
+    See Also
+    --------
+    approximate_current_flow_betweenness_centrality
+    betweenness_centrality
+    edge_betweenness_centrality
+    edge_current_flow_betweenness_centrality
+
+    Notes
+    -----
+    Current-flow betweenness can be computed in $O(I(n-1)+mn \log n)$
+    time [1]_, where $I(n-1)$ is the time needed to compute the
+    inverse Laplacian.  For a full matrix this is $O(n^3)$ but using
+    sparse methods you can achieve $O(nm{\sqrt k})$ where $k$ is the
+    Laplacian matrix condition number.
+
+    The space required is $O(nw)$ where $w$ is the width of the sparse
+    Laplacian matrix.  Worse case is $w=n$ for $O(n^2)$.
+
+    If the edges have a 'weight' attribute they will be used as
+    weights in this algorithm.  Unspecified weights are set to 1.
+
+    References
+    ----------
+    .. [1] Centrality Measures Based on Current Flow.
+       Ulrik Brandes and Daniel Fleischer,
+       Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS '05).
+       LNCS 3404, pp. 533-544. Springer-Verlag, 2005.
+       https://doi.org/10.1007/978-3-540-31856-9_44
+
+    .. [2] A measure of betweenness centrality based on random walks,
+       M. E. J. Newman, Social Networks 27, 39-54 (2005).
+    """
+    import numpy as np
+
+    from networkx.utils import reverse_cuthill_mckee_ordering
+
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("Graph not connected.")
+    N = G.number_of_nodes()
+    ordering = list(reverse_cuthill_mckee_ordering(G))
+    # make a copy with integer labels according to rcm ordering
+    # this could be done without a copy if we really wanted to
+    mapping = dict(zip(ordering, range(N)))
+    H = nx.relabel_nodes(G, mapping)
+    betweenness = dict.fromkeys(H, 0.0)  # b[n]=0 for n in H
+    for row, (s, t) in flow_matrix_row(H, weight=weight, dtype=dtype, solver=solver):
+        for ss in sources:
+            i = mapping[ss]
+            for tt in targets:
+                j = mapping[tt]
+                betweenness[s] += 0.5 * abs(row.item(i) - row.item(j))
+                betweenness[t] += 0.5 * abs(row.item(i) - row.item(j))
+    if normalized:
+        nb = (N - 1.0) * (N - 2.0)  # normalization factor
+    else:
+        nb = 2.0
+    for node in H:
+        betweenness[node] = betweenness[node] / nb + 1.0 / (2 - N)
+    return {ordering[node]: value for node, value in betweenness.items()}
+
+
+@not_implemented_for("directed")
+@nx._dispatchable(edge_attrs="weight")
+def edge_current_flow_betweenness_centrality_subset(
+    G, sources, targets, normalized=True, weight=None, dtype=float, solver="lu"
+):
+    r"""Compute current-flow betweenness centrality for edges using subsets
+    of nodes.
+
+    Current-flow betweenness centrality uses an electrical current
+    model for information spreading in contrast to betweenness
+    centrality which uses shortest paths.
+
+    Current-flow betweenness centrality is also known as
+    random-walk betweenness centrality [2]_.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    sources: list of nodes
+      Nodes to use as sources for current
+
+    targets: list of nodes
+      Nodes to use as sinks for current
+
+    normalized : bool, optional (default=True)
+      If True the betweenness values are normalized by b=b/(n-1)(n-2) where
+      n is the number of nodes in G.
+
+    weight : string or None, optional (default=None)
+      Key for edge data used as the edge weight.
+      If None, then use 1 as each edge weight.
+      The weight reflects the capacity or the strength of the
+      edge.
+
+    dtype: data type (float)
+      Default data type for internal matrices.
+      Set to np.float32 for lower memory consumption.
+
+    solver: string (default='lu')
+       Type of linear solver to use for computing the flow matrix.
+       Options are "full" (uses most memory), "lu" (recommended), and
+       "cg" (uses least memory).
+
+    Returns
+    -------
+    nodes : dict
+       Dictionary of edge tuples with betweenness centrality as the value.
+
+    See Also
+    --------
+    betweenness_centrality
+    edge_betweenness_centrality
+    current_flow_betweenness_centrality
+
+    Notes
+    -----
+    Current-flow betweenness can be computed in $O(I(n-1)+mn \log n)$
+    time [1]_, where $I(n-1)$ is the time needed to compute the
+    inverse Laplacian.  For a full matrix this is $O(n^3)$ but using
+    sparse methods you can achieve $O(nm{\sqrt k})$ where $k$ is the
+    Laplacian matrix condition number.
+
+    The space required is $O(nw)$ where $w$ is the width of the sparse
+    Laplacian matrix.  Worse case is $w=n$ for $O(n^2)$.
+
+    If the edges have a 'weight' attribute they will be used as
+    weights in this algorithm.  Unspecified weights are set to 1.
+
+    References
+    ----------
+    .. [1] Centrality Measures Based on Current Flow.
+       Ulrik Brandes and Daniel Fleischer,
+       Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS '05).
+       LNCS 3404, pp. 533-544. Springer-Verlag, 2005.
+       https://doi.org/10.1007/978-3-540-31856-9_44
+
+    .. [2] A measure of betweenness centrality based on random walks,
+       M. E. J. Newman, Social Networks 27, 39-54 (2005).
+    """
+    import numpy as np
+
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("Graph not connected.")
+    N = G.number_of_nodes()
+    ordering = list(reverse_cuthill_mckee_ordering(G))
+    # make a copy with integer labels according to rcm ordering
+    # this could be done without a copy if we really wanted to
+    mapping = dict(zip(ordering, range(N)))
+    H = nx.relabel_nodes(G, mapping)
+    edges = (tuple(sorted((u, v))) for u, v in H.edges())
+    betweenness = dict.fromkeys(edges, 0.0)
+    if normalized:
+        nb = (N - 1.0) * (N - 2.0)  # normalization factor
+    else:
+        nb = 2.0
+    for row, (e) in flow_matrix_row(H, weight=weight, dtype=dtype, solver=solver):
+        for ss in sources:
+            i = mapping[ss]
+            for tt in targets:
+                j = mapping[tt]
+                betweenness[e] += 0.5 * abs(row.item(i) - row.item(j))
+        betweenness[e] /= nb
+    return {(ordering[s], ordering[t]): value for (s, t), value in betweenness.items()}

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

@@ -0,0 +1,96 @@
+"""Current-flow closeness centrality measures."""
+
+import networkx as nx
+from networkx.algorithms.centrality.flow_matrix import (
+    CGInverseLaplacian,
+    FullInverseLaplacian,
+    SuperLUInverseLaplacian,
+)
+from networkx.utils import not_implemented_for, reverse_cuthill_mckee_ordering
+
+__all__ = ["current_flow_closeness_centrality", "information_centrality"]
+
+
+@not_implemented_for("directed")
+@nx._dispatchable(edge_attrs="weight")
+def current_flow_closeness_centrality(G, weight=None, dtype=float, solver="lu"):
+    """Compute current-flow closeness centrality for nodes.
+
+    Current-flow closeness centrality is variant of closeness
+    centrality based on effective resistance between nodes in
+    a network. This metric is also known as information centrality.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      The weight reflects the capacity or the strength of the
+      edge.
+
+    dtype: data type (default=float)
+      Default data type for internal matrices.
+      Set to np.float32 for lower memory consumption.
+
+    solver: string (default='lu')
+       Type of linear solver to use for computing the flow matrix.
+       Options are "full" (uses most memory), "lu" (recommended), and
+       "cg" (uses least memory).
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with current flow closeness centrality as the value.
+
+    See Also
+    --------
+    closeness_centrality
+
+    Notes
+    -----
+    The algorithm is from Brandes [1]_.
+
+    See also [2]_ for the original definition of information centrality.
+
+    References
+    ----------
+    .. [1] Ulrik Brandes and Daniel Fleischer,
+       Centrality Measures Based on Current Flow.
+       Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS '05).
+       LNCS 3404, pp. 533-544. Springer-Verlag, 2005.
+       https://doi.org/10.1007/978-3-540-31856-9_44
+
+    .. [2] Karen Stephenson and Marvin Zelen:
+       Rethinking centrality: Methods and examples.
+       Social Networks 11(1):1-37, 1989.
+       https://doi.org/10.1016/0378-8733(89)90016-6
+    """
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("Graph not connected.")
+    solvername = {
+        "full": FullInverseLaplacian,
+        "lu": SuperLUInverseLaplacian,
+        "cg": CGInverseLaplacian,
+    }
+    N = G.number_of_nodes()
+    ordering = list(reverse_cuthill_mckee_ordering(G))
+    # make a copy with integer labels according to rcm ordering
+    # this could be done without a copy if we really wanted to
+    H = nx.relabel_nodes(G, dict(zip(ordering, range(N))))
+    betweenness = dict.fromkeys(H, 0.0)  # b[n]=0 for n in H
+    N = H.number_of_nodes()
+    L = nx.laplacian_matrix(H, nodelist=range(N), weight=weight).asformat("csc")
+    L = L.astype(dtype)
+    C2 = solvername[solver](L, width=1, dtype=dtype)  # initialize solver
+    for v in H:
+        col = C2.get_row(v)
+        for w in H:
+            betweenness[v] += col.item(v) - 2 * col.item(w)
+            betweenness[w] += col.item(v)
+    return {ordering[node]: 1 / value for node, value in betweenness.items()}
+
+
+information_centrality = current_flow_closeness_centrality

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

@@ -0,0 +1,150 @@
+"""Degree centrality measures."""
+
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = ["degree_centrality", "in_degree_centrality", "out_degree_centrality"]
+
+
+@nx._dispatchable
+def degree_centrality(G):
+    """Compute the degree centrality for nodes.
+
+    The degree centrality for a node v is the fraction of nodes it
+    is connected to.
+
+    Parameters
+    ----------
+    G : graph
+      A networkx graph
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with degree centrality as the value.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
+    >>> nx.degree_centrality(G)
+    {0: 1.0, 1: 1.0, 2: 0.6666666666666666, 3: 0.6666666666666666}
+
+    See Also
+    --------
+    betweenness_centrality, load_centrality, eigenvector_centrality
+
+    Notes
+    -----
+    The degree centrality values are normalized by dividing by the maximum
+    possible degree in a simple graph n-1 where n is the number of nodes in G.
+
+    For multigraphs or graphs with self loops the maximum degree might
+    be higher than n-1 and values of degree centrality greater than 1
+    are possible.
+    """
+    if len(G) <= 1:
+        return {n: 1 for n in G}
+
+    s = 1.0 / (len(G) - 1.0)
+    centrality = {n: d * s for n, d in G.degree()}
+    return centrality
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def in_degree_centrality(G):
+    """Compute the in-degree centrality for nodes.
+
+    The in-degree centrality for a node v is the fraction of nodes its
+    incoming edges are connected to.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph
+
+    Returns
+    -------
+    nodes : dictionary
+        Dictionary of nodes with in-degree centrality as values.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
+    >>> nx.in_degree_centrality(G)
+    {0: 0.0, 1: 0.3333333333333333, 2: 0.6666666666666666, 3: 0.6666666666666666}
+
+    See Also
+    --------
+    degree_centrality, out_degree_centrality
+
+    Notes
+    -----
+    The degree centrality values are normalized by dividing by the maximum
+    possible degree in a simple graph n-1 where n is the number of nodes in G.
+
+    For multigraphs or graphs with self loops the maximum degree might
+    be higher than n-1 and values of degree centrality greater than 1
+    are possible.
+    """
+    if len(G) <= 1:
+        return {n: 1 for n in G}
+
+    s = 1.0 / (len(G) - 1.0)
+    centrality = {n: d * s for n, d in G.in_degree()}
+    return centrality
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def out_degree_centrality(G):
+    """Compute the out-degree centrality for nodes.
+
+    The out-degree centrality for a node v is the fraction of nodes its
+    outgoing edges are connected to.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph
+
+    Returns
+    -------
+    nodes : dictionary
+        Dictionary of nodes with out-degree centrality as values.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
+    >>> nx.out_degree_centrality(G)
+    {0: 1.0, 1: 0.6666666666666666, 2: 0.0, 3: 0.0}
+
+    See Also
+    --------
+    degree_centrality, in_degree_centrality
+
+    Notes
+    -----
+    The degree centrality values are normalized by dividing by the maximum
+    possible degree in a simple graph n-1 where n is the number of nodes in G.
+
+    For multigraphs or graphs with self loops the maximum degree might
+    be higher than n-1 and values of degree centrality greater than 1
+    are possible.
+    """
+    if len(G) <= 1:
+        return {n: 1 for n in G}
+
+    s = 1.0 / (len(G) - 1.0)
+    centrality = {n: d * s for n, d in G.out_degree()}
+    return centrality

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

@@ -0,0 +1,357 @@
+"""Functions for computing eigenvector centrality."""
+
+import math
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["eigenvector_centrality", "eigenvector_centrality_numpy"]
+
+
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def eigenvector_centrality(G, max_iter=100, tol=1.0e-6, nstart=None, weight=None):
+    r"""Compute the eigenvector centrality for the graph G.
+
+    Eigenvector centrality computes the centrality for a node by adding
+    the centrality of its predecessors. The centrality for node $i$ is the
+    $i$-th element of a left eigenvector associated with the eigenvalue $\lambda$
+    of maximum modulus that is positive. Such an eigenvector $x$ is
+    defined up to a multiplicative constant by the equation
+
+    .. math::
+
+         \lambda x^T = x^T A,
+
+    where $A$ is the adjacency matrix of the graph G. By definition of
+    row-column product, the equation above is equivalent to
+
+    .. math::
+
+        \lambda x_i = \sum_{j\to i}x_j.
+
+    That is, adding the eigenvector centralities of the predecessors of
+    $i$ one obtains the eigenvector centrality of $i$ multiplied by
+    $\lambda$. In the case of undirected graphs, $x$ also solves the familiar
+    right-eigenvector equation $Ax = \lambda x$.
+
+    By virtue of the Perron–Frobenius theorem [1]_, if G is strongly
+    connected there is a unique eigenvector $x$, and all its entries
+    are strictly positive.
+
+    If G is not strongly connected there might be several left
+    eigenvectors associated with $\lambda$, and some of their elements
+    might be zero.
+
+    Parameters
+    ----------
+    G : graph
+      A networkx graph.
+
+    max_iter : integer, optional (default=100)
+      Maximum number of power iterations.
+
+    tol : float, optional (default=1.0e-6)
+      Error tolerance (in Euclidean norm) used to check convergence in
+      power iteration.
+
+    nstart : dictionary, optional (default=None)
+      Starting value of power iteration for each node. Must have a nonzero
+      projection on the desired eigenvector for the power method to converge.
+      If None, this implementation uses an all-ones vector, which is a safe
+      choice.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal. Otherwise holds the
+      name of the edge attribute used as weight. In this measure the
+      weight is interpreted as the connection strength.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with eigenvector centrality as the value. The
+       associated vector has unit Euclidean norm and the values are
+       nonegative.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> centrality = nx.eigenvector_centrality(G)
+    >>> sorted((v, f"{c:0.2f}") for v, c in centrality.items())
+    [(0, '0.37'), (1, '0.60'), (2, '0.60'), (3, '0.37')]
+
+    Raises
+    ------
+    NetworkXPointlessConcept
+        If the graph G is the null graph.
+
+    NetworkXError
+        If each value in `nstart` is zero.
+
+    PowerIterationFailedConvergence
+        If the algorithm fails to converge to the specified tolerance
+        within the specified number of iterations of the power iteration
+        method.
+
+    See Also
+    --------
+    eigenvector_centrality_numpy
+    :func:`~networkx.algorithms.link_analysis.pagerank_alg.pagerank`
+    :func:`~networkx.algorithms.link_analysis.hits_alg.hits`
+
+    Notes
+    -----
+    Eigenvector centrality was introduced by Landau [2]_ for chess
+    tournaments. It was later rediscovered by Wei [3]_ and then
+    popularized by Kendall [4]_ in the context of sport ranking. Berge
+    introduced a general definition for graphs based on social connections
+    [5]_. Bonacich [6]_ reintroduced again eigenvector centrality and made
+    it popular in link analysis.
+
+    This function computes the left dominant eigenvector, which corresponds
+    to adding the centrality of predecessors: this is the usual approach.
+    To add the centrality of successors first reverse the graph with
+    ``G.reverse()``.
+
+    The implementation uses power iteration [7]_ to compute a dominant
+    eigenvector starting from the provided vector `nstart`. Convergence is
+    guaranteed as long as `nstart` has a nonzero projection on a dominant
+    eigenvector, which certainly happens using the default value.
+
+    The method stops when the change in the computed vector between two
+    iterations is smaller than an error tolerance of ``G.number_of_nodes()
+    * tol`` or after ``max_iter`` iterations, but in the second case it
+    raises an exception.
+
+    This implementation uses $(A + I)$ rather than the adjacency matrix
+    $A$ because the change preserves eigenvectors, but it shifts the
+    spectrum, thus guaranteeing convergence even for networks with
+    negative eigenvalues of maximum modulus.
+
+    References
+    ----------
+    .. [1] Abraham Berman and Robert J. Plemmons.
+       "Nonnegative Matrices in the Mathematical Sciences."
+       Classics in Applied Mathematics. SIAM, 1994.
+
+    .. [2] Edmund Landau.
+       "Zur relativen Wertbemessung der Turnierresultate."
+       Deutsches Wochenschach, 11:366–369, 1895.
+
+    .. [3] Teh-Hsing Wei.
+       "The Algebraic Foundations of Ranking Theory."
+       PhD thesis, University of Cambridge, 1952.
+
+    .. [4] Maurice G. Kendall.
+       "Further contributions to the theory of paired comparisons."
+       Biometrics, 11(1):43–62, 1955.
+       https://www.jstor.org/stable/3001479
+
+    .. [5] Claude Berge
+       "Théorie des graphes et ses applications."
+       Dunod, Paris, France, 1958.
+
+    .. [6] Phillip Bonacich.
+       "Technique for analyzing overlapping memberships."
+       Sociological Methodology, 4:176–185, 1972.
+       https://www.jstor.org/stable/270732
+
+    .. [7] Power iteration:: https://en.wikipedia.org/wiki/Power_iteration
+
+    """
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept(
+            "cannot compute centrality for the null graph"
+        )
+    # If no initial vector is provided, start with the all-ones vector.
+    if nstart is None:
+        nstart = {v: 1 for v in G}
+    if all(v == 0 for v in nstart.values()):
+        raise nx.NetworkXError("initial vector cannot have all zero values")
+    # Normalize the initial vector so that each entry is in [0, 1]. This is
+    # guaranteed to never have a divide-by-zero error by the previous line.
+    nstart_sum = sum(nstart.values())
+    x = {k: v / nstart_sum for k, v in nstart.items()}
+    nnodes = G.number_of_nodes()
+    # make up to max_iter iterations
+    for _ in range(max_iter):
+        xlast = x
+        x = xlast.copy()  # Start with xlast times I to iterate with (A+I)
+        # do the multiplication y^T = x^T A (left eigenvector)
+        for n in x:
+            for nbr in G[n]:
+                w = G[n][nbr].get(weight, 1) if weight else 1
+                x[nbr] += xlast[n] * w
+        # Normalize the vector. The normalization denominator `norm`
+        # should never be zero by the Perron--Frobenius
+        # theorem. However, in case it is due to numerical error, we
+        # assume the norm to be one instead.
+        norm = math.hypot(*x.values()) or 1
+        x = {k: v / norm for k, v in x.items()}
+        # Check for convergence (in the L_1 norm).
+        if sum(abs(x[n] - xlast[n]) for n in x) < nnodes * tol:
+            return x
+    raise nx.PowerIterationFailedConvergence(max_iter)
+
+
+@nx._dispatchable(edge_attrs="weight")
+def eigenvector_centrality_numpy(G, weight=None, max_iter=50, tol=0):
+    r"""Compute the eigenvector centrality for the graph `G`.
+
+    Eigenvector centrality computes the centrality for a node by adding
+    the centrality of its predecessors. The centrality for node $i$ is the
+    $i$-th element of a left eigenvector associated with the eigenvalue $\lambda$
+    of maximum modulus that is positive. Such an eigenvector $x$ is
+    defined up to a multiplicative constant by the equation
+
+    .. math::
+
+         \lambda x^T = x^T A,
+
+    where $A$ is the adjacency matrix of the graph `G`. By definition of
+    row-column product, the equation above is equivalent to
+
+    .. math::
+
+        \lambda x_i = \sum_{j\to i}x_j.
+
+    That is, adding the eigenvector centralities of the predecessors of
+    $i$ one obtains the eigenvector centrality of $i$ multiplied by
+    $\lambda$. In the case of undirected graphs, $x$ also solves the familiar
+    right-eigenvector equation $Ax = \lambda x$.
+
+    By virtue of the Perron--Frobenius theorem [1]_, if `G` is (strongly)
+    connected, there is a unique eigenvector $x$, and all its entries
+    are strictly positive.
+
+    However, if `G` is not (strongly) connected, there might be several left
+    eigenvectors associated with $\lambda$, and some of their elements
+    might be zero.
+    Depending on the method used to choose eigenvectors, round-off error can affect
+    which of the infinitely many eigenvectors is reported.
+    This can lead to inconsistent results for the same graph,
+    which the underlying implementation is not robust to.
+    For this reason, only (strongly) connected graphs are accepted.
+
+    Parameters
+    ----------
+    G : graph
+        A connected NetworkX graph.
+
+    weight : None or string, optional (default=None)
+        If ``None``, all edge weights are considered equal. Otherwise holds the
+        name of the edge attribute used as weight. In this measure the
+        weight is interpreted as the connection strength.
+
+    max_iter : integer, optional (default=50)
+        Maximum number of Arnoldi update iterations allowed.
+
+    tol : float, optional (default=0)
+        Relative accuracy for eigenvalues (stopping criterion).
+        The default value of 0 implies machine precision.
+
+    Returns
+    -------
+    nodes : dict of nodes
+        Dictionary of nodes with eigenvector centrality as the value. The
+        associated vector has unit Euclidean norm and the values are
+        nonnegative.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> centrality = nx.eigenvector_centrality_numpy(G)
+    >>> print([f"{node} {centrality[node]:0.2f}" for node in centrality])
+    ['0 0.37', '1 0.60', '2 0.60', '3 0.37']
+
+    Raises
+    ------
+    NetworkXPointlessConcept
+        If the graph `G` is the null graph.
+
+    ArpackNoConvergence
+        When the requested convergence is not obtained. The currently
+        converged eigenvalues and eigenvectors can be found as
+        eigenvalues and eigenvectors attributes of the exception object.
+
+    AmbiguousSolution
+        If `G` is not connected.
+
+    See Also
+    --------
+    :func:`scipy.sparse.linalg.eigs`
+    eigenvector_centrality
+    :func:`~networkx.algorithms.link_analysis.pagerank_alg.pagerank`
+    :func:`~networkx.algorithms.link_analysis.hits_alg.hits`
+
+    Notes
+    -----
+    Eigenvector centrality was introduced by Landau [2]_ for chess
+    tournaments. It was later rediscovered by Wei [3]_ and then
+    popularized by Kendall [4]_ in the context of sport ranking. Berge
+    introduced a general definition for graphs based on social connections
+    [5]_. Bonacich [6]_ reintroduced again eigenvector centrality and made
+    it popular in link analysis.
+
+    This function computes the left dominant eigenvector, which corresponds
+    to adding the centrality of predecessors: this is the usual approach.
+    To add the centrality of successors first reverse the graph with
+    ``G.reverse()``.
+
+    This implementation uses the
+    :func:`SciPy sparse eigenvalue solver<scipy.sparse.linalg.eigs>` (ARPACK)
+    to find the largest eigenvalue/eigenvector pair using Arnoldi iterations
+    [7]_.
+
+    References
+    ----------
+    .. [1] Abraham Berman and Robert J. Plemmons.
+       "Nonnegative Matrices in the Mathematical Sciences".
+       Classics in Applied Mathematics. SIAM, 1994.
+
+    .. [2] Edmund Landau.
+       "Zur relativen Wertbemessung der Turnierresultate".
+       Deutsches Wochenschach, 11:366--369, 1895.
+
+    .. [3] Teh-Hsing Wei.
+       "The Algebraic Foundations of Ranking Theory".
+       PhD thesis, University of Cambridge, 1952.
+
+    .. [4] Maurice G. Kendall.
+       "Further contributions to the theory of paired comparisons".
+       Biometrics, 11(1):43--62, 1955.
+       https://www.jstor.org/stable/3001479
+
+    .. [5] Claude Berge.
+       "Théorie des graphes et ses applications".
+       Dunod, Paris, France, 1958.
+
+    .. [6] Phillip Bonacich.
+       "Technique for analyzing overlapping memberships".
+       Sociological Methodology, 4:176--185, 1972.
+       https://www.jstor.org/stable/270732
+
+    .. [7] Arnoldi, W. E. (1951).
+       "The principle of minimized iterations in the solution of the matrix eigenvalue problem".
+       Quarterly of Applied Mathematics. 9 (1): 17--29.
+       https://doi.org/10.1090/qam/42792
+    """
+    import numpy as np
+    import scipy as sp
+
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept(
+            "cannot compute centrality for the null graph"
+        )
+    connected = nx.is_strongly_connected(G) if G.is_directed() else nx.is_connected(G)
+    if not connected:  # See gh-6888.
+        raise nx.AmbiguousSolution(
+            "`eigenvector_centrality_numpy` does not give consistent results for disconnected graphs"
+        )
+    M = nx.to_scipy_sparse_array(G, nodelist=list(G), weight=weight, dtype=float)
+    _, eigenvector = sp.sparse.linalg.eigs(
+        M.T, k=1, which="LR", maxiter=max_iter, tol=tol
+    )
+    largest = eigenvector.flatten().real
+    norm = np.sign(largest.sum()) * sp.linalg.norm(largest)
+    return dict(zip(G, (largest / norm).tolist()))

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

@@ -0,0 +1,89 @@
+"""Functions for computing the harmonic centrality of a graph."""
+
+from functools import partial
+
+import networkx as nx
+
+__all__ = ["harmonic_centrality"]
+
+
+@nx._dispatchable(edge_attrs="distance")
+def harmonic_centrality(G, nbunch=None, distance=None, sources=None):
+    r"""Compute harmonic centrality for nodes.
+
+    Harmonic centrality [1]_ of a node `u` is the sum of the reciprocal
+    of the shortest path distances from all other nodes to `u`
+
+    .. math::
+
+        C(u) = \sum_{v \neq u} \frac{1}{d(v, u)}
+
+    where `d(v, u)` is the shortest-path distance between `v` and `u`.
+
+    If `sources` is given as an argument, the returned harmonic centrality
+    values are calculated as the sum of the reciprocals of the shortest
+    path distances from the nodes specified in `sources` to `u` instead
+    of from all nodes to `u`.
+
+    Notice that higher values indicate higher centrality.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    nbunch : container (default: all nodes in G)
+      Container of nodes for which harmonic centrality values are calculated.
+
+    sources : container (default: all nodes in G)
+      Container of nodes `v` over which reciprocal distances are computed.
+      Nodes not in `G` are silently ignored.
+
+    distance : edge attribute key, optional (default=None)
+      Use the specified edge attribute as the edge distance in shortest
+      path calculations.  If `None`, then each edge will have distance equal to 1.
+
+    Returns
+    -------
+    nodes : dictionary
+      Dictionary of nodes with harmonic centrality as the value.
+
+    See Also
+    --------
+    betweenness_centrality, load_centrality, eigenvector_centrality,
+    degree_centrality, closeness_centrality
+
+    Notes
+    -----
+    If the 'distance' keyword is set to an edge attribute key then the
+    shortest-path length will be computed using Dijkstra's algorithm with
+    that edge attribute as the edge weight.
+
+    References
+    ----------
+    .. [1] Boldi, Paolo, and Sebastiano Vigna. "Axioms for centrality."
+           Internet Mathematics 10.3-4 (2014): 222-262.
+    """
+
+    nbunch = set(G.nbunch_iter(nbunch) if nbunch is not None else G.nodes)
+    sources = set(G.nbunch_iter(sources) if sources is not None else G.nodes)
+
+    centrality = {u: 0 for u in nbunch}
+
+    transposed = False
+    if len(nbunch) < len(sources):
+        transposed = True
+        nbunch, sources = sources, nbunch
+        if nx.is_directed(G):
+            G = nx.reverse(G, copy=False)
+
+    spl = partial(nx.shortest_path_length, G, weight=distance)
+    for v in sources:
+        dist = spl(v)
+        for u in nbunch.intersection(dist):
+            d = dist[u]
+            if d == 0:  # handle u == v and edges with 0 weight
+                continue
+            centrality[v if transposed else u] += 1 / d
+
+    return centrality

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

@@ -0,0 +1,331 @@
+"""Katz centrality."""
+
+import math
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["katz_centrality", "katz_centrality_numpy"]
+
+
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def katz_centrality(
+    G,
+    alpha=0.1,
+    beta=1.0,
+    max_iter=1000,
+    tol=1.0e-6,
+    nstart=None,
+    normalized=True,
+    weight=None,
+):
+    r"""Compute the Katz centrality for the nodes of the graph G.
+
+    Katz centrality computes the centrality for a node based on the centrality
+    of its neighbors. It is a generalization of the eigenvector centrality. The
+    Katz centrality for node $i$ is
+
+    .. math::
+
+        x_i = \alpha \sum_{j} A_{ij} x_j + \beta,
+
+    where $A$ is the adjacency matrix of graph G with eigenvalues $\lambda$.
+
+    The parameter $\beta$ controls the initial centrality and
+
+    .. math::
+
+        \alpha < \frac{1}{\lambda_{\max}}.
+
+    Katz centrality computes the relative influence of a node within a
+    network by measuring the number of the immediate neighbors (first
+    degree nodes) and also all other nodes in the network that connect
+    to the node under consideration through these immediate neighbors.
+
+    Extra weight can be provided to immediate neighbors through the
+    parameter $\beta$.  Connections made with distant neighbors
+    are, however, penalized by an attenuation factor $\alpha$ which
+    should be strictly less than the inverse largest eigenvalue of the
+    adjacency matrix in order for the Katz centrality to be computed
+    correctly. More information is provided in [1]_.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph.
+
+    alpha : float, optional (default=0.1)
+      Attenuation factor
+
+    beta : scalar or dictionary, optional (default=1.0)
+      Weight attributed to the immediate neighborhood. If not a scalar, the
+      dictionary must have a value for every node.
+
+    max_iter : integer, optional (default=1000)
+      Maximum number of iterations in power method.
+
+    tol : float, optional (default=1.0e-6)
+      Error tolerance used to check convergence in power method iteration.
+
+    nstart : dictionary, optional
+      Starting value of Katz iteration for each node.
+
+    normalized : bool, optional (default=True)
+      If True normalize the resulting values.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      In this measure the weight is interpreted as the connection strength.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with Katz centrality as the value.
+
+    Raises
+    ------
+    NetworkXError
+       If the parameter `beta` is not a scalar but lacks a value for at least
+       one node
+
+    PowerIterationFailedConvergence
+        If the algorithm fails to converge to the specified tolerance
+        within the specified number of iterations of the power iteration
+        method.
+
+    Examples
+    --------
+    >>> import math
+    >>> G = nx.path_graph(4)
+    >>> phi = (1 + math.sqrt(5)) / 2.0  # largest eigenvalue of adj matrix
+    >>> centrality = nx.katz_centrality(G, 1 / phi - 0.01)
+    >>> for n, c in sorted(centrality.items()):
+    ...     print(f"{n} {c:.2f}")
+    0 0.37
+    1 0.60
+    2 0.60
+    3 0.37
+
+    See Also
+    --------
+    katz_centrality_numpy
+    eigenvector_centrality
+    eigenvector_centrality_numpy
+    :func:`~networkx.algorithms.link_analysis.pagerank_alg.pagerank`
+    :func:`~networkx.algorithms.link_analysis.hits_alg.hits`
+
+    Notes
+    -----
+    Katz centrality was introduced by [2]_.
+
+    This algorithm it uses the power method to find the eigenvector
+    corresponding to the largest eigenvalue of the adjacency matrix of ``G``.
+    The parameter ``alpha`` should be strictly less than the inverse of largest
+    eigenvalue of the adjacency matrix for the algorithm to converge.
+    You can use ``max(nx.adjacency_spectrum(G))`` to get $\lambda_{\max}$ the largest
+    eigenvalue of the adjacency matrix.
+    The iteration will stop after ``max_iter`` iterations or an error tolerance of
+    ``number_of_nodes(G) * tol`` has been reached.
+
+    For strongly connected graphs, as $\alpha \to 1/\lambda_{\max}$, and $\beta > 0$,
+    Katz centrality approaches the results for eigenvector centrality.
+
+    For directed graphs this finds "left" eigenvectors which corresponds
+    to the in-edges in the graph. For out-edges Katz centrality,
+    first reverse the graph with ``G.reverse()``.
+
+    References
+    ----------
+    .. [1] Mark E. J. Newman:
+       Networks: An Introduction.
+       Oxford University Press, USA, 2010, p. 720.
+    .. [2] Leo Katz:
+       A New Status Index Derived from Sociometric Index.
+       Psychometrika 18(1):39–43, 1953
+       https://link.springer.com/content/pdf/10.1007/BF02289026.pdf
+    """
+    if len(G) == 0:
+        return {}
+
+    nnodes = G.number_of_nodes()
+
+    if nstart is None:
+        # choose starting vector with entries of 0
+        x = {n: 0 for n in G}
+    else:
+        x = nstart
+
+    try:
+        b = dict.fromkeys(G, float(beta))
+    except (TypeError, ValueError, AttributeError) as err:
+        b = beta
+        if set(beta) != set(G):
+            raise nx.NetworkXError(
+                "beta dictionary must have a value for every node"
+            ) from err
+
+    # make up to max_iter iterations
+    for _ in range(max_iter):
+        xlast = x
+        x = dict.fromkeys(xlast, 0)
+        # do the multiplication y^T = Alpha * x^T A + Beta
+        for n in x:
+            for nbr in G[n]:
+                x[nbr] += xlast[n] * G[n][nbr].get(weight, 1)
+        for n in x:
+            x[n] = alpha * x[n] + b[n]
+
+        # check convergence
+        error = sum(abs(x[n] - xlast[n]) for n in x)
+        if error < nnodes * tol:
+            if normalized:
+                # normalize vector
+                try:
+                    s = 1.0 / math.hypot(*x.values())
+                except ZeroDivisionError:
+                    s = 1.0
+            else:
+                s = 1
+            for n in x:
+                x[n] *= s
+            return x
+    raise nx.PowerIterationFailedConvergence(max_iter)
+
+
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def katz_centrality_numpy(G, alpha=0.1, beta=1.0, normalized=True, weight=None):
+    r"""Compute the Katz centrality for the graph G.
+
+    Katz centrality computes the centrality for a node based on the centrality
+    of its neighbors. It is a generalization of the eigenvector centrality. The
+    Katz centrality for node $i$ is
+
+    .. math::
+
+        x_i = \alpha \sum_{j} A_{ij} x_j + \beta,
+
+    where $A$ is the adjacency matrix of graph G with eigenvalues $\lambda$.
+
+    The parameter $\beta$ controls the initial centrality and
+
+    .. math::
+
+        \alpha < \frac{1}{\lambda_{\max}}.
+
+    Katz centrality computes the relative influence of a node within a
+    network by measuring the number of the immediate neighbors (first
+    degree nodes) and also all other nodes in the network that connect
+    to the node under consideration through these immediate neighbors.
+
+    Extra weight can be provided to immediate neighbors through the
+    parameter $\beta$.  Connections made with distant neighbors
+    are, however, penalized by an attenuation factor $\alpha$ which
+    should be strictly less than the inverse largest eigenvalue of the
+    adjacency matrix in order for the Katz centrality to be computed
+    correctly. More information is provided in [1]_.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    alpha : float
+      Attenuation factor
+
+    beta : scalar or dictionary, optional (default=1.0)
+      Weight attributed to the immediate neighborhood. If not a scalar the
+      dictionary must have an value for every node.
+
+    normalized : bool
+      If True normalize the resulting values.
+
+    weight : None or string, optional
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      In this measure the weight is interpreted as the connection strength.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with Katz centrality as the value.
+
+    Raises
+    ------
+    NetworkXError
+       If the parameter `beta` is not a scalar but lacks a value for at least
+       one node
+
+    Examples
+    --------
+    >>> import math
+    >>> G = nx.path_graph(4)
+    >>> phi = (1 + math.sqrt(5)) / 2.0  # largest eigenvalue of adj matrix
+    >>> centrality = nx.katz_centrality_numpy(G, 1 / phi)
+    >>> for n, c in sorted(centrality.items()):
+    ...     print(f"{n} {c:.2f}")
+    0 0.37
+    1 0.60
+    2 0.60
+    3 0.37
+
+    See Also
+    --------
+    katz_centrality
+    eigenvector_centrality_numpy
+    eigenvector_centrality
+    :func:`~networkx.algorithms.link_analysis.pagerank_alg.pagerank`
+    :func:`~networkx.algorithms.link_analysis.hits_alg.hits`
+
+    Notes
+    -----
+    Katz centrality was introduced by [2]_.
+
+    This algorithm uses a direct linear solver to solve the above equation.
+    The parameter ``alpha`` should be strictly less than the inverse of largest
+    eigenvalue of the adjacency matrix for there to be a solution.
+    You can use ``max(nx.adjacency_spectrum(G))`` to get $\lambda_{\max}$ the largest
+    eigenvalue of the adjacency matrix.
+
+    For strongly connected graphs, as $\alpha \to 1/\lambda_{\max}$, and $\beta > 0$,
+    Katz centrality approaches the results for eigenvector centrality.
+
+    For directed graphs this finds "left" eigenvectors which corresponds
+    to the in-edges in the graph. For out-edges Katz centrality,
+    first reverse the graph with ``G.reverse()``.
+
+    References
+    ----------
+    .. [1] Mark E. J. Newman:
+       Networks: An Introduction.
+       Oxford University Press, USA, 2010, p. 173.
+    .. [2] Leo Katz:
+       A New Status Index Derived from Sociometric Index.
+       Psychometrika 18(1):39–43, 1953
+       https://link.springer.com/content/pdf/10.1007/BF02289026.pdf
+    """
+    import numpy as np
+
+    if len(G) == 0:
+        return {}
+    try:
+        nodelist = beta.keys()
+        if set(nodelist) != set(G):
+            raise nx.NetworkXError("beta dictionary must have a value for every node")
+        b = np.array(list(beta.values()), dtype=float)
+    except AttributeError:
+        nodelist = list(G)
+        try:
+            b = np.ones((len(nodelist), 1)) * beta
+        except (TypeError, ValueError, AttributeError) as err:
+            raise nx.NetworkXError("beta must be a number") from err
+
+    A = nx.adjacency_matrix(G, nodelist=nodelist, weight=weight).todense().T
+    n = A.shape[0]
+    centrality = np.linalg.solve(np.eye(n, n) - (alpha * A), b).squeeze()
+
+    # Normalize: rely on truediv to cast to float, then tolist to make Python numbers
+    norm = np.sign(sum(centrality)) * np.linalg.norm(centrality) if normalized else 1
+    return dict(zip(nodelist, (centrality / norm).tolist()))