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

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+"""Functions for computing large cliques and maximum independent sets."""
+
+import networkx as nx
+from networkx.algorithms.approximation import ramsey
+from networkx.utils import not_implemented_for
+
+__all__ = [
+    "clique_removal",
+    "max_clique",
+    "large_clique_size",
+    "maximum_independent_set",
+]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def maximum_independent_set(G):
+    """Returns an approximate maximum independent set.
+
+    Independent set or stable set is a set of vertices in a graph, no two of
+    which are adjacent. That is, it is a set I of vertices such that for every
+    two vertices in I, there is no edge connecting the two. Equivalently, each
+    edge in the graph has at most one endpoint in I. The size of an independent
+    set is the number of vertices it contains [1]_.
+
+    A maximum independent set is a largest independent set for a given graph G
+    and its size is denoted $\\alpha(G)$. The problem of finding such a set is called
+    the maximum independent set problem and is an NP-hard optimization problem.
+    As such, it is unlikely that there exists an efficient algorithm for finding
+    a maximum independent set of a graph.
+
+    The Independent Set algorithm is based on [2]_.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Undirected graph
+
+    Returns
+    -------
+    iset : Set
+        The apx-maximum independent set
+
+    Examples
+    --------
+    >>> G = nx.path_graph(10)
+    >>> nx.approximation.maximum_independent_set(G)
+    {0, 2, 4, 6, 9}
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the graph is directed or is a multigraph.
+
+    Notes
+    -----
+    Finds the $O(|V|/(log|V|)^2)$ apx of independent set in the worst case.
+
+    References
+    ----------
+    .. [1] `Wikipedia: Independent set
+        <https://en.wikipedia.org/wiki/Independent_set_(graph_theory)>`_
+    .. [2] Boppana, R., & Halldórsson, M. M. (1992).
+       Approximating maximum independent sets by excluding subgraphs.
+       BIT Numerical Mathematics, 32(2), 180–196. Springer.
+    """
+    iset, _ = clique_removal(G)
+    return iset
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def max_clique(G):
+    r"""Find the Maximum Clique
+
+    Finds the $O(|V|/(log|V|)^2)$ apx of maximum clique/independent set
+    in the worst case.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Undirected graph
+
+    Returns
+    -------
+    clique : set
+        The apx-maximum clique of the graph
+
+    Examples
+    --------
+    >>> G = nx.path_graph(10)
+    >>> nx.approximation.max_clique(G)
+    {8, 9}
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the graph is directed or is a multigraph.
+
+    Notes
+    -----
+    A clique in an undirected graph G = (V, E) is a subset of the vertex set
+    `C \subseteq V` such that for every two vertices in C there exists an edge
+    connecting the two. This is equivalent to saying that the subgraph
+    induced by C is complete (in some cases, the term clique may also refer
+    to the subgraph).
+
+    A maximum clique is a clique of the largest possible size in a given graph.
+    The clique number `\omega(G)` of a graph G is the number of
+    vertices in a maximum clique in G. The intersection number of
+    G is the smallest number of cliques that together cover all edges of G.
+
+    https://en.wikipedia.org/wiki/Maximum_clique
+
+    References
+    ----------
+    .. [1] Boppana, R., & Halldórsson, M. M. (1992).
+        Approximating maximum independent sets by excluding subgraphs.
+        BIT Numerical Mathematics, 32(2), 180–196. Springer.
+        doi:10.1007/BF01994876
+    """
+    # finding the maximum clique in a graph is equivalent to finding
+    # the independent set in the complementary graph
+    cgraph = nx.complement(G)
+    iset, _ = clique_removal(cgraph)
+    return iset
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def clique_removal(G):
+    r"""Repeatedly remove cliques from the graph.
+
+    Results in a $O(|V|/(\log |V|)^2)$ approximation of maximum clique
+    and independent set. Returns the largest independent set found, along
+    with found maximal cliques.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Undirected graph
+
+    Returns
+    -------
+    max_ind_cliques : (set, list) tuple
+        2-tuple of Maximal Independent Set and list of maximal cliques (sets).
+
+    Examples
+    --------
+    >>> G = nx.path_graph(10)
+    >>> nx.approximation.clique_removal(G)
+    ({0, 2, 4, 6, 9}, [{0, 1}, {2, 3}, {4, 5}, {6, 7}, {8, 9}])
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the graph is directed or is a multigraph.
+
+    References
+    ----------
+    .. [1] Boppana, R., & Halldórsson, M. M. (1992).
+        Approximating maximum independent sets by excluding subgraphs.
+        BIT Numerical Mathematics, 32(2), 180–196. Springer.
+    """
+    graph = G.copy()
+    c_i, i_i = ramsey.ramsey_R2(graph)
+    cliques = [c_i]
+    isets = [i_i]
+    while graph:
+        graph.remove_nodes_from(c_i)
+        c_i, i_i = ramsey.ramsey_R2(graph)
+        if c_i:
+            cliques.append(c_i)
+        if i_i:
+            isets.append(i_i)
+    # Determine the largest independent set as measured by cardinality.
+    maxiset = max(isets, key=len)
+    return maxiset, cliques
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def large_clique_size(G):
+    """Find the size of a large clique in a graph.
+
+    A *clique* is a subset of nodes in which each pair of nodes is
+    adjacent. This function is a heuristic for finding the size of a
+    large clique in the graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    Returns
+    -------
+    k: integer
+       The size of a large clique in the graph.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(10)
+    >>> nx.approximation.large_clique_size(G)
+    2
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the graph is directed or is a multigraph.
+
+    Notes
+    -----
+    This implementation is from [1]_. Its worst case time complexity is
+    :math:`O(n d^2)`, where *n* is the number of nodes in the graph and
+    *d* is the maximum degree.
+
+    This function is a heuristic, which means it may work well in
+    practice, but there is no rigorous mathematical guarantee on the
+    ratio between the returned number and the actual largest clique size
+    in the graph.
+
+    References
+    ----------
+    .. [1] Pattabiraman, Bharath, et al.
+       "Fast Algorithms for the Maximum Clique Problem on Massive Graphs
+       with Applications to Overlapping Community Detection."
+       *Internet Mathematics* 11.4-5 (2015): 421--448.
+       <https://doi.org/10.1080/15427951.2014.986778>
+
+    See also
+    --------
+
+    :func:`networkx.algorithms.approximation.clique.max_clique`
+        A function that returns an approximate maximum clique with a
+        guarantee on the approximation ratio.
+
+    :mod:`networkx.algorithms.clique`
+        Functions for finding the exact maximum clique in a graph.
+
+    """
+    degrees = G.degree
+
+    def _clique_heuristic(G, U, size, best_size):
+        if not U:
+            return max(best_size, size)
+        u = max(U, key=degrees)
+        U.remove(u)
+        N_prime = {v for v in G[u] if degrees[v] >= best_size}
+        return _clique_heuristic(G, U & N_prime, size + 1, best_size)
+
+    best_size = 0
+    nodes = (u for u in G if degrees[u] >= best_size)
+    for u in nodes:
+        neighbors = {v for v in G[u] if degrees[v] >= best_size}
+        best_size = _clique_heuristic(G, neighbors, 1, best_size)
+    return best_size

janus/lib/python3.10/site-packages/networkx/algorithms/approximation/connectivity.py

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+"""Fast approximation for node connectivity"""
+
+import itertools
+from operator import itemgetter
+
+import networkx as nx
+
+__all__ = [
+    "local_node_connectivity",
+    "node_connectivity",
+    "all_pairs_node_connectivity",
+]
+
+
+@nx._dispatchable(name="approximate_local_node_connectivity")
+def local_node_connectivity(G, source, target, cutoff=None):
+    """Compute node connectivity between source and target.
+
+    Pairwise or local node connectivity between two distinct and nonadjacent
+    nodes is the minimum number of nodes that must be removed (minimum
+    separating cutset) to disconnect them. By Menger's theorem, this is equal
+    to the number of node independent paths (paths that share no nodes other
+    than source and target). Which is what we compute in this function.
+
+    This algorithm is a fast approximation that gives an strict lower
+    bound on the actual number of node independent paths between two nodes [1]_.
+    It works for both directed and undirected graphs.
+
+    Parameters
+    ----------
+
+    G : NetworkX graph
+
+    source : node
+        Starting node for node connectivity
+
+    target : node
+        Ending node for node connectivity
+
+    cutoff : integer
+        Maximum node connectivity to consider. If None, the minimum degree
+        of source or target is used as a cutoff. Default value None.
+
+    Returns
+    -------
+    k: integer
+       pairwise node connectivity
+
+    Examples
+    --------
+    >>> # Platonic octahedral graph has node connectivity 4
+    >>> # for each non adjacent node pair
+    >>> from networkx.algorithms import approximation as approx
+    >>> G = nx.octahedral_graph()
+    >>> approx.local_node_connectivity(G, 0, 5)
+    4
+
+    Notes
+    -----
+    This algorithm [1]_ finds node independents paths between two nodes by
+    computing their shortest path using BFS, marking the nodes of the path
+    found as 'used' and then searching other shortest paths excluding the
+    nodes marked as used until no more paths exist. It is not exact because
+    a shortest path could use nodes that, if the path were longer, may belong
+    to two different node independent paths. Thus it only guarantees an
+    strict lower bound on node connectivity.
+
+    Note that the authors propose a further refinement, losing accuracy and
+    gaining speed, which is not implemented yet.
+
+    See also
+    --------
+    all_pairs_node_connectivity
+    node_connectivity
+
+    References
+    ----------
+    .. [1] White, Douglas R., and Mark Newman. 2001 A Fast Algorithm for
+        Node-Independent Paths. Santa Fe Institute Working Paper #01-07-035
+        http://eclectic.ss.uci.edu/~drwhite/working.pdf
+
+    """
+    if target == source:
+        raise nx.NetworkXError("source and target have to be different nodes.")
+
+    # Maximum possible node independent paths
+    if G.is_directed():
+        possible = min(G.out_degree(source), G.in_degree(target))
+    else:
+        possible = min(G.degree(source), G.degree(target))
+
+    K = 0
+    if not possible:
+        return K
+
+    if cutoff is None:
+        cutoff = float("inf")
+
+    exclude = set()
+    for i in range(min(possible, cutoff)):
+        try:
+            path = _bidirectional_shortest_path(G, source, target, exclude)
+            exclude.update(set(path))
+            K += 1
+        except nx.NetworkXNoPath:
+            break
+
+    return K
+
+
+@nx._dispatchable(name="approximate_node_connectivity")
+def node_connectivity(G, s=None, t=None):
+    r"""Returns an approximation for node connectivity for a graph or digraph G.
+
+    Node connectivity is equal to the minimum number of nodes that
+    must be removed to disconnect G or render it trivial. By Menger's theorem,
+    this is equal to the number of node independent paths (paths that
+    share no nodes other than source and target).
+
+    If source and target nodes are provided, this function returns the
+    local node connectivity: the minimum number of nodes that must be
+    removed to break all paths from source to target in G.
+
+    This algorithm is based on a fast approximation that gives an strict lower
+    bound on the actual number of node independent paths between two nodes [1]_.
+    It works for both directed and undirected graphs.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Undirected graph
+
+    s : node
+        Source node. Optional. Default value: None.
+
+    t : node
+        Target node. Optional. Default value: None.
+
+    Returns
+    -------
+    K : integer
+        Node connectivity of G, or local node connectivity if source
+        and target are provided.
+
+    Examples
+    --------
+    >>> # Platonic octahedral graph is 4-node-connected
+    >>> from networkx.algorithms import approximation as approx
+    >>> G = nx.octahedral_graph()
+    >>> approx.node_connectivity(G)
+    4
+
+    Notes
+    -----
+    This algorithm [1]_ finds node independents paths between two nodes by
+    computing their shortest path using BFS, marking the nodes of the path
+    found as 'used' and then searching other shortest paths excluding the
+    nodes marked as used until no more paths exist. It is not exact because
+    a shortest path could use nodes that, if the path were longer, may belong
+    to two different node independent paths. Thus it only guarantees an
+    strict lower bound on node connectivity.
+
+    See also
+    --------
+    all_pairs_node_connectivity
+    local_node_connectivity
+
+    References
+    ----------
+    .. [1] White, Douglas R., and Mark Newman. 2001 A Fast Algorithm for
+        Node-Independent Paths. Santa Fe Institute Working Paper #01-07-035
+        http://eclectic.ss.uci.edu/~drwhite/working.pdf
+
+    """
+    if (s is not None and t is None) or (s is None and t is not None):
+        raise nx.NetworkXError("Both source and target must be specified.")
+
+    # Local node connectivity
+    if s is not None and t is not None:
+        if s not in G:
+            raise nx.NetworkXError(f"node {s} not in graph")
+        if t not in G:
+            raise nx.NetworkXError(f"node {t} not in graph")
+        return local_node_connectivity(G, s, t)
+
+    # Global node connectivity
+    if G.is_directed():
+        connected_func = nx.is_weakly_connected
+        iter_func = itertools.permutations
+
+        def neighbors(v):
+            return itertools.chain(G.predecessors(v), G.successors(v))
+
+    else:
+        connected_func = nx.is_connected
+        iter_func = itertools.combinations
+        neighbors = G.neighbors
+
+    if not connected_func(G):
+        return 0
+
+    # Choose a node with minimum degree
+    v, minimum_degree = min(G.degree(), key=itemgetter(1))
+    # Node connectivity is bounded by minimum degree
+    K = minimum_degree
+    # compute local node connectivity with all non-neighbors nodes
+    # and store the minimum
+    for w in set(G) - set(neighbors(v)) - {v}:
+        K = min(K, local_node_connectivity(G, v, w, cutoff=K))
+    # Same for non adjacent pairs of neighbors of v
+    for x, y in iter_func(neighbors(v), 2):
+        if y not in G[x] and x != y:
+            K = min(K, local_node_connectivity(G, x, y, cutoff=K))
+    return K
+
+
+@nx._dispatchable(name="approximate_all_pairs_node_connectivity")
+def all_pairs_node_connectivity(G, nbunch=None, cutoff=None):
+    """Compute node connectivity between all pairs of nodes.
+
+    Pairwise or local node connectivity between two distinct and nonadjacent
+    nodes is the minimum number of nodes that must be removed (minimum
+    separating cutset) to disconnect them. By Menger's theorem, this is equal
+    to the number of node independent paths (paths that share no nodes other
+    than source and target). Which is what we compute in this function.
+
+    This algorithm is a fast approximation that gives an strict lower
+    bound on the actual number of node independent paths between two nodes [1]_.
+    It works for both directed and undirected graphs.
+
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    nbunch: container
+        Container of nodes. If provided node connectivity will be computed
+        only over pairs of nodes in nbunch.
+
+    cutoff : integer
+        Maximum node connectivity to consider. If None, the minimum degree
+        of source or target is used as a cutoff in each pair of nodes.
+        Default value None.
+
+    Returns
+    -------
+    K : dictionary
+        Dictionary, keyed by source and target, of pairwise node connectivity
+
+    Examples
+    --------
+    A 3 node cycle with one extra node attached has connectivity 2 between all
+    nodes in the cycle and connectivity 1 between the extra node and the rest:
+
+    >>> G = nx.cycle_graph(3)
+    >>> G.add_edge(2, 3)
+    >>> import pprint  # for nice dictionary formatting
+    >>> pprint.pprint(nx.all_pairs_node_connectivity(G))
+    {0: {1: 2, 2: 2, 3: 1},
+     1: {0: 2, 2: 2, 3: 1},
+     2: {0: 2, 1: 2, 3: 1},
+     3: {0: 1, 1: 1, 2: 1}}
+
+    See Also
+    --------
+    local_node_connectivity
+    node_connectivity
+
+    References
+    ----------
+    .. [1] White, Douglas R., and Mark Newman. 2001 A Fast Algorithm for
+        Node-Independent Paths. Santa Fe Institute Working Paper #01-07-035
+        http://eclectic.ss.uci.edu/~drwhite/working.pdf
+    """
+    if nbunch is None:
+        nbunch = G
+    else:
+        nbunch = set(nbunch)
+
+    directed = G.is_directed()
+    if directed:
+        iter_func = itertools.permutations
+    else:
+        iter_func = itertools.combinations
+
+    all_pairs = {n: {} for n in nbunch}
+
+    for u, v in iter_func(nbunch, 2):
+        k = local_node_connectivity(G, u, v, cutoff=cutoff)
+        all_pairs[u][v] = k
+        if not directed:
+            all_pairs[v][u] = k
+
+    return all_pairs
+
+
+def _bidirectional_shortest_path(G, source, target, exclude):
+    """Returns shortest path between source and target ignoring nodes in the
+    container 'exclude'.
+
+    Parameters
+    ----------
+
+    G : NetworkX graph
+
+    source : node
+        Starting node for path
+
+    target : node
+        Ending node for path
+
+    exclude: container
+        Container for nodes to exclude from the search for shortest paths
+
+    Returns
+    -------
+    path: list
+        Shortest path between source and target ignoring nodes in 'exclude'
+
+    Raises
+    ------
+    NetworkXNoPath
+        If there is no path or if nodes are adjacent and have only one path
+        between them
+
+    Notes
+    -----
+    This function and its helper are originally from
+    networkx.algorithms.shortest_paths.unweighted and are modified to
+    accept the extra parameter 'exclude', which is a container for nodes
+    already used in other paths that should be ignored.
+
+    References
+    ----------
+    .. [1] White, Douglas R., and Mark Newman. 2001 A Fast Algorithm for
+        Node-Independent Paths. Santa Fe Institute Working Paper #01-07-035
+        http://eclectic.ss.uci.edu/~drwhite/working.pdf
+
+    """
+    # call helper to do the real work
+    results = _bidirectional_pred_succ(G, source, target, exclude)
+    pred, succ, w = results
+
+    # build path from pred+w+succ
+    path = []
+    # from source to w
+    while w is not None:
+        path.append(w)
+        w = pred[w]
+    path.reverse()
+    # from w to target
+    w = succ[path[-1]]
+    while w is not None:
+        path.append(w)
+        w = succ[w]
+
+    return path
+
+
+def _bidirectional_pred_succ(G, source, target, exclude):
+    # does BFS from both source and target and meets in the middle
+    # excludes nodes in the container "exclude" from the search
+
+    # handle either directed or undirected
+    if G.is_directed():
+        Gpred = G.predecessors
+        Gsucc = G.successors
+    else:
+        Gpred = G.neighbors
+        Gsucc = G.neighbors
+
+    # predecessor and successors in search
+    pred = {source: None}
+    succ = {target: None}
+
+    # initialize fringes, start with forward
+    forward_fringe = [source]
+    reverse_fringe = [target]
+
+    level = 0
+
+    while forward_fringe and reverse_fringe:
+        # Make sure that we iterate one step forward and one step backwards
+        # thus source and target will only trigger "found path" when they are
+        # adjacent and then they can be safely included in the container 'exclude'
+        level += 1
+        if level % 2 != 0:
+            this_level = forward_fringe
+            forward_fringe = []
+            for v in this_level:
+                for w in Gsucc(v):
+                    if w in exclude:
+                        continue
+                    if w not in pred:
+                        forward_fringe.append(w)
+                        pred[w] = v
+                    if w in succ:
+                        return pred, succ, w  # found path
+        else:
+            this_level = reverse_fringe
+            reverse_fringe = []
+            for v in this_level:
+                for w in Gpred(v):
+                    if w in exclude:
+                        continue
+                    if w not in succ:
+                        succ[w] = v
+                        reverse_fringe.append(w)
+                    if w in pred:
+                        return pred, succ, w  # found path
+
+    raise nx.NetworkXNoPath(f"No path between {source} and {target}.")

janus/lib/python3.10/site-packages/networkx/algorithms/approximation/tests/test_approx_clust_coeff.py

@@ -0,0 +1,41 @@
+import networkx as nx
+from networkx.algorithms.approximation import average_clustering
+
+# This approximation has to be exact in regular graphs
+# with no triangles or with all possible triangles.
+
+
+def test_petersen():
+    # Actual coefficient is 0
+    G = nx.petersen_graph()
+    assert average_clustering(G, trials=len(G) // 2) == nx.average_clustering(G)
+
+
+def test_petersen_seed():
+    # Actual coefficient is 0
+    G = nx.petersen_graph()
+    assert average_clustering(G, trials=len(G) // 2, seed=1) == nx.average_clustering(G)
+
+
+def test_tetrahedral():
+    # Actual coefficient is 1
+    G = nx.tetrahedral_graph()
+    assert average_clustering(G, trials=len(G) // 2) == nx.average_clustering(G)
+
+
+def test_dodecahedral():
+    # Actual coefficient is 0
+    G = nx.dodecahedral_graph()
+    assert average_clustering(G, trials=len(G) // 2) == nx.average_clustering(G)
+
+
+def test_empty():
+    G = nx.empty_graph(5)
+    assert average_clustering(G, trials=len(G) // 2) == 0
+
+
+def test_complete():
+    G = nx.complete_graph(5)
+    assert average_clustering(G, trials=len(G) // 2) == 1
+    G = nx.complete_graph(7)
+    assert average_clustering(G, trials=len(G) // 2) == 1

janus/lib/python3.10/site-packages/networkx/algorithms/approximation/tests/test_dominating_set.py

@@ -0,0 +1,78 @@
+import pytest
+
+import networkx as nx
+from networkx.algorithms.approximation import (
+    min_edge_dominating_set,
+    min_weighted_dominating_set,
+)
+
+
+class TestMinWeightDominatingSet:
+    def test_min_weighted_dominating_set(self):
+        graph = nx.Graph()
+        graph.add_edge(1, 2)
+        graph.add_edge(1, 5)
+        graph.add_edge(2, 3)
+        graph.add_edge(2, 5)
+        graph.add_edge(3, 4)
+        graph.add_edge(3, 6)
+        graph.add_edge(5, 6)
+
+        vertices = {1, 2, 3, 4, 5, 6}
+        # due to ties, this might be hard to test tight bounds
+        dom_set = min_weighted_dominating_set(graph)
+        for vertex in vertices - dom_set:
+            neighbors = set(graph.neighbors(vertex))
+            assert len(neighbors & dom_set) > 0, "Non dominating set found!"
+
+    def test_star_graph(self):
+        """Tests that an approximate dominating set for the star graph,
+        even when the center node does not have the smallest integer
+        label, gives just the center node.
+
+        For more information, see #1527.
+
+        """
+        # Create a star graph in which the center node has the highest
+        # label instead of the lowest.
+        G = nx.star_graph(10)
+        G = nx.relabel_nodes(G, {0: 9, 9: 0})
+        assert min_weighted_dominating_set(G) == {9}
+
+    def test_null_graph(self):
+        """Tests that the unique dominating set for the null graph is an empty set"""
+        G = nx.Graph()
+        assert min_weighted_dominating_set(G) == set()
+
+    def test_min_edge_dominating_set(self):
+        graph = nx.path_graph(5)
+        dom_set = min_edge_dominating_set(graph)
+
+        # this is a crappy way to test, but good enough for now.
+        for edge in graph.edges():
+            if edge in dom_set:
+                continue
+            else:
+                u, v = edge
+                found = False
+                for dom_edge in dom_set:
+                    found |= u == dom_edge[0] or u == dom_edge[1]
+                assert found, "Non adjacent edge found!"
+
+        graph = nx.complete_graph(10)
+        dom_set = min_edge_dominating_set(graph)
+
+        # this is a crappy way to test, but good enough for now.
+        for edge in graph.edges():
+            if edge in dom_set:
+                continue
+            else:
+                u, v = edge
+                found = False
+                for dom_edge in dom_set:
+                    found |= u == dom_edge[0] or u == dom_edge[1]
+                assert found, "Non adjacent edge found!"
+
+        graph = nx.Graph()  # empty Networkx graph
+        with pytest.raises(ValueError, match="Expected non-empty NetworkX graph!"):
+            min_edge_dominating_set(graph)

janus/lib/python3.10/site-packages/networkx/algorithms/approximation/tests/test_maxcut.py

@@ -0,0 +1,94 @@
+import random
+
+import pytest
+
+import networkx as nx
+from networkx.algorithms.approximation import maxcut
+
+
+@pytest.mark.parametrize(
+    "f", (nx.approximation.randomized_partitioning, nx.approximation.one_exchange)
+)
+@pytest.mark.parametrize("graph_constructor", (nx.DiGraph, nx.MultiGraph))
+def test_raises_on_directed_and_multigraphs(f, graph_constructor):
+    G = graph_constructor([(0, 1), (1, 2)])
+    with pytest.raises(nx.NetworkXNotImplemented):
+        f(G)
+
+
+def _is_valid_cut(G, set1, set2):
+    union = set1.union(set2)
+    assert union == set(G.nodes)
+    assert len(set1) + len(set2) == G.number_of_nodes()
+
+
+def _cut_is_locally_optimal(G, cut_size, set1):
+    # test if cut can be locally improved
+    for i, node in enumerate(set1):
+        cut_size_without_node = nx.algorithms.cut_size(
+            G, set1 - {node}, weight="weight"
+        )
+        assert cut_size_without_node <= cut_size
+
+
+def test_random_partitioning():
+    G = nx.complete_graph(5)
+    _, (set1, set2) = maxcut.randomized_partitioning(G, seed=5)
+    _is_valid_cut(G, set1, set2)
+
+
+def test_random_partitioning_all_to_one():
+    G = nx.complete_graph(5)
+    _, (set1, set2) = maxcut.randomized_partitioning(G, p=1)
+    _is_valid_cut(G, set1, set2)
+    assert len(set1) == G.number_of_nodes()
+    assert len(set2) == 0
+
+
+def test_one_exchange_basic():
+    G = nx.complete_graph(5)
+    random.seed(5)
+    for u, v, w in G.edges(data=True):
+        w["weight"] = random.randrange(-100, 100, 1) / 10
+
+    initial_cut = set(random.sample(sorted(G.nodes()), k=5))
+    cut_size, (set1, set2) = maxcut.one_exchange(
+        G, initial_cut, weight="weight", seed=5
+    )
+
+    _is_valid_cut(G, set1, set2)
+    _cut_is_locally_optimal(G, cut_size, set1)
+
+
+def test_one_exchange_optimal():
+    # Greedy one exchange should find the optimal solution for this graph (14)
+    G = nx.Graph()
+    G.add_edge(1, 2, weight=3)
+    G.add_edge(1, 3, weight=3)
+    G.add_edge(1, 4, weight=3)
+    G.add_edge(1, 5, weight=3)
+    G.add_edge(2, 3, weight=5)
+
+    cut_size, (set1, set2) = maxcut.one_exchange(G, weight="weight", seed=5)
+
+    _is_valid_cut(G, set1, set2)
+    _cut_is_locally_optimal(G, cut_size, set1)
+    # check global optimality
+    assert cut_size == 14
+
+
+def test_negative_weights():
+    G = nx.complete_graph(5)
+    random.seed(5)
+    for u, v, w in G.edges(data=True):
+        w["weight"] = -1 * random.random()
+
+    initial_cut = set(random.sample(sorted(G.nodes()), k=5))
+    cut_size, (set1, set2) = maxcut.one_exchange(G, initial_cut, weight="weight")
+
+    # make sure it is a valid cut
+    _is_valid_cut(G, set1, set2)
+    # check local optimality
+    _cut_is_locally_optimal(G, cut_size, set1)
+    # test that all nodes are in the same partition
+    assert len(set1) == len(G.nodes) or len(set2) == len(G.nodes)

janus/lib/python3.10/site-packages/networkx/algorithms/approximation/tests/test_vertex_cover.py

@@ -0,0 +1,68 @@
+import networkx as nx
+from networkx.algorithms.approximation import min_weighted_vertex_cover
+
+
+def is_cover(G, node_cover):
+    return all({u, v} & node_cover for u, v in G.edges())
+
+
+class TestMWVC:
+    """Unit tests for the approximate minimum weighted vertex cover
+    function,
+    :func:`~networkx.algorithms.approximation.vertex_cover.min_weighted_vertex_cover`.
+
+    """
+
+    def test_unweighted_directed(self):
+        # Create a star graph in which half the nodes are directed in
+        # and half are directed out.
+        G = nx.DiGraph()
+        G.add_edges_from((0, v) for v in range(1, 26))
+        G.add_edges_from((v, 0) for v in range(26, 51))
+        cover = min_weighted_vertex_cover(G)
+        assert 1 == len(cover)
+        assert is_cover(G, cover)
+
+    def test_unweighted_undirected(self):
+        # create a simple star graph
+        size = 50
+        sg = nx.star_graph(size)
+        cover = min_weighted_vertex_cover(sg)
+        assert 1 == len(cover)
+        assert is_cover(sg, cover)
+
+    def test_weighted(self):
+        wg = nx.Graph()
+        wg.add_node(0, weight=10)
+        wg.add_node(1, weight=1)
+        wg.add_node(2, weight=1)
+        wg.add_node(3, weight=1)
+        wg.add_node(4, weight=1)
+
+        wg.add_edge(0, 1)
+        wg.add_edge(0, 2)
+        wg.add_edge(0, 3)
+        wg.add_edge(0, 4)
+
+        wg.add_edge(1, 2)
+        wg.add_edge(2, 3)
+        wg.add_edge(3, 4)
+        wg.add_edge(4, 1)
+
+        cover = min_weighted_vertex_cover(wg, weight="weight")
+        csum = sum(wg.nodes[node]["weight"] for node in cover)
+        assert 4 == csum
+        assert is_cover(wg, cover)
+
+    def test_unweighted_self_loop(self):
+        slg = nx.Graph()
+        slg.add_node(0)
+        slg.add_node(1)
+        slg.add_node(2)
+
+        slg.add_edge(0, 1)
+        slg.add_edge(2, 2)
+
+        cover = min_weighted_vertex_cover(slg)
+        assert 2 == len(cover)
+        assert is_cover(slg, cover)

janus/lib/python3.10/site-packages/networkx/algorithms/assortativity/__init__.py

@@ -0,0 +1,5 @@
+from networkx.algorithms.assortativity.connectivity import *
+from networkx.algorithms.assortativity.correlation import *
+from networkx.algorithms.assortativity.mixing import *
+from networkx.algorithms.assortativity.neighbor_degree import *
+from networkx.algorithms.assortativity.pairs import *

janus/lib/python3.10/site-packages/networkx/algorithms/assortativity/connectivity.py

@@ -0,0 +1,122 @@
+from collections import defaultdict
+
+import networkx as nx
+
+__all__ = ["average_degree_connectivity"]
+
+
+@nx._dispatchable(edge_attrs="weight")
+def average_degree_connectivity(
+    G, source="in+out", target="in+out", nodes=None, weight=None
+):
+    r"""Compute the average degree connectivity of graph.
+
+    The average degree connectivity is the average nearest neighbor degree of
+    nodes with degree k. For weighted graphs, an analogous measure can
+    be computed using the weighted average neighbors degree defined in
+    [1]_, for a node `i`, as
+
+    .. math::
+
+        k_{nn,i}^{w} = \frac{1}{s_i} \sum_{j \in N(i)} w_{ij} k_j
+
+    where `s_i` is the weighted degree of node `i`,
+    `w_{ij}` is the weight of the edge that links `i` and `j`,
+    and `N(i)` are the neighbors of node `i`.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source :  "in"|"out"|"in+out" (default:"in+out")
+       Directed graphs only. Use "in"- or "out"-degree for source node.
+
+    target : "in"|"out"|"in+out" (default:"in+out"
+       Directed graphs only. Use "in"- or "out"-degree for target node.
+
+    nodes : list or iterable (optional)
+        Compute neighbor connectivity for these nodes. The default is all
+        nodes.
+
+    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.
+
+    Returns
+    -------
+    d : dict
+       A dictionary keyed by degree k with the value of average connectivity.
+
+    Raises
+    ------
+    NetworkXError
+        If either `source` or `target` are not one of 'in',
+        'out', or 'in+out'.
+        If either `source` or `target` is passed for an undirected graph.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> G.edges[1, 2]["weight"] = 3
+    >>> nx.average_degree_connectivity(G)
+    {1: 2.0, 2: 1.5}
+    >>> nx.average_degree_connectivity(G, weight="weight")
+    {1: 2.0, 2: 1.75}
+
+    See Also
+    --------
+    average_neighbor_degree
+
+    References
+    ----------
+    .. [1] A. Barrat, M. Barthélemy, R. Pastor-Satorras, and A. Vespignani,
+       "The architecture of complex weighted networks".
+       PNAS 101 (11): 3747–3752 (2004).
+    """
+    # First, determine the type of neighbors and the type of degree to use.
+    if G.is_directed():
+        if source not in ("in", "out", "in+out"):
+            raise nx.NetworkXError('source must be one of "in", "out", or "in+out"')
+        if target not in ("in", "out", "in+out"):
+            raise nx.NetworkXError('target must be one of "in", "out", or "in+out"')
+        direction = {"out": G.out_degree, "in": G.in_degree, "in+out": G.degree}
+        neighbor_funcs = {
+            "out": G.successors,
+            "in": G.predecessors,
+            "in+out": G.neighbors,
+        }
+        source_degree = direction[source]
+        target_degree = direction[target]
+        neighbors = neighbor_funcs[source]
+        # `reverse` indicates whether to look at the in-edge when
+        # computing the weight of an edge.
+        reverse = source == "in"
+    else:
+        if source != "in+out" or target != "in+out":
+            raise nx.NetworkXError(
+                f"source and target arguments are only supported for directed graphs"
+            )
+        source_degree = G.degree
+        target_degree = G.degree
+        neighbors = G.neighbors
+        reverse = False
+    dsum = defaultdict(int)
+    dnorm = defaultdict(int)
+    # Check if `source_nodes` is actually a single node in the graph.
+    source_nodes = source_degree(nodes)
+    if nodes in G:
+        source_nodes = [(nodes, source_degree(nodes))]
+    for n, k in source_nodes:
+        nbrdeg = target_degree(neighbors(n))
+        if weight is None:
+            s = sum(d for n, d in nbrdeg)
+        else:  # weight nbr degree by weight of (n,nbr) edge
+            if reverse:
+                s = sum(G[nbr][n].get(weight, 1) * d for nbr, d in nbrdeg)
+            else:
+                s = sum(G[n][nbr].get(weight, 1) * d for nbr, d in nbrdeg)
+        dnorm[k] += source_degree(n, weight=weight)
+        dsum[k] += s
+
+    # normalize
+    return {k: avg if dnorm[k] == 0 else avg / dnorm[k] for k, avg in dsum.items()}

janus/lib/python3.10/site-packages/networkx/algorithms/assortativity/correlation.py

@@ -0,0 +1,302 @@
+"""Node assortativity coefficients and correlation measures."""
+
+import networkx as nx
+from networkx.algorithms.assortativity.mixing import (
+    attribute_mixing_matrix,
+    degree_mixing_matrix,
+)
+from networkx.algorithms.assortativity.pairs import node_degree_xy
+
+__all__ = [
+    "degree_pearson_correlation_coefficient",
+    "degree_assortativity_coefficient",
+    "attribute_assortativity_coefficient",
+    "numeric_assortativity_coefficient",
+]
+
+
+@nx._dispatchable(edge_attrs="weight")
+def degree_assortativity_coefficient(G, x="out", y="in", weight=None, nodes=None):
+    """Compute degree assortativity of graph.
+
+    Assortativity measures the similarity of connections
+    in the graph with respect to the node degree.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    x: string ('in','out')
+       The degree type for source node (directed graphs only).
+
+    y: string ('in','out')
+       The degree type for target node (directed graphs only).
+
+    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.
+
+    nodes: list or iterable (optional)
+        Compute degree assortativity only for nodes in container.
+        The default is all nodes.
+
+    Returns
+    -------
+    r : float
+       Assortativity of graph by degree.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> r = nx.degree_assortativity_coefficient(G)
+    >>> print(f"{r:3.1f}")
+    -0.5
+
+    See Also
+    --------
+    attribute_assortativity_coefficient
+    numeric_assortativity_coefficient
+    degree_mixing_dict
+    degree_mixing_matrix
+
+    Notes
+    -----
+    This computes Eq. (21) in Ref. [1]_ , where e is the joint
+    probability distribution (mixing matrix) of the degrees.  If G is
+    directed than the matrix e is the joint probability of the
+    user-specified degree type for the source and target.
+
+    References
+    ----------
+    .. [1] M. E. J. Newman, Mixing patterns in networks,
+       Physical Review E, 67 026126, 2003
+    .. [2] Foster, J.G., Foster, D.V., Grassberger, P. & Paczuski, M.
+       Edge direction and the structure of networks, PNAS 107, 10815-20 (2010).
+    """
+    if nodes is None:
+        nodes = G.nodes
+
+    degrees = None
+
+    if G.is_directed():
+        indeg = (
+            {d for _, d in G.in_degree(nodes, weight=weight)}
+            if "in" in (x, y)
+            else set()
+        )
+        outdeg = (
+            {d for _, d in G.out_degree(nodes, weight=weight)}
+            if "out" in (x, y)
+            else set()
+        )
+        degrees = set.union(indeg, outdeg)
+    else:
+        degrees = {d for _, d in G.degree(nodes, weight=weight)}
+
+    mapping = {d: i for i, d in enumerate(degrees)}
+    M = degree_mixing_matrix(G, x=x, y=y, nodes=nodes, weight=weight, mapping=mapping)
+
+    return _numeric_ac(M, mapping=mapping)
+
+
+@nx._dispatchable(edge_attrs="weight")
+def degree_pearson_correlation_coefficient(G, x="out", y="in", weight=None, nodes=None):
+    """Compute degree assortativity of graph.
+
+    Assortativity measures the similarity of connections
+    in the graph with respect to the node degree.
+
+    This is the same as degree_assortativity_coefficient but uses the
+    potentially faster scipy.stats.pearsonr function.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    x: string ('in','out')
+       The degree type for source node (directed graphs only).
+
+    y: string ('in','out')
+       The degree type for target node (directed graphs only).
+
+    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.
+
+    nodes: list or iterable (optional)
+        Compute pearson correlation of degrees only for specified nodes.
+        The default is all nodes.
+
+    Returns
+    -------
+    r : float
+       Assortativity of graph by degree.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> r = nx.degree_pearson_correlation_coefficient(G)
+    >>> print(f"{r:3.1f}")
+    -0.5
+
+    Notes
+    -----
+    This calls scipy.stats.pearsonr.
+
+    References
+    ----------
+    .. [1] M. E. J. Newman, Mixing patterns in networks
+           Physical Review E, 67 026126, 2003
+    .. [2] Foster, J.G., Foster, D.V., Grassberger, P. & Paczuski, M.
+       Edge direction and the structure of networks, PNAS 107, 10815-20 (2010).
+    """
+    import scipy as sp
+
+    xy = node_degree_xy(G, x=x, y=y, nodes=nodes, weight=weight)
+    x, y = zip(*xy)
+    return float(sp.stats.pearsonr(x, y)[0])
+
+
+@nx._dispatchable(node_attrs="attribute")
+def attribute_assortativity_coefficient(G, attribute, nodes=None):
+    """Compute assortativity for node attributes.
+
+    Assortativity measures the similarity of connections
+    in the graph with respect to the given attribute.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    attribute : string
+        Node attribute key
+
+    nodes: list or iterable (optional)
+        Compute attribute assortativity for nodes in container.
+        The default is all nodes.
+
+    Returns
+    -------
+    r: float
+       Assortativity of graph for given attribute
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> G.add_nodes_from([0, 1], color="red")
+    >>> G.add_nodes_from([2, 3], color="blue")
+    >>> G.add_edges_from([(0, 1), (2, 3)])
+    >>> print(nx.attribute_assortativity_coefficient(G, "color"))
+    1.0
+
+    Notes
+    -----
+    This computes Eq. (2) in Ref. [1]_ , (trace(M)-sum(M^2))/(1-sum(M^2)),
+    where M is the joint probability distribution (mixing matrix)
+    of the specified attribute.
+
+    References
+    ----------
+    .. [1] M. E. J. Newman, Mixing patterns in networks,
+       Physical Review E, 67 026126, 2003
+    """
+    M = attribute_mixing_matrix(G, attribute, nodes)
+    return attribute_ac(M)
+
+
+@nx._dispatchable(node_attrs="attribute")
+def numeric_assortativity_coefficient(G, attribute, nodes=None):
+    """Compute assortativity for numerical node attributes.
+
+    Assortativity measures the similarity of connections
+    in the graph with respect to the given numeric attribute.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    attribute : string
+        Node attribute key.
+
+    nodes: list or iterable (optional)
+        Compute numeric assortativity only for attributes of nodes in
+        container. The default is all nodes.
+
+    Returns
+    -------
+    r: float
+       Assortativity of graph for given attribute
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> G.add_nodes_from([0, 1], size=2)
+    >>> G.add_nodes_from([2, 3], size=3)
+    >>> G.add_edges_from([(0, 1), (2, 3)])
+    >>> print(nx.numeric_assortativity_coefficient(G, "size"))
+    1.0
+
+    Notes
+    -----
+    This computes Eq. (21) in Ref. [1]_ , which is the Pearson correlation
+    coefficient of the specified (scalar valued) attribute across edges.
+
+    References
+    ----------
+    .. [1] M. E. J. Newman, Mixing patterns in networks
+           Physical Review E, 67 026126, 2003
+    """
+    if nodes is None:
+        nodes = G.nodes
+    vals = {G.nodes[n][attribute] for n in nodes}
+    mapping = {d: i for i, d in enumerate(vals)}
+    M = attribute_mixing_matrix(G, attribute, nodes, mapping)
+    return _numeric_ac(M, mapping)
+
+
+def attribute_ac(M):
+    """Compute assortativity for attribute matrix M.
+
+    Parameters
+    ----------
+    M : numpy.ndarray
+        2D ndarray representing the attribute mixing matrix.
+
+    Notes
+    -----
+    This computes Eq. (2) in Ref. [1]_ , (trace(e)-sum(e^2))/(1-sum(e^2)),
+    where e is the joint probability distribution (mixing matrix)
+    of the specified attribute.
+
+    References
+    ----------
+    .. [1] M. E. J. Newman, Mixing patterns in networks,
+       Physical Review E, 67 026126, 2003
+    """
+    if M.sum() != 1.0:
+        M = M / M.sum()
+    s = (M @ M).sum()
+    t = M.trace()
+    r = (t - s) / (1 - s)
+    return float(r)
+
+
+def _numeric_ac(M, mapping):
+    # M is a 2D numpy array
+    # numeric assortativity coefficient, pearsonr
+    import numpy as np
+
+    if M.sum() != 1.0:
+        M = M / M.sum()
+    x = np.array(list(mapping.keys()))
+    y = x  # x and y have the same support
+    idx = list(mapping.values())
+    a = M.sum(axis=0)
+    b = M.sum(axis=1)
+    vara = (a[idx] * x**2).sum() - ((a[idx] * x).sum()) ** 2
+    varb = (b[idx] * y**2).sum() - ((b[idx] * y).sum()) ** 2
+    xy = np.outer(x, y)
+    ab = np.outer(a[idx], b[idx])
+    return float((xy * (M - ab)).sum() / np.sqrt(vara * varb))

janus/lib/python3.10/site-packages/networkx/algorithms/assortativity/mixing.py

@@ -0,0 +1,255 @@
+"""
+Mixing matrices for node attributes and degree.
+"""
+
+import networkx as nx
+from networkx.algorithms.assortativity.pairs import node_attribute_xy, node_degree_xy
+from networkx.utils import dict_to_numpy_array
+
+__all__ = [
+    "attribute_mixing_matrix",
+    "attribute_mixing_dict",
+    "degree_mixing_matrix",
+    "degree_mixing_dict",
+    "mixing_dict",
+]
+
+
+@nx._dispatchable(node_attrs="attribute")
+def attribute_mixing_dict(G, attribute, nodes=None, normalized=False):
+    """Returns dictionary representation of mixing matrix for attribute.
+
+    Parameters
+    ----------
+    G : graph
+       NetworkX graph object.
+
+    attribute : string
+       Node attribute key.
+
+    nodes: list or iterable (optional)
+        Unse nodes in container to build the dict. The default is all nodes.
+
+    normalized : bool (default=False)
+       Return counts if False or probabilities if True.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> G.add_nodes_from([0, 1], color="red")
+    >>> G.add_nodes_from([2, 3], color="blue")
+    >>> G.add_edge(1, 3)
+    >>> d = nx.attribute_mixing_dict(G, "color")
+    >>> print(d["red"]["blue"])
+    1
+    >>> print(d["blue"]["red"])  # d symmetric for undirected graphs
+    1
+
+    Returns
+    -------
+    d : dictionary
+       Counts or joint probability of occurrence of attribute pairs.
+    """
+    xy_iter = node_attribute_xy(G, attribute, nodes)
+    return mixing_dict(xy_iter, normalized=normalized)
+
+
+@nx._dispatchable(node_attrs="attribute")
+def attribute_mixing_matrix(G, attribute, nodes=None, mapping=None, normalized=True):
+    """Returns mixing matrix for attribute.
+
+    Parameters
+    ----------
+    G : graph
+       NetworkX graph object.
+
+    attribute : string
+       Node attribute key.
+
+    nodes: list or iterable (optional)
+        Use only nodes in container to build the matrix. The default is
+        all nodes.
+
+    mapping : dictionary, optional
+       Mapping from node attribute to integer index in matrix.
+       If not specified, an arbitrary ordering will be used.
+
+    normalized : bool (default=True)
+       Return counts if False or probabilities if True.
+
+    Returns
+    -------
+    m: numpy array
+       Counts or joint probability of occurrence of attribute pairs.
+
+    Notes
+    -----
+    If each node has a unique attribute value, the unnormalized mixing matrix
+    will be equal to the adjacency matrix. To get a denser mixing matrix,
+    the rounding can be performed to form groups of nodes with equal values.
+    For example, the exact height of persons in cm (180.79155222, 163.9080892,
+    163.30095355, 167.99016217, 168.21590163, ...) can be rounded to (180, 163,
+    163, 168, 168, ...).
+
+    Definitions of attribute mixing matrix vary on whether the matrix
+    should include rows for attribute values that don't arise. Here we
+    do not include such empty-rows. But you can force them to appear
+    by inputting a `mapping` that includes those values.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(3)
+    >>> gender = {0: "male", 1: "female", 2: "female"}
+    >>> nx.set_node_attributes(G, gender, "gender")
+    >>> mapping = {"male": 0, "female": 1}
+    >>> mix_mat = nx.attribute_mixing_matrix(G, "gender", mapping=mapping)
+    >>> mix_mat
+    array([[0.  , 0.25],
+           [0.25, 0.5 ]])
+    """
+    d = attribute_mixing_dict(G, attribute, nodes)
+    a = dict_to_numpy_array(d, mapping=mapping)
+    if normalized:
+        a = a / a.sum()
+    return a
+
+
+@nx._dispatchable(edge_attrs="weight")
+def degree_mixing_dict(G, x="out", y="in", weight=None, nodes=None, normalized=False):
+    """Returns dictionary representation of mixing matrix for degree.
+
+    Parameters
+    ----------
+    G : graph
+        NetworkX graph object.
+
+    x: string ('in','out')
+       The degree type for source node (directed graphs only).
+
+    y: string ('in','out')
+       The degree type for target node (directed graphs only).
+
+    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.
+
+    normalized : bool (default=False)
+        Return counts if False or probabilities if True.
+
+    Returns
+    -------
+    d: dictionary
+       Counts or joint probability of occurrence of degree pairs.
+    """
+    xy_iter = node_degree_xy(G, x=x, y=y, nodes=nodes, weight=weight)
+    return mixing_dict(xy_iter, normalized=normalized)
+
+
+@nx._dispatchable(edge_attrs="weight")
+def degree_mixing_matrix(
+    G, x="out", y="in", weight=None, nodes=None, normalized=True, mapping=None
+):
+    """Returns mixing matrix for attribute.
+
+    Parameters
+    ----------
+    G : graph
+       NetworkX graph object.
+
+    x: string ('in','out')
+       The degree type for source node (directed graphs only).
+
+    y: string ('in','out')
+       The degree type for target node (directed graphs only).
+
+    nodes: list or iterable (optional)
+        Build the matrix using only nodes in container.
+        The default is all nodes.
+
+    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.
+
+    normalized : bool (default=True)
+       Return counts if False or probabilities if True.
+
+    mapping : dictionary, optional
+       Mapping from node degree to integer index in matrix.
+       If not specified, an arbitrary ordering will be used.
+
+    Returns
+    -------
+    m: numpy array
+       Counts, or joint probability, of occurrence of node degree.
+
+    Notes
+    -----
+    Definitions of degree mixing matrix vary on whether the matrix
+    should include rows for degree values that don't arise. Here we
+    do not include such empty-rows. But you can force them to appear
+    by inputting a `mapping` that includes those values. See examples.
+
+    Examples
+    --------
+    >>> G = nx.star_graph(3)
+    >>> mix_mat = nx.degree_mixing_matrix(G)
+    >>> mix_mat
+    array([[0. , 0.5],
+           [0.5, 0. ]])
+
+    If you want every possible degree to appear as a row, even if no nodes
+    have that degree, use `mapping` as follows,
+
+    >>> max_degree = max(deg for n, deg in G.degree)
+    >>> mapping = {x: x for x in range(max_degree + 1)}  # identity mapping
+    >>> mix_mat = nx.degree_mixing_matrix(G, mapping=mapping)
+    >>> mix_mat
+    array([[0. , 0. , 0. , 0. ],
+           [0. , 0. , 0. , 0.5],
+           [0. , 0. , 0. , 0. ],
+           [0. , 0.5, 0. , 0. ]])
+    """
+    d = degree_mixing_dict(G, x=x, y=y, nodes=nodes, weight=weight)
+    a = dict_to_numpy_array(d, mapping=mapping)
+    if normalized:
+        a = a / a.sum()
+    return a
+
+
+def mixing_dict(xy, normalized=False):
+    """Returns a dictionary representation of mixing matrix.
+
+    Parameters
+    ----------
+    xy : list or container of two-tuples
+       Pairs of (x,y) items.
+
+    attribute : string
+       Node attribute key
+
+    normalized : bool (default=False)
+       Return counts if False or probabilities if True.
+
+    Returns
+    -------
+    d: dictionary
+       Counts or Joint probability of occurrence of values in xy.
+    """
+    d = {}
+    psum = 0.0
+    for x, y in xy:
+        if x not in d:
+            d[x] = {}
+        if y not in d:
+            d[y] = {}
+        v = d[x].get(y, 0)
+        d[x][y] = v + 1
+        psum += 1
+
+    if normalized:
+        for _, jdict in d.items():
+            for j in jdict:
+                jdict[j] /= psum
+    return d

janus/lib/python3.10/site-packages/networkx/algorithms/assortativity/neighbor_degree.py

@@ -0,0 +1,160 @@
+import networkx as nx
+
+__all__ = ["average_neighbor_degree"]
+
+
+@nx._dispatchable(edge_attrs="weight")
+def average_neighbor_degree(G, source="out", target="out", nodes=None, weight=None):
+    r"""Returns the average degree of the neighborhood of each node.
+
+    In an undirected graph, the neighborhood `N(i)` of node `i` contains the
+    nodes that are connected to `i` by an edge.
+
+    For directed graphs, `N(i)` is defined according to the parameter `source`:
+
+        - if source is 'in', then `N(i)` consists of predecessors of node `i`.
+        - if source is 'out', then `N(i)` consists of successors of node `i`.
+        - if source is 'in+out', then `N(i)` is both predecessors and successors.
+
+    The average neighborhood degree of a node `i` is
+
+    .. math::
+
+        k_{nn,i} = \frac{1}{|N(i)|} \sum_{j \in N(i)} k_j
+
+    where `N(i)` are the neighbors of node `i` and `k_j` is
+    the degree of node `j` which belongs to `N(i)`. For weighted
+    graphs, an analogous measure can be defined [1]_,
+
+    .. math::
+
+        k_{nn,i}^{w} = \frac{1}{s_i} \sum_{j \in N(i)} w_{ij} k_j
+
+    where `s_i` is the weighted degree of node `i`, `w_{ij}`
+    is the weight of the edge that links `i` and `j` and
+    `N(i)` are the neighbors of node `i`.
+
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : string ("in"|"out"|"in+out"), optional (default="out")
+       Directed graphs only.
+       Use "in"- or "out"-neighbors of source node.
+
+    target : string ("in"|"out"|"in+out"), optional (default="out")
+       Directed graphs only.
+       Use "in"- or "out"-degree for target node.
+
+    nodes : list or iterable, optional (default=G.nodes)
+        Compute neighbor degree only for specified nodes.
+
+    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.
+
+    Returns
+    -------
+    d: dict
+       A dictionary keyed by node to the average degree of its neighbors.
+
+    Raises
+    ------
+    NetworkXError
+        If either `source` or `target` are not one of 'in', 'out', or 'in+out'.
+        If either `source` or `target` is passed for an undirected graph.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> G.edges[0, 1]["weight"] = 5
+    >>> G.edges[2, 3]["weight"] = 3
+
+    >>> nx.average_neighbor_degree(G)
+    {0: 2.0, 1: 1.5, 2: 1.5, 3: 2.0}
+    >>> nx.average_neighbor_degree(G, weight="weight")
+    {0: 2.0, 1: 1.1666666666666667, 2: 1.25, 3: 2.0}
+
+    >>> G = nx.DiGraph()
+    >>> nx.add_path(G, [0, 1, 2, 3])
+    >>> nx.average_neighbor_degree(G, source="in", target="in")
+    {0: 0.0, 1: 0.0, 2: 1.0, 3: 1.0}
+
+    >>> nx.average_neighbor_degree(G, source="out", target="out")
+    {0: 1.0, 1: 1.0, 2: 0.0, 3: 0.0}
+
+    See Also
+    --------
+    average_degree_connectivity
+
+    References
+    ----------
+    .. [1] A. Barrat, M. Barthélemy, R. Pastor-Satorras, and A. Vespignani,
+       "The architecture of complex weighted networks".
+       PNAS 101 (11): 3747–3752 (2004).
+    """
+    if G.is_directed():
+        if source == "in":
+            source_degree = G.in_degree
+        elif source == "out":
+            source_degree = G.out_degree
+        elif source == "in+out":
+            source_degree = G.degree
+        else:
+            raise nx.NetworkXError(
+                f"source argument {source} must be 'in', 'out' or 'in+out'"
+            )
+
+        if target == "in":
+            target_degree = G.in_degree
+        elif target == "out":
+            target_degree = G.out_degree
+        elif target == "in+out":
+            target_degree = G.degree
+        else:
+            raise nx.NetworkXError(
+                f"target argument {target} must be 'in', 'out' or 'in+out'"
+            )
+    else:
+        if source != "out" or target != "out":
+            raise nx.NetworkXError(
+                f"source and target arguments are only supported for directed graphs"
+            )
+        source_degree = target_degree = G.degree
+
+    # precompute target degrees -- should *not* be weighted degree
+    t_deg = dict(target_degree())
+
+    # Set up both predecessor and successor neighbor dicts leaving empty if not needed
+    G_P = G_S = {n: {} for n in G}
+    if G.is_directed():
+        # "in" or "in+out" cases: G_P contains predecessors
+        if "in" in source:
+            G_P = G.pred
+        # "out" or "in+out" cases: G_S contains successors
+        if "out" in source:
+            G_S = G.succ
+    else:
+        # undirected leave G_P empty but G_S is the adjacency
+        G_S = G.adj
+
+    # Main loop: Compute average degree of neighbors
+    avg = {}
+    for n, deg in source_degree(nodes, weight=weight):
+        # handle degree zero average
+        if deg == 0:
+            avg[n] = 0.0
+            continue
+
+        # we sum over both G_P and G_S, but one of the two is usually empty.
+        if weight is None:
+            avg[n] = (
+                sum(t_deg[nbr] for nbr in G_S[n]) + sum(t_deg[nbr] for nbr in G_P[n])
+            ) / deg
+        else:
+            avg[n] = (
+                sum(dd.get(weight, 1) * t_deg[nbr] for nbr, dd in G_S[n].items())
+                + sum(dd.get(weight, 1) * t_deg[nbr] for nbr, dd in G_P[n].items())
+            ) / deg
+    return avg

janus/lib/python3.10/site-packages/networkx/algorithms/assortativity/pairs.py

@@ -0,0 +1,127 @@
+"""Generators of x-y pairs of node data."""
+
+import networkx as nx
+
+__all__ = ["node_attribute_xy", "node_degree_xy"]
+
+
+@nx._dispatchable(node_attrs="attribute")
+def node_attribute_xy(G, attribute, nodes=None):
+    """Yields 2-tuples of node attribute values for all edges in `G`.
+
+    This generator yields, for each edge in `G` incident to a node in `nodes`,
+    a 2-tuple of form ``(attribute value,  attribute value)`` for the parameter
+    specified node-attribute.
+
+    Parameters
+    ----------
+    G: NetworkX graph
+
+    attribute: key
+        The node attribute key.
+
+    nodes: list or iterable (optional)
+        Use only edges that are incident to specified nodes.
+        The default is all nodes.
+
+    Yields
+    ------
+    (x, y): 2-tuple
+        Generates 2-tuple of (attribute, attribute) values.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_node(1, color="red")
+    >>> G.add_node(2, color="blue")
+    >>> G.add_node(3, color="green")
+    >>> G.add_edge(1, 2)
+    >>> list(nx.node_attribute_xy(G, "color"))
+    [('red', 'blue')]
+
+    Notes
+    -----
+    For undirected graphs, each edge is produced twice, once for each edge
+    representation (u, v) and (v, u), with the exception of self-loop edges
+    which only appear once.
+    """
+    if nodes is None:
+        nodes = set(G)
+    else:
+        nodes = set(nodes)
+    Gnodes = G.nodes
+    for u, nbrsdict in G.adjacency():
+        if u not in nodes:
+            continue
+        uattr = Gnodes[u].get(attribute, None)
+        if G.is_multigraph():
+            for v, keys in nbrsdict.items():
+                vattr = Gnodes[v].get(attribute, None)
+                for _ in keys:
+                    yield (uattr, vattr)
+        else:
+            for v in nbrsdict:
+                vattr = Gnodes[v].get(attribute, None)
+                yield (uattr, vattr)
+
+
+@nx._dispatchable(edge_attrs="weight")
+def node_degree_xy(G, x="out", y="in", weight=None, nodes=None):
+    """Yields 2-tuples of ``(degree, degree)`` values for edges in `G`.
+
+    This generator yields, for each edge in `G` incident to a node in `nodes`,
+    a 2-tuple of form ``(degree, degree)``. The node degrees are weighted
+    when a `weight` attribute is specified.
+
+    Parameters
+    ----------
+    G: NetworkX graph
+
+    x: string ('in','out')
+       The degree type for source node (directed graphs only).
+
+    y: string ('in','out')
+       The degree type for target node (directed graphs only).
+
+    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.
+
+    nodes: list or iterable (optional)
+        Use only edges that are adjacency to specified nodes.
+        The default is all nodes.
+
+    Yields
+    ------
+    (x, y): 2-tuple
+        Generates 2-tuple of (degree, degree) values.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_edge(1, 2)
+    >>> list(nx.node_degree_xy(G, x="out", y="in"))
+    [(1, 1)]
+    >>> list(nx.node_degree_xy(G, x="in", y="out"))
+    [(0, 0)]
+
+    Notes
+    -----
+    For undirected graphs, each edge is produced twice, once for each edge
+    representation (u, v) and (v, u), with the exception of self-loop edges
+    which only appear once.
+    """
+    nodes = set(G) if nodes is None else set(nodes)
+    if G.is_directed():
+        direction = {"out": G.out_degree, "in": G.in_degree}
+        xdeg = direction[x]
+        ydeg = direction[y]
+    else:
+        xdeg = ydeg = G.degree
+
+    for u, degu in xdeg(nodes, weight=weight):
+        # use G.edges to treat multigraphs correctly
+        neighbors = (nbr for _, nbr in G.edges(u) if nbr in nodes)
+        for _, degv in ydeg(neighbors, weight=weight):
+            yield degu, degv

janus/lib/python3.10/site-packages/networkx/algorithms/assortativity/tests/base_test.py

@@ -0,0 +1,81 @@
+import networkx as nx
+
+
+class BaseTestAttributeMixing:
+    @classmethod
+    def setup_class(cls):
+        G = nx.Graph()
+        G.add_nodes_from([0, 1], fish="one")
+        G.add_nodes_from([2, 3], fish="two")
+        G.add_nodes_from([4], fish="red")
+        G.add_nodes_from([5], fish="blue")
+        G.add_edges_from([(0, 1), (2, 3), (0, 4), (2, 5)])
+        cls.G = G
+
+        D = nx.DiGraph()
+        D.add_nodes_from([0, 1], fish="one")
+        D.add_nodes_from([2, 3], fish="two")
+        D.add_nodes_from([4], fish="red")
+        D.add_nodes_from([5], fish="blue")
+        D.add_edges_from([(0, 1), (2, 3), (0, 4), (2, 5)])
+        cls.D = D
+
+        M = nx.MultiGraph()
+        M.add_nodes_from([0, 1], fish="one")
+        M.add_nodes_from([2, 3], fish="two")
+        M.add_nodes_from([4], fish="red")
+        M.add_nodes_from([5], fish="blue")
+        M.add_edges_from([(0, 1), (0, 1), (2, 3)])
+        cls.M = M
+
+        S = nx.Graph()
+        S.add_nodes_from([0, 1], fish="one")
+        S.add_nodes_from([2, 3], fish="two")
+        S.add_nodes_from([4], fish="red")
+        S.add_nodes_from([5], fish="blue")
+        S.add_edge(0, 0)
+        S.add_edge(2, 2)
+        cls.S = S
+
+        N = nx.Graph()
+        N.add_nodes_from([0, 1], margin=-2)
+        N.add_nodes_from([2, 3], margin=-2)
+        N.add_nodes_from([4], margin=-3)
+        N.add_nodes_from([5], margin=-4)
+        N.add_edges_from([(0, 1), (2, 3), (0, 4), (2, 5)])
+        cls.N = N
+
+        F = nx.Graph()
+        F.add_edges_from([(0, 3), (1, 3), (2, 3)], weight=0.5)
+        F.add_edge(0, 2, weight=1)
+        nx.set_node_attributes(F, dict(F.degree(weight="weight")), "margin")
+        cls.F = F
+
+        K = nx.Graph()
+        K.add_nodes_from([1, 2], margin=-1)
+        K.add_nodes_from([3], margin=1)
+        K.add_nodes_from([4], margin=2)
+        K.add_edges_from([(3, 4), (1, 2), (1, 3)])
+        cls.K = K
+
+
+class BaseTestDegreeMixing:
+    @classmethod
+    def setup_class(cls):
+        cls.P4 = nx.path_graph(4)
+        cls.D = nx.DiGraph()
+        cls.D.add_edges_from([(0, 2), (0, 3), (1, 3), (2, 3)])
+        cls.D2 = nx.DiGraph()
+        cls.D2.add_edges_from([(0, 3), (1, 0), (1, 2), (2, 4), (4, 1), (4, 3), (4, 2)])
+        cls.M = nx.MultiGraph()
+        nx.add_path(cls.M, range(4))
+        cls.M.add_edge(0, 1)
+        cls.S = nx.Graph()
+        cls.S.add_edges_from([(0, 0), (1, 1)])
+        cls.W = nx.Graph()
+        cls.W.add_edges_from([(0, 3), (1, 3), (2, 3)], weight=0.5)
+        cls.W.add_edge(0, 2, weight=1)
+        S1 = nx.star_graph(4)
+        S2 = nx.star_graph(4)
+        cls.DS = nx.disjoint_union(S1, S2)
+        cls.DS.add_edge(4, 5)

janus/lib/python3.10/site-packages/networkx/algorithms/assortativity/tests/test_connectivity.py

@@ -0,0 +1,143 @@
+from itertools import permutations
+
+import pytest
+
+import networkx as nx
+
+
+class TestNeighborConnectivity:
+    def test_degree_p4(self):
+        G = nx.path_graph(4)
+        answer = {1: 2.0, 2: 1.5}
+        nd = nx.average_degree_connectivity(G)
+        assert nd == answer
+
+        D = G.to_directed()
+        answer = {2: 2.0, 4: 1.5}
+        nd = nx.average_degree_connectivity(D)
+        assert nd == answer
+
+        answer = {1: 2.0, 2: 1.5}
+        D = G.to_directed()
+        nd = nx.average_degree_connectivity(D, source="in", target="in")
+        assert nd == answer
+
+        D = G.to_directed()
+        nd = nx.average_degree_connectivity(D, source="in", target="in")
+        assert nd == answer
+
+    def test_degree_p4_weighted(self):
+        G = nx.path_graph(4)
+        G[1][2]["weight"] = 4
+        answer = {1: 2.0, 2: 1.8}
+        nd = nx.average_degree_connectivity(G, weight="weight")
+        assert nd == answer
+        answer = {1: 2.0, 2: 1.5}
+        nd = nx.average_degree_connectivity(G)
+        assert nd == answer
+
+        D = G.to_directed()
+        answer = {2: 2.0, 4: 1.8}
+        nd = nx.average_degree_connectivity(D, weight="weight")
+        assert nd == answer
+
+        answer = {1: 2.0, 2: 1.8}
+        D = G.to_directed()
+        nd = nx.average_degree_connectivity(
+            D, weight="weight", source="in", target="in"
+        )
+        assert nd == answer
+
+        D = G.to_directed()
+        nd = nx.average_degree_connectivity(
+            D, source="in", target="out", weight="weight"
+        )
+        assert nd == answer
+
+    def test_weight_keyword(self):
+        G = nx.path_graph(4)
+        G[1][2]["other"] = 4
+        answer = {1: 2.0, 2: 1.8}
+        nd = nx.average_degree_connectivity(G, weight="other")
+        assert nd == answer
+        answer = {1: 2.0, 2: 1.5}
+        nd = nx.average_degree_connectivity(G, weight=None)
+        assert nd == answer
+
+        D = G.to_directed()
+        answer = {2: 2.0, 4: 1.8}
+        nd = nx.average_degree_connectivity(D, weight="other")
+        assert nd == answer
+
+        answer = {1: 2.0, 2: 1.8}
+        D = G.to_directed()
+        nd = nx.average_degree_connectivity(D, weight="other", source="in", target="in")
+        assert nd == answer
+
+        D = G.to_directed()
+        nd = nx.average_degree_connectivity(D, weight="other", source="in", target="in")
+        assert nd == answer
+
+    def test_degree_barrat(self):
+        G = nx.star_graph(5)
+        G.add_edges_from([(5, 6), (5, 7), (5, 8), (5, 9)])
+        G[0][5]["weight"] = 5
+        nd = nx.average_degree_connectivity(G)[5]
+        assert nd == 1.8
+        nd = nx.average_degree_connectivity(G, weight="weight")[5]
+        assert nd == pytest.approx(3.222222, abs=1e-5)
+
+    def test_zero_deg(self):
+        G = nx.DiGraph()
+        G.add_edge(1, 2)
+        G.add_edge(1, 3)
+        G.add_edge(1, 4)
+        c = nx.average_degree_connectivity(G)
+        assert c == {1: 0, 3: 1}
+        c = nx.average_degree_connectivity(G, source="in", target="in")
+        assert c == {0: 0, 1: 0}
+        c = nx.average_degree_connectivity(G, source="in", target="out")
+        assert c == {0: 0, 1: 3}
+        c = nx.average_degree_connectivity(G, source="in", target="in+out")
+        assert c == {0: 0, 1: 3}
+        c = nx.average_degree_connectivity(G, source="out", target="out")
+        assert c == {0: 0, 3: 0}
+        c = nx.average_degree_connectivity(G, source="out", target="in")
+        assert c == {0: 0, 3: 1}
+        c = nx.average_degree_connectivity(G, source="out", target="in+out")
+        assert c == {0: 0, 3: 1}
+
+    def test_in_out_weight(self):
+        G = nx.DiGraph()
+        G.add_edge(1, 2, weight=1)
+        G.add_edge(1, 3, weight=1)
+        G.add_edge(3, 1, weight=1)
+        for s, t in permutations(["in", "out", "in+out"], 2):
+            c = nx.average_degree_connectivity(G, source=s, target=t)
+            cw = nx.average_degree_connectivity(G, source=s, target=t, weight="weight")
+            assert c == cw
+
+    def test_invalid_source(self):
+        with pytest.raises(nx.NetworkXError):
+            G = nx.DiGraph()
+            nx.average_degree_connectivity(G, source="bogus")
+
+    def test_invalid_target(self):
+        with pytest.raises(nx.NetworkXError):
+            G = nx.DiGraph()
+            nx.average_degree_connectivity(G, target="bogus")
+
+    def test_invalid_undirected_graph(self):
+        G = nx.Graph()
+        with pytest.raises(nx.NetworkXError):
+            nx.average_degree_connectivity(G, target="bogus")
+        with pytest.raises(nx.NetworkXError):
+            nx.average_degree_connectivity(G, source="bogus")
+
+    def test_single_node(self):
+        # TODO Is this really the intended behavior for providing a
+        # single node as the argument `nodes`? Shouldn't the function
+        # just return the connectivity value itself?
+        G = nx.trivial_graph()
+        conn = nx.average_degree_connectivity(G, nodes=0)
+        assert conn == {0: 0}

janus/lib/python3.10/site-packages/networkx/algorithms/assortativity/tests/test_correlation.py

@@ -0,0 +1,123 @@
+import pytest
+
+np = pytest.importorskip("numpy")
+pytest.importorskip("scipy")
+
+
+import networkx as nx
+from networkx.algorithms.assortativity.correlation import attribute_ac
+
+from .base_test import BaseTestAttributeMixing, BaseTestDegreeMixing
+
+
+class TestDegreeMixingCorrelation(BaseTestDegreeMixing):
+    def test_degree_assortativity_undirected(self):
+        r = nx.degree_assortativity_coefficient(self.P4)
+        np.testing.assert_almost_equal(r, -1.0 / 2, decimal=4)
+
+    def test_degree_assortativity_node_kwargs(self):
+        G = nx.Graph()
+        edges = [(0, 1), (0, 3), (1, 2), (1, 3), (1, 4), (5, 9), (9, 0)]
+        G.add_edges_from(edges)
+        r = nx.degree_assortativity_coefficient(G, nodes=[1, 2, 4])
+        np.testing.assert_almost_equal(r, -1.0, decimal=4)
+
+    def test_degree_assortativity_directed(self):
+        r = nx.degree_assortativity_coefficient(self.D)
+        np.testing.assert_almost_equal(r, -0.57735, decimal=4)
+
+    def test_degree_assortativity_directed2(self):
+        """Test degree assortativity for a directed graph where the set of
+        in/out degree does not equal the total degree."""
+        r = nx.degree_assortativity_coefficient(self.D2)
+        np.testing.assert_almost_equal(r, 0.14852, decimal=4)
+
+    def test_degree_assortativity_multigraph(self):
+        r = nx.degree_assortativity_coefficient(self.M)
+        np.testing.assert_almost_equal(r, -1.0 / 7.0, decimal=4)
+
+    def test_degree_pearson_assortativity_undirected(self):
+        r = nx.degree_pearson_correlation_coefficient(self.P4)
+        np.testing.assert_almost_equal(r, -1.0 / 2, decimal=4)
+
+    def test_degree_pearson_assortativity_directed(self):
+        r = nx.degree_pearson_correlation_coefficient(self.D)
+        np.testing.assert_almost_equal(r, -0.57735, decimal=4)
+
+    def test_degree_pearson_assortativity_directed2(self):
+        """Test degree assortativity with Pearson for a directed graph where
+        the set of in/out degree does not equal the total degree."""
+        r = nx.degree_pearson_correlation_coefficient(self.D2)
+        np.testing.assert_almost_equal(r, 0.14852, decimal=4)
+
+    def test_degree_pearson_assortativity_multigraph(self):
+        r = nx.degree_pearson_correlation_coefficient(self.M)
+        np.testing.assert_almost_equal(r, -1.0 / 7.0, decimal=4)
+
+    def test_degree_assortativity_weighted(self):
+        r = nx.degree_assortativity_coefficient(self.W, weight="weight")
+        np.testing.assert_almost_equal(r, -0.1429, decimal=4)
+
+    def test_degree_assortativity_double_star(self):
+        r = nx.degree_assortativity_coefficient(self.DS)
+        np.testing.assert_almost_equal(r, -0.9339, decimal=4)
+
+
+class TestAttributeMixingCorrelation(BaseTestAttributeMixing):
+    def test_attribute_assortativity_undirected(self):
+        r = nx.attribute_assortativity_coefficient(self.G, "fish")
+        assert r == 6.0 / 22.0
+
+    def test_attribute_assortativity_directed(self):
+        r = nx.attribute_assortativity_coefficient(self.D, "fish")
+        assert r == 1.0 / 3.0
+
+    def test_attribute_assortativity_multigraph(self):
+        r = nx.attribute_assortativity_coefficient(self.M, "fish")
+        assert r == 1.0
+
+    def test_attribute_assortativity_coefficient(self):
+        # from "Mixing patterns in networks"
+        # fmt: off
+        a = np.array([[0.258, 0.016, 0.035, 0.013],
+                      [0.012, 0.157, 0.058, 0.019],
+                      [0.013, 0.023, 0.306, 0.035],
+                      [0.005, 0.007, 0.024, 0.016]])
+        # fmt: on
+        r = attribute_ac(a)
+        np.testing.assert_almost_equal(r, 0.623, decimal=3)
+
+    def test_attribute_assortativity_coefficient2(self):
+        # fmt: off
+        a = np.array([[0.18, 0.02, 0.01, 0.03],
+                      [0.02, 0.20, 0.03, 0.02],
+                      [0.01, 0.03, 0.16, 0.01],
+                      [0.03, 0.02, 0.01, 0.22]])
+        # fmt: on
+        r = attribute_ac(a)
+        np.testing.assert_almost_equal(r, 0.68, decimal=2)
+
+    def test_attribute_assortativity(self):
+        a = np.array([[50, 50, 0], [50, 50, 0], [0, 0, 2]])
+        r = attribute_ac(a)
+        np.testing.assert_almost_equal(r, 0.029, decimal=3)
+
+    def test_attribute_assortativity_negative(self):
+        r = nx.numeric_assortativity_coefficient(self.N, "margin")
+        np.testing.assert_almost_equal(r, -0.2903, decimal=4)
+
+    def test_assortativity_node_kwargs(self):
+        G = nx.Graph()
+        G.add_nodes_from([0, 1], size=2)
+        G.add_nodes_from([2, 3], size=3)
+        G.add_edges_from([(0, 1), (2, 3)])
+        r = nx.numeric_assortativity_coefficient(G, "size", nodes=[0, 3])
+        np.testing.assert_almost_equal(r, 1.0, decimal=4)
+
+    def test_attribute_assortativity_float(self):
+        r = nx.numeric_assortativity_coefficient(self.F, "margin")
+        np.testing.assert_almost_equal(r, -0.1429, decimal=4)
+
+    def test_attribute_assortativity_mixed(self):
+        r = nx.numeric_assortativity_coefficient(self.K, "margin")
+        np.testing.assert_almost_equal(r, 0.4340, decimal=4)

janus/lib/python3.10/site-packages/networkx/algorithms/assortativity/tests/test_mixing.py

@@ -0,0 +1,176 @@
+import pytest
+
+np = pytest.importorskip("numpy")
+
+
+import networkx as nx
+
+from .base_test import BaseTestAttributeMixing, BaseTestDegreeMixing
+
+
+class TestDegreeMixingDict(BaseTestDegreeMixing):
+    def test_degree_mixing_dict_undirected(self):
+        d = nx.degree_mixing_dict(self.P4)
+        d_result = {1: {2: 2}, 2: {1: 2, 2: 2}}
+        assert d == d_result
+
+    def test_degree_mixing_dict_undirected_normalized(self):
+        d = nx.degree_mixing_dict(self.P4, normalized=True)
+        d_result = {1: {2: 1.0 / 3}, 2: {1: 1.0 / 3, 2: 1.0 / 3}}
+        assert d == d_result
+
+    def test_degree_mixing_dict_directed(self):
+        d = nx.degree_mixing_dict(self.D)
+        print(d)
+        d_result = {1: {3: 2}, 2: {1: 1, 3: 1}, 3: {}}
+        assert d == d_result
+
+    def test_degree_mixing_dict_multigraph(self):
+        d = nx.degree_mixing_dict(self.M)
+        d_result = {1: {2: 1}, 2: {1: 1, 3: 3}, 3: {2: 3}}
+        assert d == d_result
+
+    def test_degree_mixing_dict_weighted(self):
+        d = nx.degree_mixing_dict(self.W, weight="weight")
+        d_result = {0.5: {1.5: 1}, 1.5: {1.5: 6, 0.5: 1}}
+        assert d == d_result
+
+
+class TestDegreeMixingMatrix(BaseTestDegreeMixing):
+    def test_degree_mixing_matrix_undirected(self):
+        # fmt: off
+        a_result = np.array([[0, 2],
+                             [2, 2]]
+                            )
+        # fmt: on
+        a = nx.degree_mixing_matrix(self.P4, normalized=False)
+        np.testing.assert_equal(a, a_result)
+        a = nx.degree_mixing_matrix(self.P4)
+        np.testing.assert_equal(a, a_result / a_result.sum())
+
+    def test_degree_mixing_matrix_directed(self):
+        # fmt: off
+        a_result = np.array([[0, 0, 2],
+                             [1, 0, 1],
+                             [0, 0, 0]]
+                            )
+        # fmt: on
+        a = nx.degree_mixing_matrix(self.D, normalized=False)
+        np.testing.assert_equal(a, a_result)
+        a = nx.degree_mixing_matrix(self.D)
+        np.testing.assert_equal(a, a_result / a_result.sum())
+
+    def test_degree_mixing_matrix_multigraph(self):
+        # fmt: off
+        a_result = np.array([[0, 1, 0],
+                             [1, 0, 3],
+                             [0, 3, 0]]
+                            )
+        # fmt: on
+        a = nx.degree_mixing_matrix(self.M, normalized=False)
+        np.testing.assert_equal(a, a_result)
+        a = nx.degree_mixing_matrix(self.M)
+        np.testing.assert_equal(a, a_result / a_result.sum())
+
+    def test_degree_mixing_matrix_selfloop(self):
+        # fmt: off
+        a_result = np.array([[2]])
+        # fmt: on
+        a = nx.degree_mixing_matrix(self.S, normalized=False)
+        np.testing.assert_equal(a, a_result)
+        a = nx.degree_mixing_matrix(self.S)
+        np.testing.assert_equal(a, a_result / a_result.sum())
+
+    def test_degree_mixing_matrix_weighted(self):
+        a_result = np.array([[0.0, 1.0], [1.0, 6.0]])
+        a = nx.degree_mixing_matrix(self.W, weight="weight", normalized=False)
+        np.testing.assert_equal(a, a_result)
+        a = nx.degree_mixing_matrix(self.W, weight="weight")
+        np.testing.assert_equal(a, a_result / float(a_result.sum()))
+
+    def test_degree_mixing_matrix_mapping(self):
+        a_result = np.array([[6.0, 1.0], [1.0, 0.0]])
+        mapping = {0.5: 1, 1.5: 0}
+        a = nx.degree_mixing_matrix(
+            self.W, weight="weight", normalized=False, mapping=mapping
+        )
+        np.testing.assert_equal(a, a_result)
+
+
+class TestAttributeMixingDict(BaseTestAttributeMixing):
+    def test_attribute_mixing_dict_undirected(self):
+        d = nx.attribute_mixing_dict(self.G, "fish")
+        d_result = {
+            "one": {"one": 2, "red": 1},
+            "two": {"two": 2, "blue": 1},
+            "red": {"one": 1},
+            "blue": {"two": 1},
+        }
+        assert d == d_result
+
+    def test_attribute_mixing_dict_directed(self):
+        d = nx.attribute_mixing_dict(self.D, "fish")
+        d_result = {
+            "one": {"one": 1, "red": 1},
+            "two": {"two": 1, "blue": 1},
+            "red": {},
+            "blue": {},
+        }
+        assert d == d_result
+
+    def test_attribute_mixing_dict_multigraph(self):
+        d = nx.attribute_mixing_dict(self.M, "fish")
+        d_result = {"one": {"one": 4}, "two": {"two": 2}}
+        assert d == d_result
+
+
+class TestAttributeMixingMatrix(BaseTestAttributeMixing):
+    def test_attribute_mixing_matrix_undirected(self):
+        mapping = {"one": 0, "two": 1, "red": 2, "blue": 3}
+        a_result = np.array([[2, 0, 1, 0], [0, 2, 0, 1], [1, 0, 0, 0], [0, 1, 0, 0]])
+        a = nx.attribute_mixing_matrix(
+            self.G, "fish", mapping=mapping, normalized=False
+        )
+        np.testing.assert_equal(a, a_result)
+        a = nx.attribute_mixing_matrix(self.G, "fish", mapping=mapping)
+        np.testing.assert_equal(a, a_result / a_result.sum())
+
+    def test_attribute_mixing_matrix_directed(self):
+        mapping = {"one": 0, "two": 1, "red": 2, "blue": 3}
+        a_result = np.array([[1, 0, 1, 0], [0, 1, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0]])
+        a = nx.attribute_mixing_matrix(
+            self.D, "fish", mapping=mapping, normalized=False
+        )
+        np.testing.assert_equal(a, a_result)
+        a = nx.attribute_mixing_matrix(self.D, "fish", mapping=mapping)
+        np.testing.assert_equal(a, a_result / a_result.sum())
+
+    def test_attribute_mixing_matrix_multigraph(self):
+        mapping = {"one": 0, "two": 1, "red": 2, "blue": 3}
+        a_result = np.array([[4, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])
+        a = nx.attribute_mixing_matrix(
+            self.M, "fish", mapping=mapping, normalized=False
+        )
+        np.testing.assert_equal(a, a_result)
+        a = nx.attribute_mixing_matrix(self.M, "fish", mapping=mapping)
+        np.testing.assert_equal(a, a_result / a_result.sum())
+
+    def test_attribute_mixing_matrix_negative(self):
+        mapping = {-2: 0, -3: 1, -4: 2}
+        a_result = np.array([[4.0, 1.0, 1.0], [1.0, 0.0, 0.0], [1.0, 0.0, 0.0]])
+        a = nx.attribute_mixing_matrix(
+            self.N, "margin", mapping=mapping, normalized=False
+        )
+        np.testing.assert_equal(a, a_result)
+        a = nx.attribute_mixing_matrix(self.N, "margin", mapping=mapping)
+        np.testing.assert_equal(a, a_result / float(a_result.sum()))
+
+    def test_attribute_mixing_matrix_float(self):
+        mapping = {0.5: 1, 1.5: 0}
+        a_result = np.array([[6.0, 1.0], [1.0, 0.0]])
+        a = nx.attribute_mixing_matrix(
+            self.F, "margin", mapping=mapping, normalized=False
+        )
+        np.testing.assert_equal(a, a_result)
+        a = nx.attribute_mixing_matrix(self.F, "margin", mapping=mapping)
+        np.testing.assert_equal(a, a_result / a_result.sum())

janus/lib/python3.10/site-packages/networkx/algorithms/assortativity/tests/test_neighbor_degree.py

@@ -0,0 +1,108 @@
+import pytest
+
+import networkx as nx
+
+
+class TestAverageNeighbor:
+    def test_degree_p4(self):
+        G = nx.path_graph(4)
+        answer = {0: 2, 1: 1.5, 2: 1.5, 3: 2}
+        nd = nx.average_neighbor_degree(G)
+        assert nd == answer
+
+        D = G.to_directed()
+        nd = nx.average_neighbor_degree(D)
+        assert nd == answer
+
+        D = nx.DiGraph(G.edges(data=True))
+        nd = nx.average_neighbor_degree(D)
+        assert nd == {0: 1, 1: 1, 2: 0, 3: 0}
+        nd = nx.average_neighbor_degree(D, "in", "out")
+        assert nd == {0: 0, 1: 1, 2: 1, 3: 1}
+        nd = nx.average_neighbor_degree(D, "out", "in")
+        assert nd == {0: 1, 1: 1, 2: 1, 3: 0}
+        nd = nx.average_neighbor_degree(D, "in", "in")
+        assert nd == {0: 0, 1: 0, 2: 1, 3: 1}
+
+    def test_degree_p4_weighted(self):
+        G = nx.path_graph(4)
+        G[1][2]["weight"] = 4
+        answer = {0: 2, 1: 1.8, 2: 1.8, 3: 2}
+        nd = nx.average_neighbor_degree(G, weight="weight")
+        assert nd == answer
+
+        D = G.to_directed()
+        nd = nx.average_neighbor_degree(D, weight="weight")
+        assert nd == answer
+
+        D = nx.DiGraph(G.edges(data=True))
+        print(D.edges(data=True))
+        nd = nx.average_neighbor_degree(D, weight="weight")
+        assert nd == {0: 1, 1: 1, 2: 0, 3: 0}
+        nd = nx.average_neighbor_degree(D, "out", "out", weight="weight")
+        assert nd == {0: 1, 1: 1, 2: 0, 3: 0}
+        nd = nx.average_neighbor_degree(D, "in", "in", weight="weight")
+        assert nd == {0: 0, 1: 0, 2: 1, 3: 1}
+        nd = nx.average_neighbor_degree(D, "in", "out", weight="weight")
+        assert nd == {0: 0, 1: 1, 2: 1, 3: 1}
+        nd = nx.average_neighbor_degree(D, "out", "in", weight="weight")
+        assert nd == {0: 1, 1: 1, 2: 1, 3: 0}
+        nd = nx.average_neighbor_degree(D, source="in+out", weight="weight")
+        assert nd == {0: 1.0, 1: 1.0, 2: 0.8, 3: 1.0}
+        nd = nx.average_neighbor_degree(D, target="in+out", weight="weight")
+        assert nd == {0: 2.0, 1: 2.0, 2: 1.0, 3: 0.0}
+
+        D = G.to_directed()
+        nd = nx.average_neighbor_degree(D, weight="weight")
+        assert nd == answer
+        nd = nx.average_neighbor_degree(D, source="out", target="out", weight="weight")
+        assert nd == answer
+
+        D = G.to_directed()
+        nd = nx.average_neighbor_degree(D, source="in", target="in", weight="weight")
+        assert nd == answer
+
+    def test_degree_k4(self):
+        G = nx.complete_graph(4)
+        answer = {0: 3, 1: 3, 2: 3, 3: 3}
+        nd = nx.average_neighbor_degree(G)
+        assert nd == answer
+
+        D = G.to_directed()
+        nd = nx.average_neighbor_degree(D)
+        assert nd == answer
+
+        D = G.to_directed()
+        nd = nx.average_neighbor_degree(D)
+        assert nd == answer
+
+        D = G.to_directed()
+        nd = nx.average_neighbor_degree(D, source="in", target="in")
+        assert nd == answer
+
+    def test_degree_k4_nodes(self):
+        G = nx.complete_graph(4)
+        answer = {1: 3.0, 2: 3.0}
+        nd = nx.average_neighbor_degree(G, nodes=[1, 2])
+        assert nd == answer
+
+    def test_degree_barrat(self):
+        G = nx.star_graph(5)
+        G.add_edges_from([(5, 6), (5, 7), (5, 8), (5, 9)])
+        G[0][5]["weight"] = 5
+        nd = nx.average_neighbor_degree(G)[5]
+        assert nd == 1.8
+        nd = nx.average_neighbor_degree(G, weight="weight")[5]
+        assert nd == pytest.approx(3.222222, abs=1e-5)
+
+    def test_error_invalid_source_target(self):
+        G = nx.path_graph(4)
+        with pytest.raises(nx.NetworkXError):
+            nx.average_neighbor_degree(G, "error")
+        with pytest.raises(nx.NetworkXError):
+            nx.average_neighbor_degree(G, "in", "error")
+        G = G.to_directed()
+        with pytest.raises(nx.NetworkXError):
+            nx.average_neighbor_degree(G, "error")
+        with pytest.raises(nx.NetworkXError):
+            nx.average_neighbor_degree(G, "in", "error")

janus/lib/python3.10/site-packages/networkx/algorithms/assortativity/tests/test_pairs.py

@@ -0,0 +1,87 @@
+import networkx as nx
+
+from .base_test import BaseTestAttributeMixing, BaseTestDegreeMixing
+
+
+class TestAttributeMixingXY(BaseTestAttributeMixing):
+    def test_node_attribute_xy_undirected(self):
+        attrxy = sorted(nx.node_attribute_xy(self.G, "fish"))
+        attrxy_result = sorted(
+            [
+                ("one", "one"),
+                ("one", "one"),
+                ("two", "two"),
+                ("two", "two"),
+                ("one", "red"),
+                ("red", "one"),
+                ("blue", "two"),
+                ("two", "blue"),
+            ]
+        )
+        assert attrxy == attrxy_result
+
+    def test_node_attribute_xy_undirected_nodes(self):
+        attrxy = sorted(nx.node_attribute_xy(self.G, "fish", nodes=["one", "yellow"]))
+        attrxy_result = sorted([])
+        assert attrxy == attrxy_result
+
+    def test_node_attribute_xy_directed(self):
+        attrxy = sorted(nx.node_attribute_xy(self.D, "fish"))
+        attrxy_result = sorted(
+            [("one", "one"), ("two", "two"), ("one", "red"), ("two", "blue")]
+        )
+        assert attrxy == attrxy_result
+
+    def test_node_attribute_xy_multigraph(self):
+        attrxy = sorted(nx.node_attribute_xy(self.M, "fish"))
+        attrxy_result = [
+            ("one", "one"),
+            ("one", "one"),
+            ("one", "one"),
+            ("one", "one"),
+            ("two", "two"),
+            ("two", "two"),
+        ]
+        assert attrxy == attrxy_result
+
+    def test_node_attribute_xy_selfloop(self):
+        attrxy = sorted(nx.node_attribute_xy(self.S, "fish"))
+        attrxy_result = [("one", "one"), ("two", "two")]
+        assert attrxy == attrxy_result
+
+
+class TestDegreeMixingXY(BaseTestDegreeMixing):
+    def test_node_degree_xy_undirected(self):
+        xy = sorted(nx.node_degree_xy(self.P4))
+        xy_result = sorted([(1, 2), (2, 1), (2, 2), (2, 2), (1, 2), (2, 1)])
+        assert xy == xy_result
+
+    def test_node_degree_xy_undirected_nodes(self):
+        xy = sorted(nx.node_degree_xy(self.P4, nodes=[0, 1, -1]))
+        xy_result = sorted([(1, 2), (2, 1)])
+        assert xy == xy_result
+
+    def test_node_degree_xy_directed(self):
+        xy = sorted(nx.node_degree_xy(self.D))
+        xy_result = sorted([(2, 1), (2, 3), (1, 3), (1, 3)])
+        assert xy == xy_result
+
+    def test_node_degree_xy_multigraph(self):
+        xy = sorted(nx.node_degree_xy(self.M))
+        xy_result = sorted(
+            [(2, 3), (2, 3), (3, 2), (3, 2), (2, 3), (3, 2), (1, 2), (2, 1)]
+        )
+        assert xy == xy_result
+
+    def test_node_degree_xy_selfloop(self):
+        xy = sorted(nx.node_degree_xy(self.S))
+        xy_result = sorted([(2, 2), (2, 2)])
+        assert xy == xy_result
+
+    def test_node_degree_xy_weighted(self):
+        G = nx.Graph()
+        G.add_edge(1, 2, weight=7)
+        G.add_edge(2, 3, weight=10)
+        xy = sorted(nx.node_degree_xy(G, weight="weight"))
+        xy_result = sorted([(7, 17), (17, 10), (17, 7), (10, 17)])
+        assert xy == xy_result

janus/lib/python3.10/site-packages/networkx/algorithms/coloring/__init__.py

@@ -0,0 +1,4 @@
+from networkx.algorithms.coloring.greedy_coloring import *
+from networkx.algorithms.coloring.equitable_coloring import equitable_color
+
+__all__ = ["greedy_color", "equitable_color"]

janus/lib/python3.10/site-packages/networkx/algorithms/coloring/greedy_coloring.py

@@ -0,0 +1,565 @@
+"""
+Greedy graph coloring using various strategies.
+"""
+
+import itertools
+from collections import defaultdict, deque
+
+import networkx as nx
+from networkx.utils import arbitrary_element, py_random_state
+
+__all__ = [
+    "greedy_color",
+    "strategy_connected_sequential",
+    "strategy_connected_sequential_bfs",
+    "strategy_connected_sequential_dfs",
+    "strategy_independent_set",
+    "strategy_largest_first",
+    "strategy_random_sequential",
+    "strategy_saturation_largest_first",
+    "strategy_smallest_last",
+]
+
+
+def strategy_largest_first(G, colors):
+    """Returns a list of the nodes of ``G`` in decreasing order by
+    degree.
+
+    ``G`` is a NetworkX graph. ``colors`` is ignored.
+
+    """
+    return sorted(G, key=G.degree, reverse=True)
+
+
+@py_random_state(2)
+def strategy_random_sequential(G, colors, seed=None):
+    """Returns a random permutation of the nodes of ``G`` as a list.
+
+    ``G`` is a NetworkX graph. ``colors`` is ignored.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+    """
+    nodes = list(G)
+    seed.shuffle(nodes)
+    return nodes
+
+
+def strategy_smallest_last(G, colors):
+    """Returns a deque of the nodes of ``G``, "smallest" last.
+
+    Specifically, the degrees of each node are tracked in a bucket queue.
+    From this, the node of minimum degree is repeatedly popped from the
+    graph, updating its neighbors' degrees.
+
+    ``G`` is a NetworkX graph. ``colors`` is ignored.
+
+    This implementation of the strategy runs in $O(n + m)$ time
+    (ignoring polylogarithmic factors), where $n$ is the number of nodes
+    and $m$ is the number of edges.
+
+    This strategy is related to :func:`strategy_independent_set`: if we
+    interpret each node removed as an independent set of size one, then
+    this strategy chooses an independent set of size one instead of a
+    maximal independent set.
+
+    """
+    H = G.copy()
+    result = deque()
+
+    # Build initial degree list (i.e. the bucket queue data structure)
+    degrees = defaultdict(set)  # set(), for fast random-access removals
+    lbound = float("inf")
+    for node, d in H.degree():
+        degrees[d].add(node)
+        lbound = min(lbound, d)  # Lower bound on min-degree.
+
+    def find_min_degree():
+        # Save time by starting the iterator at `lbound`, not 0.
+        # The value that we find will be our new `lbound`, which we set later.
+        return next(d for d in itertools.count(lbound) if d in degrees)
+
+    for _ in G:
+        # Pop a min-degree node and add it to the list.
+        min_degree = find_min_degree()
+        u = degrees[min_degree].pop()
+        if not degrees[min_degree]:  # Clean up the degree list.
+            del degrees[min_degree]
+        result.appendleft(u)
+
+        # Update degrees of removed node's neighbors.
+        for v in H[u]:
+            degree = H.degree(v)
+            degrees[degree].remove(v)
+            if not degrees[degree]:  # Clean up the degree list.
+                del degrees[degree]
+            degrees[degree - 1].add(v)
+
+        # Finally, remove the node.
+        H.remove_node(u)
+        lbound = min_degree - 1  # Subtract 1 in case of tied neighbors.
+
+    return result
+
+
+def _maximal_independent_set(G):
+    """Returns a maximal independent set of nodes in ``G`` by repeatedly
+    choosing an independent node of minimum degree (with respect to the
+    subgraph of unchosen nodes).
+
+    """
+    result = set()
+    remaining = set(G)
+    while remaining:
+        G = G.subgraph(remaining)
+        v = min(remaining, key=G.degree)
+        result.add(v)
+        remaining -= set(G[v]) | {v}
+    return result
+
+
+def strategy_independent_set(G, colors):
+    """Uses a greedy independent set removal strategy to determine the
+    colors.
+
+    This function updates ``colors`` **in-place** and return ``None``,
+    unlike the other strategy functions in this module.
+
+    This algorithm repeatedly finds and removes a maximal independent
+    set, assigning each node in the set an unused color.
+
+    ``G`` is a NetworkX graph.
+
+    This strategy is related to :func:`strategy_smallest_last`: in that
+    strategy, an independent set of size one is chosen at each step
+    instead of a maximal independent set.
+
+    """
+    remaining_nodes = set(G)
+    while len(remaining_nodes) > 0:
+        nodes = _maximal_independent_set(G.subgraph(remaining_nodes))
+        remaining_nodes -= nodes
+        yield from nodes
+
+
+def strategy_connected_sequential_bfs(G, colors):
+    """Returns an iterable over nodes in ``G`` in the order given by a
+    breadth-first traversal.
+
+    The generated sequence has the property that for each node except
+    the first, at least one neighbor appeared earlier in the sequence.
+
+    ``G`` is a NetworkX graph. ``colors`` is ignored.
+
+    """
+    return strategy_connected_sequential(G, colors, "bfs")
+
+
+def strategy_connected_sequential_dfs(G, colors):
+    """Returns an iterable over nodes in ``G`` in the order given by a
+    depth-first traversal.
+
+    The generated sequence has the property that for each node except
+    the first, at least one neighbor appeared earlier in the sequence.
+
+    ``G`` is a NetworkX graph. ``colors`` is ignored.
+
+    """
+    return strategy_connected_sequential(G, colors, "dfs")
+
+
+def strategy_connected_sequential(G, colors, traversal="bfs"):
+    """Returns an iterable over nodes in ``G`` in the order given by a
+    breadth-first or depth-first traversal.
+
+    ``traversal`` must be one of the strings ``'dfs'`` or ``'bfs'``,
+    representing depth-first traversal or breadth-first traversal,
+    respectively.
+
+    The generated sequence has the property that for each node except
+    the first, at least one neighbor appeared earlier in the sequence.
+
+    ``G`` is a NetworkX graph. ``colors`` is ignored.
+
+    """
+    if traversal == "bfs":
+        traverse = nx.bfs_edges
+    elif traversal == "dfs":
+        traverse = nx.dfs_edges
+    else:
+        raise nx.NetworkXError(
+            "Please specify one of the strings 'bfs' or"
+            " 'dfs' for connected sequential ordering"
+        )
+    for component in nx.connected_components(G):
+        source = arbitrary_element(component)
+        # Yield the source node, then all the nodes in the specified
+        # traversal order.
+        yield source
+        for _, end in traverse(G.subgraph(component), source):
+            yield end
+
+
+def strategy_saturation_largest_first(G, colors):
+    """Iterates over all the nodes of ``G`` in "saturation order" (also
+    known as "DSATUR").
+
+    ``G`` is a NetworkX graph. ``colors`` is a dictionary mapping nodes of
+    ``G`` to colors, for those nodes that have already been colored.
+
+    """
+    distinct_colors = {v: set() for v in G}
+
+    # Add the node color assignments given in colors to the
+    # distinct colors set for each neighbor of that node
+    for node, color in colors.items():
+        for neighbor in G[node]:
+            distinct_colors[neighbor].add(color)
+
+    # Check that the color assignments in colors are valid
+    # i.e. no neighboring nodes have the same color
+    if len(colors) >= 2:
+        for node, color in colors.items():
+            if color in distinct_colors[node]:
+                raise nx.NetworkXError("Neighboring nodes must have different colors")
+
+    # If 0 nodes have been colored, simply choose the node of highest degree.
+    if not colors:
+        node = max(G, key=G.degree)
+        yield node
+        # Add the color 0 to the distinct colors set for each
+        # neighbor of that node.
+        for v in G[node]:
+            distinct_colors[v].add(0)
+
+    while len(G) != len(colors):
+        # Update the distinct color sets for the neighbors.
+        for node, color in colors.items():
+            for neighbor in G[node]:
+                distinct_colors[neighbor].add(color)
+
+        # Compute the maximum saturation and the set of nodes that
+        # achieve that saturation.
+        saturation = {v: len(c) for v, c in distinct_colors.items() if v not in colors}
+        # Yield the node with the highest saturation, and break ties by
+        # degree.
+        node = max(saturation, key=lambda v: (saturation[v], G.degree(v)))
+        yield node
+
+
+#: Dictionary mapping name of a strategy as a string to the strategy function.
+STRATEGIES = {
+    "largest_first": strategy_largest_first,
+    "random_sequential": strategy_random_sequential,
+    "smallest_last": strategy_smallest_last,
+    "independent_set": strategy_independent_set,
+    "connected_sequential_bfs": strategy_connected_sequential_bfs,
+    "connected_sequential_dfs": strategy_connected_sequential_dfs,
+    "connected_sequential": strategy_connected_sequential,
+    "saturation_largest_first": strategy_saturation_largest_first,
+    "DSATUR": strategy_saturation_largest_first,
+}
+
+
+@nx._dispatchable
+def greedy_color(G, strategy="largest_first", interchange=False):
+    """Color a graph using various strategies of greedy graph coloring.
+
+    Attempts to color a graph using as few colors as possible, where no
+    neighbors of a node can have same color as the node itself. The
+    given strategy determines the order in which nodes are colored.
+
+    The strategies are described in [1]_, and smallest-last is based on
+    [2]_.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    strategy : string or function(G, colors)
+       A function (or a string representing a function) that provides
+       the coloring strategy, by returning nodes in the ordering they
+       should be colored. ``G`` is the graph, and ``colors`` is a
+       dictionary of the currently assigned colors, keyed by nodes. The
+       function must return an iterable over all the nodes in ``G``.
+
+       If the strategy function is an iterator generator (that is, a
+       function with ``yield`` statements), keep in mind that the
+       ``colors`` dictionary will be updated after each ``yield``, since
+       this function chooses colors greedily.
+
+       If ``strategy`` is a string, it must be one of the following,
+       each of which represents one of the built-in strategy functions.
+
+       * ``'largest_first'``
+       * ``'random_sequential'``
+       * ``'smallest_last'``
+       * ``'independent_set'``
+       * ``'connected_sequential_bfs'``
+       * ``'connected_sequential_dfs'``
+       * ``'connected_sequential'`` (alias for the previous strategy)
+       * ``'saturation_largest_first'``
+       * ``'DSATUR'`` (alias for the previous strategy)
+
+    interchange: bool
+       Will use the color interchange algorithm described by [3]_ if set
+       to ``True``.
+
+       Note that ``saturation_largest_first`` and ``independent_set``
+       do not work with interchange. Furthermore, if you use
+       interchange with your own strategy function, you cannot rely
+       on the values in the ``colors`` argument.
+
+    Returns
+    -------
+    A dictionary with keys representing nodes and values representing
+    corresponding coloring.
+
+    Examples
+    --------
+    >>> G = nx.cycle_graph(4)
+    >>> d = nx.coloring.greedy_color(G, strategy="largest_first")
+    >>> d in [{0: 0, 1: 1, 2: 0, 3: 1}, {0: 1, 1: 0, 2: 1, 3: 0}]
+    True
+
+    Raises
+    ------
+    NetworkXPointlessConcept
+        If ``strategy`` is ``saturation_largest_first`` or
+        ``independent_set`` and ``interchange`` is ``True``.
+
+    References
+    ----------
+    .. [1] Adrian Kosowski, and Krzysztof Manuszewski,
+       Classical Coloring of Graphs, Graph Colorings, 2-19, 2004.
+       ISBN 0-8218-3458-4.
+    .. [2] David W. Matula, and Leland L. Beck, "Smallest-last
+       ordering and clustering and graph coloring algorithms." *J. ACM* 30,
+       3 (July 1983), 417–427. <https://doi.org/10.1145/2402.322385>
+    .. [3] Maciej M. Sysło, Narsingh Deo, Janusz S. Kowalik,
+       Discrete Optimization Algorithms with Pascal Programs, 415-424, 1983.
+       ISBN 0-486-45353-7.
+
+    """
+    if len(G) == 0:
+        return {}
+    # Determine the strategy provided by the caller.
+    strategy = STRATEGIES.get(strategy, strategy)
+    if not callable(strategy):
+        raise nx.NetworkXError(
+            f"strategy must be callable or a valid string. {strategy} not valid."
+        )
+    # Perform some validation on the arguments before executing any
+    # strategy functions.
+    if interchange:
+        if strategy is strategy_independent_set:
+            msg = "interchange cannot be used with independent_set"
+            raise nx.NetworkXPointlessConcept(msg)
+        if strategy is strategy_saturation_largest_first:
+            msg = "interchange cannot be used with" " saturation_largest_first"
+            raise nx.NetworkXPointlessConcept(msg)
+    colors = {}
+    nodes = strategy(G, colors)
+    if interchange:
+        return _greedy_coloring_with_interchange(G, nodes)
+    for u in nodes:
+        # Set to keep track of colors of neighbors
+        nbr_colors = {colors[v] for v in G[u] if v in colors}
+        # Find the first unused color.
+        for color in itertools.count():
+            if color not in nbr_colors:
+                break
+        # Assign the new color to the current node.
+        colors[u] = color
+    return colors
+
+
+# Tools for coloring with interchanges
+class _Node:
+    __slots__ = ["node_id", "color", "adj_list", "adj_color"]
+
+    def __init__(self, node_id, n):
+        self.node_id = node_id
+        self.color = -1
+        self.adj_list = None
+        self.adj_color = [None for _ in range(n)]
+
+    def __repr__(self):
+        return (
+            f"Node_id: {self.node_id}, Color: {self.color}, "
+            f"Adj_list: ({self.adj_list}), adj_color: ({self.adj_color})"
+        )
+
+    def assign_color(self, adj_entry, color):
+        adj_entry.col_prev = None
+        adj_entry.col_next = self.adj_color[color]
+        self.adj_color[color] = adj_entry
+        if adj_entry.col_next is not None:
+            adj_entry.col_next.col_prev = adj_entry
+
+    def clear_color(self, adj_entry, color):
+        if adj_entry.col_prev is None:
+            self.adj_color[color] = adj_entry.col_next
+        else:
+            adj_entry.col_prev.col_next = adj_entry.col_next
+        if adj_entry.col_next is not None:
+            adj_entry.col_next.col_prev = adj_entry.col_prev
+
+    def iter_neighbors(self):
+        adj_node = self.adj_list
+        while adj_node is not None:
+            yield adj_node
+            adj_node = adj_node.next
+
+    def iter_neighbors_color(self, color):
+        adj_color_node = self.adj_color[color]
+        while adj_color_node is not None:
+            yield adj_color_node.node_id
+            adj_color_node = adj_color_node.col_next
+
+
+class _AdjEntry:
+    __slots__ = ["node_id", "next", "mate", "col_next", "col_prev"]
+
+    def __init__(self, node_id):
+        self.node_id = node_id
+        self.next = None
+        self.mate = None
+        self.col_next = None
+        self.col_prev = None
+
+    def __repr__(self):
+        col_next = None if self.col_next is None else self.col_next.node_id
+        col_prev = None if self.col_prev is None else self.col_prev.node_id
+        return (
+            f"Node_id: {self.node_id}, Next: ({self.next}), "
+            f"Mate: ({self.mate.node_id}), "
+            f"col_next: ({col_next}), col_prev: ({col_prev})"
+        )
+
+
+def _greedy_coloring_with_interchange(G, nodes):
+    """Return a coloring for `original_graph` using interchange approach
+
+    This procedure is an adaption of the algorithm described by [1]_,
+    and is an implementation of coloring with interchange. Please be
+    advised, that the datastructures used are rather complex because
+    they are optimized to minimize the time spent identifying
+    subcomponents of the graph, which are possible candidates for color
+    interchange.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        The graph to be colored
+
+    nodes : list
+        nodes ordered using the strategy of choice
+
+    Returns
+    -------
+    dict :
+        A dictionary keyed by node to a color value
+
+    References
+    ----------
+    .. [1] Maciej M. Syslo, Narsingh Deo, Janusz S. Kowalik,
+       Discrete Optimization Algorithms with Pascal Programs, 415-424, 1983.
+       ISBN 0-486-45353-7.
+    """
+    n = len(G)
+
+    graph = {node: _Node(node, n) for node in G}
+
+    for node1, node2 in G.edges():
+        adj_entry1 = _AdjEntry(node2)
+        adj_entry2 = _AdjEntry(node1)
+        adj_entry1.mate = adj_entry2
+        adj_entry2.mate = adj_entry1
+        node1_head = graph[node1].adj_list
+        adj_entry1.next = node1_head
+        graph[node1].adj_list = adj_entry1
+        node2_head = graph[node2].adj_list
+        adj_entry2.next = node2_head
+        graph[node2].adj_list = adj_entry2
+
+    k = 0
+    for node in nodes:
+        # Find the smallest possible, unused color
+        neighbors = graph[node].iter_neighbors()
+        col_used = {graph[adj_node.node_id].color for adj_node in neighbors}
+        col_used.discard(-1)
+        k1 = next(itertools.dropwhile(lambda x: x in col_used, itertools.count()))
+
+        # k1 is now the lowest available color
+        if k1 > k:
+            connected = True
+            visited = set()
+            col1 = -1
+            col2 = -1
+            while connected and col1 < k:
+                col1 += 1
+                neighbor_cols = graph[node].iter_neighbors_color(col1)
+                col1_adj = list(neighbor_cols)
+
+                col2 = col1
+                while connected and col2 < k:
+                    col2 += 1
+                    visited = set(col1_adj)
+                    frontier = list(col1_adj)
+                    i = 0
+                    while i < len(frontier):
+                        search_node = frontier[i]
+                        i += 1
+                        col_opp = col2 if graph[search_node].color == col1 else col1
+                        neighbor_cols = graph[search_node].iter_neighbors_color(col_opp)
+
+                        for neighbor in neighbor_cols:
+                            if neighbor not in visited:
+                                visited.add(neighbor)
+                                frontier.append(neighbor)
+
+                    # Search if node is not adj to any col2 vertex
+                    connected = (
+                        len(
+                            visited.intersection(graph[node].iter_neighbors_color(col2))
+                        )
+                        > 0
+                    )
+
+            # If connected is false then we can swap !!!
+            if not connected:
+                # Update all the nodes in the component
+                for search_node in visited:
+                    graph[search_node].color = (
+                        col2 if graph[search_node].color == col1 else col1
+                    )
+                    col2_adj = graph[search_node].adj_color[col2]
+                    graph[search_node].adj_color[col2] = graph[search_node].adj_color[
+                        col1
+                    ]
+                    graph[search_node].adj_color[col1] = col2_adj
+
+                # Update all the neighboring nodes
+                for search_node in visited:
+                    col = graph[search_node].color
+                    col_opp = col1 if col == col2 else col2
+                    for adj_node in graph[search_node].iter_neighbors():
+                        if graph[adj_node.node_id].color != col_opp:
+                            # Direct reference to entry
+                            adj_mate = adj_node.mate
+                            graph[adj_node.node_id].clear_color(adj_mate, col_opp)
+                            graph[adj_node.node_id].assign_color(adj_mate, col)
+                k1 = col1
+
+        # We can color this node color k1
+        graph[node].color = k1
+        k = max(k1, k)
+
+        # Update the neighbors of this node
+        for adj_node in graph[node].iter_neighbors():
+            adj_mate = adj_node.mate
+            graph[adj_node.node_id].assign_color(adj_mate, k1)
+
+    return {node.node_id: node.color for node in graph.values()}