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

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+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)

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

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+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

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

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+"""
+Equitable coloring of graphs with bounded degree.
+"""
+
+from collections import defaultdict
+
+import networkx as nx
+
+__all__ = ["equitable_color"]
+
+
+@nx._dispatchable
+def is_coloring(G, coloring):
+    """Determine if the coloring is a valid coloring for the graph G."""
+    # Verify that the coloring is valid.
+    return all(coloring[s] != coloring[d] for s, d in G.edges)
+
+
+@nx._dispatchable
+def is_equitable(G, coloring, num_colors=None):
+    """Determines if the coloring is valid and equitable for the graph G."""
+
+    if not is_coloring(G, coloring):
+        return False
+
+    # Verify whether it is equitable.
+    color_set_size = defaultdict(int)
+    for color in coloring.values():
+        color_set_size[color] += 1
+
+    if num_colors is not None:
+        for color in range(num_colors):
+            if color not in color_set_size:
+                # These colors do not have any vertices attached to them.
+                color_set_size[color] = 0
+
+    # If there are more than 2 distinct values, the coloring cannot be equitable
+    all_set_sizes = set(color_set_size.values())
+    if len(all_set_sizes) == 0 and num_colors is None:  # Was an empty graph
+        return True
+    elif len(all_set_sizes) == 1:
+        return True
+    elif len(all_set_sizes) == 2:
+        a, b = list(all_set_sizes)
+        return abs(a - b) <= 1
+    else:  # len(all_set_sizes) > 2:
+        return False
+
+
+def make_C_from_F(F):
+    C = defaultdict(list)
+    for node, color in F.items():
+        C[color].append(node)
+
+    return C
+
+
+def make_N_from_L_C(L, C):
+    nodes = L.keys()
+    colors = C.keys()
+    return {
+        (node, color): sum(1 for v in L[node] if v in C[color])
+        for node in nodes
+        for color in colors
+    }
+
+
+def make_H_from_C_N(C, N):
+    return {
+        (c1, c2): sum(1 for node in C[c1] if N[(node, c2)] == 0) for c1 in C for c2 in C
+    }
+
+
+def change_color(u, X, Y, N, H, F, C, L):
+    """Change the color of 'u' from X to Y and update N, H, F, C."""
+    assert F[u] == X and X != Y
+
+    # Change the class of 'u' from X to Y
+    F[u] = Y
+
+    for k in C:
+        # 'u' witnesses an edge from k -> Y instead of from k -> X now.
+        if N[u, k] == 0:
+            H[(X, k)] -= 1
+            H[(Y, k)] += 1
+
+    for v in L[u]:
+        # 'v' has lost a neighbor in X and gained one in Y
+        N[(v, X)] -= 1
+        N[(v, Y)] += 1
+
+        if N[(v, X)] == 0:
+            # 'v' witnesses F[v] -> X
+            H[(F[v], X)] += 1
+
+        if N[(v, Y)] == 1:
+            # 'v' no longer witnesses F[v] -> Y
+            H[(F[v], Y)] -= 1
+
+    C[X].remove(u)
+    C[Y].append(u)
+
+
+def move_witnesses(src_color, dst_color, N, H, F, C, T_cal, L):
+    """Move witness along a path from src_color to dst_color."""
+    X = src_color
+    while X != dst_color:
+        Y = T_cal[X]
+        # Move _any_ witness from X to Y = T_cal[X]
+        w = next(x for x in C[X] if N[(x, Y)] == 0)
+        change_color(w, X, Y, N=N, H=H, F=F, C=C, L=L)
+        X = Y
+
+
+@nx._dispatchable(mutates_input=True)
+def pad_graph(G, num_colors):
+    """Add a disconnected complete clique K_p such that the number of nodes in
+    the graph becomes a multiple of `num_colors`.
+
+    Assumes that the graph's nodes are labelled using integers.
+
+    Returns the number of nodes with each color.
+    """
+
+    n_ = len(G)
+    r = num_colors - 1
+
+    # Ensure that the number of nodes in G is a multiple of (r + 1)
+    s = n_ // (r + 1)
+    if n_ != s * (r + 1):
+        p = (r + 1) - n_ % (r + 1)
+        s += 1
+
+        # Complete graph K_p between (imaginary) nodes [n_, ... , n_ + p]
+        K = nx.relabel_nodes(nx.complete_graph(p), {idx: idx + n_ for idx in range(p)})
+        G.add_edges_from(K.edges)
+
+    return s
+
+
+def procedure_P(V_minus, V_plus, N, H, F, C, L, excluded_colors=None):
+    """Procedure P as described in the paper."""
+
+    if excluded_colors is None:
+        excluded_colors = set()
+
+    A_cal = set()
+    T_cal = {}
+    R_cal = []
+
+    # BFS to determine A_cal, i.e. colors reachable from V-
+    reachable = [V_minus]
+    marked = set(reachable)
+    idx = 0
+
+    while idx < len(reachable):
+        pop = reachable[idx]
+        idx += 1
+
+        A_cal.add(pop)
+        R_cal.append(pop)
+
+        # TODO: Checking whether a color has been visited can be made faster by
+        # using a look-up table instead of testing for membership in a set by a
+        # logarithmic factor.
+        next_layer = []
+        for k in C:
+            if (
+                H[(k, pop)] > 0
+                and k not in A_cal
+                and k not in excluded_colors
+                and k not in marked
+            ):
+                next_layer.append(k)
+
+        for dst in next_layer:
+            # Record that `dst` can reach `pop`
+            T_cal[dst] = pop
+
+        marked.update(next_layer)
+        reachable.extend(next_layer)
+
+    # Variables for the algorithm
+    b = len(C) - len(A_cal)
+
+    if V_plus in A_cal:
+        # Easy case: V+ is in A_cal
+        # Move one node from V+ to V- using T_cal to find the parents.
+        move_witnesses(V_plus, V_minus, N=N, H=H, F=F, C=C, T_cal=T_cal, L=L)
+    else:
+        # If there is a solo edge, we can resolve the situation by
+        # moving witnesses from B to A, making G[A] equitable and then
+        # recursively balancing G[B - w] with a different V_minus and
+        # but the same V_plus.
+
+        A_0 = set()
+        A_cal_0 = set()
+        num_terminal_sets_found = 0
+        made_equitable = False
+
+        for W_1 in R_cal[::-1]:
+            for v in C[W_1]:
+                X = None
+
+                for U in C:
+                    if N[(v, U)] == 0 and U in A_cal and U != W_1:
+                        X = U
+
+                # v does not witness an edge in H[A_cal]
+                if X is None:
+                    continue
+
+                for U in C:
+                    # Note: Departing from the paper here.
+                    if N[(v, U)] >= 1 and U not in A_cal:
+                        X_prime = U
+                        w = v
+
+                        try:
+                            # Finding the solo neighbor of w in X_prime
+                            y = next(
+                                node
+                                for node in L[w]
+                                if F[node] == X_prime and N[(node, W_1)] == 1
+                            )
+                        except StopIteration:
+                            pass
+                        else:
+                            W = W_1
+
+                            # Move w from W to X, now X has one extra node.
+                            change_color(w, W, X, N=N, H=H, F=F, C=C, L=L)
+
+                            # Move witness from X to V_minus, making the coloring
+                            # equitable.
+                            move_witnesses(
+                                src_color=X,
+                                dst_color=V_minus,
+                                N=N,
+                                H=H,
+                                F=F,
+                                C=C,
+                                T_cal=T_cal,
+                                L=L,
+                            )
+
+                            # Move y from X_prime to W, making W the correct size.
+                            change_color(y, X_prime, W, N=N, H=H, F=F, C=C, L=L)
+
+                            # Then call the procedure on G[B - y]
+                            procedure_P(
+                                V_minus=X_prime,
+                                V_plus=V_plus,
+                                N=N,
+                                H=H,
+                                C=C,
+                                F=F,
+                                L=L,
+                                excluded_colors=excluded_colors.union(A_cal),
+                            )
+                            made_equitable = True
+                            break
+
+                if made_equitable:
+                    break
+            else:
+                # No node in W_1 was found such that
+                # it had a solo-neighbor.
+                A_cal_0.add(W_1)
+                A_0.update(C[W_1])
+                num_terminal_sets_found += 1
+
+            if num_terminal_sets_found == b:
+                # Otherwise, construct the maximal independent set and find
+                # a pair of z_1, z_2 as in Case II.
+
+                # BFS to determine B_cal': the set of colors reachable from V+
+                B_cal_prime = set()
+                T_cal_prime = {}
+
+                reachable = [V_plus]
+                marked = set(reachable)
+                idx = 0
+                while idx < len(reachable):
+                    pop = reachable[idx]
+                    idx += 1
+
+                    B_cal_prime.add(pop)
+
+                    # No need to check for excluded_colors here because
+                    # they only exclude colors from A_cal
+                    next_layer = [
+                        k
+                        for k in C
+                        if H[(pop, k)] > 0 and k not in B_cal_prime and k not in marked
+                    ]
+
+                    for dst in next_layer:
+                        T_cal_prime[pop] = dst
+
+                    marked.update(next_layer)
+                    reachable.extend(next_layer)
+
+                # Construct the independent set of G[B']
+                I_set = set()
+                I_covered = set()
+                W_covering = {}
+
+                B_prime = [node for k in B_cal_prime for node in C[k]]
+
+                # Add the nodes in V_plus to I first.
+                for z in C[V_plus] + B_prime:
+                    if z in I_covered or F[z] not in B_cal_prime:
+                        continue
+
+                    I_set.add(z)
+                    I_covered.add(z)
+                    I_covered.update(list(L[z]))
+
+                    for w in L[z]:
+                        if F[w] in A_cal_0 and N[(z, F[w])] == 1:
+                            if w not in W_covering:
+                                W_covering[w] = z
+                            else:
+                                # Found z1, z2 which have the same solo
+                                # neighbor in some W
+                                z_1 = W_covering[w]
+                                # z_2 = z
+
+                                Z = F[z_1]
+                                W = F[w]
+
+                                # shift nodes along W, V-
+                                move_witnesses(
+                                    W, V_minus, N=N, H=H, F=F, C=C, T_cal=T_cal, L=L
+                                )
+
+                                # shift nodes along V+ to Z
+                                move_witnesses(
+                                    V_plus,
+                                    Z,
+                                    N=N,
+                                    H=H,
+                                    F=F,
+                                    C=C,
+                                    T_cal=T_cal_prime,
+                                    L=L,
+                                )
+
+                                # change color of z_1 to W
+                                change_color(z_1, Z, W, N=N, H=H, F=F, C=C, L=L)
+
+                                # change color of w to some color in B_cal
+                                W_plus = next(
+                                    k for k in C if N[(w, k)] == 0 and k not in A_cal
+                                )
+                                change_color(w, W, W_plus, N=N, H=H, F=F, C=C, L=L)
+
+                                # recurse with G[B \cup W*]
+                                excluded_colors.update(
+                                    [k for k in C if k != W and k not in B_cal_prime]
+                                )
+                                procedure_P(
+                                    V_minus=W,
+                                    V_plus=W_plus,
+                                    N=N,
+                                    H=H,
+                                    C=C,
+                                    F=F,
+                                    L=L,
+                                    excluded_colors=excluded_colors,
+                                )
+
+                                made_equitable = True
+                                break
+
+                    if made_equitable:
+                        break
+                else:
+                    assert False, (
+                        "Must find a w which is the solo neighbor "
+                        "of two vertices in B_cal_prime."
+                    )
+
+            if made_equitable:
+                break
+
+
+@nx._dispatchable
+def equitable_color(G, num_colors):
+    """Provides an equitable coloring for nodes of `G`.
+
+    Attempts to color a graph using `num_colors` colors, where no neighbors of
+    a node can have same color as the node itself and the number of nodes with
+    each color differ by at most 1. `num_colors` must be greater than the
+    maximum degree of `G`. The algorithm is described in [1]_ and has
+    complexity O(num_colors * n**2).
+
+    Parameters
+    ----------
+    G : networkX graph
+       The nodes of this graph will be colored.
+
+    num_colors : number of colors to use
+       This number must be at least one more than the maximum degree of nodes
+       in the graph.
+
+    Returns
+    -------
+    A dictionary with keys representing nodes and values representing
+    corresponding coloring.
+
+    Examples
+    --------
+    >>> G = nx.cycle_graph(4)
+    >>> nx.coloring.equitable_color(G, num_colors=3)  # doctest: +SKIP
+    {0: 2, 1: 1, 2: 2, 3: 0}
+
+    Raises
+    ------
+    NetworkXAlgorithmError
+        If `num_colors` is not at least the maximum degree of the graph `G`
+
+    References
+    ----------
+    .. [1] Kierstead, H. A., Kostochka, A. V., Mydlarz, M., & Szemerédi, E.
+        (2010). A fast algorithm for equitable coloring. Combinatorica, 30(2),
+        217-224.
+    """
+
+    # Map nodes to integers for simplicity later.
+    nodes_to_int = {}
+    int_to_nodes = {}
+
+    for idx, node in enumerate(G.nodes):
+        nodes_to_int[node] = idx
+        int_to_nodes[idx] = node
+
+    G = nx.relabel_nodes(G, nodes_to_int, copy=True)
+
+    # Basic graph statistics and sanity check.
+    if len(G.nodes) > 0:
+        r_ = max(G.degree(node) for node in G.nodes)
+    else:
+        r_ = 0
+
+    if r_ >= num_colors:
+        raise nx.NetworkXAlgorithmError(
+            f"Graph has maximum degree {r_}, needs "
+            f"{r_ + 1} (> {num_colors}) colors for guaranteed coloring."
+        )
+
+    # Ensure that the number of nodes in G is a multiple of (r + 1)
+    pad_graph(G, num_colors)
+
+    # Starting the algorithm.
+    # L = {node: list(G.neighbors(node)) for node in G.nodes}
+    L_ = {node: [] for node in G.nodes}
+
+    # Arbitrary equitable allocation of colors to nodes.
+    F = {node: idx % num_colors for idx, node in enumerate(G.nodes)}
+
+    C = make_C_from_F(F)
+
+    # The neighborhood is empty initially.
+    N = make_N_from_L_C(L_, C)
+
+    # Currently all nodes witness all edges.
+    H = make_H_from_C_N(C, N)
+
+    # Start of algorithm.
+    edges_seen = set()
+
+    for u in sorted(G.nodes):
+        for v in sorted(G.neighbors(u)):
+            # Do not double count edges if (v, u) has already been seen.
+            if (v, u) in edges_seen:
+                continue
+
+            edges_seen.add((u, v))
+
+            L_[u].append(v)
+            L_[v].append(u)
+
+            N[(u, F[v])] += 1
+            N[(v, F[u])] += 1
+
+            if F[u] != F[v]:
+                # Were 'u' and 'v' witnesses for F[u] -> F[v] or F[v] -> F[u]?
+                if N[(u, F[v])] == 1:
+                    H[F[u], F[v]] -= 1  # u cannot witness an edge between F[u], F[v]
+
+                if N[(v, F[u])] == 1:
+                    H[F[v], F[u]] -= 1  # v cannot witness an edge between F[v], F[u]
+
+        if N[(u, F[u])] != 0:
+            # Find the first color where 'u' does not have any neighbors.
+            Y = next(k for k in C if N[(u, k)] == 0)
+            X = F[u]
+            change_color(u, X, Y, N=N, H=H, F=F, C=C, L=L_)
+
+            # Procedure P
+            procedure_P(V_minus=X, V_plus=Y, N=N, H=H, F=F, C=C, L=L_)
+
+    return {int_to_nodes[x]: F[x] for x in int_to_nodes}

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

@@ -0,0 +1,6 @@
+from .connected import *
+from .strongly_connected import *
+from .weakly_connected import *
+from .attracting import *
+from .biconnected import *
+from .semiconnected import *

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

@@ -0,0 +1,115 @@
+"""Attracting components."""
+
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = [
+    "number_attracting_components",
+    "attracting_components",
+    "is_attracting_component",
+]
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def attracting_components(G):
+    """Generates the attracting components in `G`.
+
+    An attracting component in a directed graph `G` is a strongly connected
+    component with the property that a random walker on the graph will never
+    leave the component, once it enters the component.
+
+    The nodes in attracting components can also be thought of as recurrent
+    nodes.  If a random walker enters the attractor containing the node, then
+    the node will be visited infinitely often.
+
+    To obtain induced subgraphs on each component use:
+    ``(G.subgraph(c).copy() for c in attracting_components(G))``
+
+    Parameters
+    ----------
+    G : DiGraph, MultiDiGraph
+        The graph to be analyzed.
+
+    Returns
+    -------
+    attractors : generator of sets
+        A generator of sets of nodes, one for each attracting component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is undirected.
+
+    See Also
+    --------
+    number_attracting_components
+    is_attracting_component
+
+    """
+    scc = list(nx.strongly_connected_components(G))
+    cG = nx.condensation(G, scc)
+    for n in cG:
+        if cG.out_degree(n) == 0:
+            yield scc[n]
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def number_attracting_components(G):
+    """Returns the number of attracting components in `G`.
+
+    Parameters
+    ----------
+    G : DiGraph, MultiDiGraph
+        The graph to be analyzed.
+
+    Returns
+    -------
+    n : int
+        The number of attracting components in G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is undirected.
+
+    See Also
+    --------
+    attracting_components
+    is_attracting_component
+
+    """
+    return sum(1 for ac in attracting_components(G))
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def is_attracting_component(G):
+    """Returns True if `G` consists of a single attracting component.
+
+    Parameters
+    ----------
+    G : DiGraph, MultiDiGraph
+        The graph to be analyzed.
+
+    Returns
+    -------
+    attracting : bool
+        True if `G` has a single attracting component. Otherwise, False.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is undirected.
+
+    See Also
+    --------
+    attracting_components
+    number_attracting_components
+
+    """
+    ac = list(attracting_components(G))
+    if len(ac) == 1:
+        return len(ac[0]) == len(G)
+    return False

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

@@ -0,0 +1,394 @@
+"""Biconnected components and articulation points."""
+
+from itertools import chain
+
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = [
+    "biconnected_components",
+    "biconnected_component_edges",
+    "is_biconnected",
+    "articulation_points",
+]
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def is_biconnected(G):
+    """Returns True if the graph is biconnected, False otherwise.
+
+    A graph is biconnected if, and only if, it cannot be disconnected by
+    removing only one node (and all edges incident on that node).  If
+    removing a node increases the number of disconnected components
+    in the graph, that node is called an articulation point, or cut
+    vertex.  A biconnected graph has no articulation points.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        An undirected graph.
+
+    Returns
+    -------
+    biconnected : bool
+        True if the graph is biconnected, False otherwise.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is not undirected.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> print(nx.is_biconnected(G))
+    False
+    >>> G.add_edge(0, 3)
+    >>> print(nx.is_biconnected(G))
+    True
+
+    See Also
+    --------
+    biconnected_components
+    articulation_points
+    biconnected_component_edges
+    is_strongly_connected
+    is_weakly_connected
+    is_connected
+    is_semiconnected
+
+    Notes
+    -----
+    The algorithm to find articulation points and biconnected
+    components is implemented using a non-recursive depth-first-search
+    (DFS) that keeps track of the highest level that back edges reach
+    in the DFS tree.  A node `n` is an articulation point if, and only
+    if, there exists a subtree rooted at `n` such that there is no
+    back edge from any successor of `n` that links to a predecessor of
+    `n` in the DFS tree.  By keeping track of all the edges traversed
+    by the DFS we can obtain the biconnected components because all
+    edges of a bicomponent will be traversed consecutively between
+    articulation points.
+
+    References
+    ----------
+    .. [1] Hopcroft, J.; Tarjan, R. (1973).
+       "Efficient algorithms for graph manipulation".
+       Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
+
+    """
+    bccs = biconnected_components(G)
+    try:
+        bcc = next(bccs)
+    except StopIteration:
+        # No bicomponents (empty graph?)
+        return False
+    try:
+        next(bccs)
+    except StopIteration:
+        # Only one bicomponent
+        return len(bcc) == len(G)
+    else:
+        # Multiple bicomponents
+        return False
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def biconnected_component_edges(G):
+    """Returns a generator of lists of edges, one list for each biconnected
+    component of the input graph.
+
+    Biconnected components are maximal subgraphs such that the removal of a
+    node (and all edges incident on that node) will not disconnect the
+    subgraph.  Note that nodes may be part of more than one biconnected
+    component.  Those nodes are articulation points, or cut vertices.
+    However, each edge belongs to one, and only one, biconnected component.
+
+    Notice that by convention a dyad is considered a biconnected component.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        An undirected graph.
+
+    Returns
+    -------
+    edges : generator of lists
+        Generator of lists of edges, one list for each bicomponent.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is not undirected.
+
+    Examples
+    --------
+    >>> G = nx.barbell_graph(4, 2)
+    >>> print(nx.is_biconnected(G))
+    False
+    >>> bicomponents_edges = list(nx.biconnected_component_edges(G))
+    >>> len(bicomponents_edges)
+    5
+    >>> G.add_edge(2, 8)
+    >>> print(nx.is_biconnected(G))
+    True
+    >>> bicomponents_edges = list(nx.biconnected_component_edges(G))
+    >>> len(bicomponents_edges)
+    1
+
+    See Also
+    --------
+    is_biconnected,
+    biconnected_components,
+    articulation_points,
+
+    Notes
+    -----
+    The algorithm to find articulation points and biconnected
+    components is implemented using a non-recursive depth-first-search
+    (DFS) that keeps track of the highest level that back edges reach
+    in the DFS tree.  A node `n` is an articulation point if, and only
+    if, there exists a subtree rooted at `n` such that there is no
+    back edge from any successor of `n` that links to a predecessor of
+    `n` in the DFS tree.  By keeping track of all the edges traversed
+    by the DFS we can obtain the biconnected components because all
+    edges of a bicomponent will be traversed consecutively between
+    articulation points.
+
+    References
+    ----------
+    .. [1] Hopcroft, J.; Tarjan, R. (1973).
+           "Efficient algorithms for graph manipulation".
+           Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
+
+    """
+    yield from _biconnected_dfs(G, components=True)
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def biconnected_components(G):
+    """Returns a generator of sets of nodes, one set for each biconnected
+    component of the graph
+
+    Biconnected components are maximal subgraphs such that the removal of a
+    node (and all edges incident on that node) will not disconnect the
+    subgraph. Note that nodes may be part of more than one biconnected
+    component.  Those nodes are articulation points, or cut vertices.  The
+    removal of articulation points will increase the number of connected
+    components of the graph.
+
+    Notice that by convention a dyad is considered a biconnected component.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        An undirected graph.
+
+    Returns
+    -------
+    nodes : generator
+        Generator of sets of nodes, one set for each biconnected component.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is not undirected.
+
+    Examples
+    --------
+    >>> G = nx.lollipop_graph(5, 1)
+    >>> print(nx.is_biconnected(G))
+    False
+    >>> bicomponents = list(nx.biconnected_components(G))
+    >>> len(bicomponents)
+    2
+    >>> G.add_edge(0, 5)
+    >>> print(nx.is_biconnected(G))
+    True
+    >>> bicomponents = list(nx.biconnected_components(G))
+    >>> len(bicomponents)
+    1
+
+    You can generate a sorted list of biconnected components, largest
+    first, using sort.
+
+    >>> G.remove_edge(0, 5)
+    >>> [len(c) for c in sorted(nx.biconnected_components(G), key=len, reverse=True)]
+    [5, 2]
+
+    If you only want the largest connected component, it's more
+    efficient to use max instead of sort.
+
+    >>> Gc = max(nx.biconnected_components(G), key=len)
+
+    To create the components as subgraphs use:
+    ``(G.subgraph(c).copy() for c in biconnected_components(G))``
+
+    See Also
+    --------
+    is_biconnected
+    articulation_points
+    biconnected_component_edges
+    k_components : this function is a special case where k=2
+    bridge_components : similar to this function, but is defined using
+        2-edge-connectivity instead of 2-node-connectivity.
+
+    Notes
+    -----
+    The algorithm to find articulation points and biconnected
+    components is implemented using a non-recursive depth-first-search
+    (DFS) that keeps track of the highest level that back edges reach
+    in the DFS tree.  A node `n` is an articulation point if, and only
+    if, there exists a subtree rooted at `n` such that there is no
+    back edge from any successor of `n` that links to a predecessor of
+    `n` in the DFS tree.  By keeping track of all the edges traversed
+    by the DFS we can obtain the biconnected components because all
+    edges of a bicomponent will be traversed consecutively between
+    articulation points.
+
+    References
+    ----------
+    .. [1] Hopcroft, J.; Tarjan, R. (1973).
+           "Efficient algorithms for graph manipulation".
+           Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
+
+    """
+    for comp in _biconnected_dfs(G, components=True):
+        yield set(chain.from_iterable(comp))
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def articulation_points(G):
+    """Yield the articulation points, or cut vertices, of a graph.
+
+    An articulation point or cut vertex is any node whose removal (along with
+    all its incident edges) increases the number of connected components of
+    a graph.  An undirected connected graph without articulation points is
+    biconnected. Articulation points belong to more than one biconnected
+    component of a graph.
+
+    Notice that by convention a dyad is considered a biconnected component.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        An undirected graph.
+
+    Yields
+    ------
+    node
+        An articulation point in the graph.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is not undirected.
+
+    Examples
+    --------
+
+    >>> G = nx.barbell_graph(4, 2)
+    >>> print(nx.is_biconnected(G))
+    False
+    >>> len(list(nx.articulation_points(G)))
+    4
+    >>> G.add_edge(2, 8)
+    >>> print(nx.is_biconnected(G))
+    True
+    >>> len(list(nx.articulation_points(G)))
+    0
+
+    See Also
+    --------
+    is_biconnected
+    biconnected_components
+    biconnected_component_edges
+
+    Notes
+    -----
+    The algorithm to find articulation points and biconnected
+    components is implemented using a non-recursive depth-first-search
+    (DFS) that keeps track of the highest level that back edges reach
+    in the DFS tree.  A node `n` is an articulation point if, and only
+    if, there exists a subtree rooted at `n` such that there is no
+    back edge from any successor of `n` that links to a predecessor of
+    `n` in the DFS tree.  By keeping track of all the edges traversed
+    by the DFS we can obtain the biconnected components because all
+    edges of a bicomponent will be traversed consecutively between
+    articulation points.
+
+    References
+    ----------
+    .. [1] Hopcroft, J.; Tarjan, R. (1973).
+           "Efficient algorithms for graph manipulation".
+           Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
+
+    """
+    seen = set()
+    for articulation in _biconnected_dfs(G, components=False):
+        if articulation not in seen:
+            seen.add(articulation)
+            yield articulation
+
+
+@not_implemented_for("directed")
+def _biconnected_dfs(G, components=True):
+    # depth-first search algorithm to generate articulation points
+    # and biconnected components
+    visited = set()
+    for start in G:
+        if start in visited:
+            continue
+        discovery = {start: 0}  # time of first discovery of node during search
+        low = {start: 0}
+        root_children = 0
+        visited.add(start)
+        edge_stack = []
+        stack = [(start, start, iter(G[start]))]
+        edge_index = {}
+        while stack:
+            grandparent, parent, children = stack[-1]
+            try:
+                child = next(children)
+                if grandparent == child:
+                    continue
+                if child in visited:
+                    if discovery[child] <= discovery[parent]:  # back edge
+                        low[parent] = min(low[parent], discovery[child])
+                        if components:
+                            edge_index[parent, child] = len(edge_stack)
+                            edge_stack.append((parent, child))
+                else:
+                    low[child] = discovery[child] = len(discovery)
+                    visited.add(child)
+                    stack.append((parent, child, iter(G[child])))
+                    if components:
+                        edge_index[parent, child] = len(edge_stack)
+                        edge_stack.append((parent, child))
+
+            except StopIteration:
+                stack.pop()
+                if len(stack) > 1:
+                    if low[parent] >= discovery[grandparent]:
+                        if components:
+                            ind = edge_index[grandparent, parent]
+                            yield edge_stack[ind:]
+                            del edge_stack[ind:]
+
+                        else:
+                            yield grandparent
+                    low[grandparent] = min(low[parent], low[grandparent])
+                elif stack:  # length 1 so grandparent is root
+                    root_children += 1
+                    if components:
+                        ind = edge_index[grandparent, parent]
+                        yield edge_stack[ind:]
+                        del edge_stack[ind:]
+        if not components:
+            # root node is articulation point if it has more than 1 child
+            if root_children > 1:
+                yield start

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

@@ -0,0 +1,216 @@
+"""Connected components."""
+
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+from ...utils import arbitrary_element
+
+__all__ = [
+    "number_connected_components",
+    "connected_components",
+    "is_connected",
+    "node_connected_component",
+]
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def connected_components(G):
+    """Generate connected components.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph
+
+    Returns
+    -------
+    comp : generator of sets
+       A generator of sets of nodes, one for each component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    Examples
+    --------
+    Generate a sorted list of connected components, largest first.
+
+    >>> G = nx.path_graph(4)
+    >>> nx.add_path(G, [10, 11, 12])
+    >>> [len(c) for c in sorted(nx.connected_components(G), key=len, reverse=True)]
+    [4, 3]
+
+    If you only want the largest connected component, it's more
+    efficient to use max instead of sort.
+
+    >>> largest_cc = max(nx.connected_components(G), key=len)
+
+    To create the induced subgraph of each component use:
+
+    >>> S = [G.subgraph(c).copy() for c in nx.connected_components(G)]
+
+    See Also
+    --------
+    strongly_connected_components
+    weakly_connected_components
+
+    Notes
+    -----
+    For undirected graphs only.
+
+    """
+    seen = set()
+    n = len(G)
+    for v in G:
+        if v not in seen:
+            c = _plain_bfs(G, n, v)
+            seen.update(c)
+            yield c
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def number_connected_components(G):
+    """Returns the number of connected components.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    Returns
+    -------
+    n : integer
+       Number of connected components
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (1, 2), (5, 6), (3, 4)])
+    >>> nx.number_connected_components(G)
+    3
+
+    See Also
+    --------
+    connected_components
+    number_weakly_connected_components
+    number_strongly_connected_components
+
+    Notes
+    -----
+    For undirected graphs only.
+
+    """
+    return sum(1 for cc in connected_components(G))
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def is_connected(G):
+    """Returns True if the graph is connected, False otherwise.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+       An undirected graph.
+
+    Returns
+    -------
+    connected : bool
+      True if the graph is connected, false otherwise.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> print(nx.is_connected(G))
+    True
+
+    See Also
+    --------
+    is_strongly_connected
+    is_weakly_connected
+    is_semiconnected
+    is_biconnected
+    connected_components
+
+    Notes
+    -----
+    For undirected graphs only.
+
+    """
+    n = len(G)
+    if n == 0:
+        raise nx.NetworkXPointlessConcept(
+            "Connectivity is undefined for the null graph."
+        )
+    return sum(1 for node in _plain_bfs(G, n, arbitrary_element(G))) == len(G)
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def node_connected_component(G, n):
+    """Returns the set of nodes in the component of graph containing node n.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+       An undirected graph.
+
+    n : node label
+       A node in G
+
+    Returns
+    -------
+    comp : set
+       A set of nodes in the component of G containing node n.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (1, 2), (5, 6), (3, 4)])
+    >>> nx.node_connected_component(G, 0)  # nodes of component that contains node 0
+    {0, 1, 2}
+
+    See Also
+    --------
+    connected_components
+
+    Notes
+    -----
+    For undirected graphs only.
+
+    """
+    return _plain_bfs(G, len(G), n)
+
+
+def _plain_bfs(G, n, source):
+    """A fast BFS node generator"""
+    adj = G._adj
+    seen = {source}
+    nextlevel = [source]
+    while nextlevel:
+        thislevel = nextlevel
+        nextlevel = []
+        for v in thislevel:
+            for w in adj[v]:
+                if w not in seen:
+                    seen.add(w)
+                    nextlevel.append(w)
+            if len(seen) == n:
+                return seen
+    return seen

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

@@ -0,0 +1,71 @@
+"""Semiconnectedness."""
+
+import networkx as nx
+from networkx.utils import not_implemented_for, pairwise
+
+__all__ = ["is_semiconnected"]
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def is_semiconnected(G):
+    r"""Returns True if the graph is semiconnected, False otherwise.
+
+    A graph is semiconnected if and only if for any pair of nodes, either one
+    is reachable from the other, or they are mutually reachable.
+
+    This function uses a theorem that states that a DAG is semiconnected
+    if for any topological sort, for node $v_n$ in that sort, there is an
+    edge $(v_i, v_{i+1})$. That allows us to check if a non-DAG `G` is
+    semiconnected by condensing the graph: i.e. constructing a new graph `H`
+    with nodes being the strongly connected components of `G`, and edges
+    (scc_1, scc_2) if there is a edge $(v_1, v_2)$ in `G` for some
+    $v_1 \in scc_1$ and $v_2 \in scc_2$. That results in a DAG, so we compute
+    the topological sort of `H` and check if for every $n$ there is an edge
+    $(scc_n, scc_{n+1})$.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A directed graph.
+
+    Returns
+    -------
+    semiconnected : bool
+        True if the graph is semiconnected, False otherwise.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is undirected.
+
+    NetworkXPointlessConcept
+        If the graph is empty.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4, create_using=nx.DiGraph())
+    >>> print(nx.is_semiconnected(G))
+    True
+    >>> G = nx.DiGraph([(1, 2), (3, 2)])
+    >>> print(nx.is_semiconnected(G))
+    False
+
+    See Also
+    --------
+    is_strongly_connected
+    is_weakly_connected
+    is_connected
+    is_biconnected
+    """
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept(
+            "Connectivity is undefined for the null graph."
+        )
+
+    if not nx.is_weakly_connected(G):
+        return False
+
+    H = nx.condensation(G)
+
+    return all(H.has_edge(u, v) for u, v in pairwise(nx.topological_sort(H)))

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

@@ -0,0 +1,351 @@
+"""Strongly connected components."""
+
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = [
+    "number_strongly_connected_components",
+    "strongly_connected_components",
+    "is_strongly_connected",
+    "kosaraju_strongly_connected_components",
+    "condensation",
+]
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def strongly_connected_components(G):
+    """Generate nodes in strongly connected components of graph.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        A directed graph.
+
+    Returns
+    -------
+    comp : generator of sets
+        A generator of sets of nodes, one for each strongly connected
+        component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    Generate a sorted list of strongly connected components, largest first.
+
+    >>> G = nx.cycle_graph(4, create_using=nx.DiGraph())
+    >>> nx.add_cycle(G, [10, 11, 12])
+    >>> [
+    ...     len(c)
+    ...     for c in sorted(nx.strongly_connected_components(G), key=len, reverse=True)
+    ... ]
+    [4, 3]
+
+    If you only want the largest component, it's more efficient to
+    use max instead of sort.
+
+    >>> largest = max(nx.strongly_connected_components(G), key=len)
+
+    See Also
+    --------
+    connected_components
+    weakly_connected_components
+    kosaraju_strongly_connected_components
+
+    Notes
+    -----
+    Uses Tarjan's algorithm[1]_ with Nuutila's modifications[2]_.
+    Nonrecursive version of algorithm.
+
+    References
+    ----------
+    .. [1] Depth-first search and linear graph algorithms, R. Tarjan
+       SIAM Journal of Computing 1(2):146-160, (1972).
+
+    .. [2] On finding the strongly connected components in a directed graph.
+       E. Nuutila and E. Soisalon-Soinen
+       Information Processing Letters 49(1): 9-14, (1994)..
+
+    """
+    preorder = {}
+    lowlink = {}
+    scc_found = set()
+    scc_queue = []
+    i = 0  # Preorder counter
+    neighbors = {v: iter(G[v]) for v in G}
+    for source in G:
+        if source not in scc_found:
+            queue = [source]
+            while queue:
+                v = queue[-1]
+                if v not in preorder:
+                    i = i + 1
+                    preorder[v] = i
+                done = True
+                for w in neighbors[v]:
+                    if w not in preorder:
+                        queue.append(w)
+                        done = False
+                        break
+                if done:
+                    lowlink[v] = preorder[v]
+                    for w in G[v]:
+                        if w not in scc_found:
+                            if preorder[w] > preorder[v]:
+                                lowlink[v] = min([lowlink[v], lowlink[w]])
+                            else:
+                                lowlink[v] = min([lowlink[v], preorder[w]])
+                    queue.pop()
+                    if lowlink[v] == preorder[v]:
+                        scc = {v}
+                        while scc_queue and preorder[scc_queue[-1]] > preorder[v]:
+                            k = scc_queue.pop()
+                            scc.add(k)
+                        scc_found.update(scc)
+                        yield scc
+                    else:
+                        scc_queue.append(v)
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def kosaraju_strongly_connected_components(G, source=None):
+    """Generate nodes in strongly connected components of graph.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        A directed graph.
+
+    Returns
+    -------
+    comp : generator of sets
+        A generator of sets of nodes, one for each strongly connected
+        component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    Generate a sorted list of strongly connected components, largest first.
+
+    >>> G = nx.cycle_graph(4, create_using=nx.DiGraph())
+    >>> nx.add_cycle(G, [10, 11, 12])
+    >>> [
+    ...     len(c)
+    ...     for c in sorted(
+    ...         nx.kosaraju_strongly_connected_components(G), key=len, reverse=True
+    ...     )
+    ... ]
+    [4, 3]
+
+    If you only want the largest component, it's more efficient to
+    use max instead of sort.
+
+    >>> largest = max(nx.kosaraju_strongly_connected_components(G), key=len)
+
+    See Also
+    --------
+    strongly_connected_components
+
+    Notes
+    -----
+    Uses Kosaraju's algorithm.
+
+    """
+    post = list(nx.dfs_postorder_nodes(G.reverse(copy=False), source=source))
+
+    seen = set()
+    while post:
+        r = post.pop()
+        if r in seen:
+            continue
+        c = nx.dfs_preorder_nodes(G, r)
+        new = {v for v in c if v not in seen}
+        seen.update(new)
+        yield new
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def number_strongly_connected_components(G):
+    """Returns number of strongly connected components in graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       A directed graph.
+
+    Returns
+    -------
+    n : integer
+       Number of strongly connected components
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph(
+    ...     [(0, 1), (1, 2), (2, 0), (2, 3), (4, 5), (3, 4), (5, 6), (6, 3), (6, 7)]
+    ... )
+    >>> nx.number_strongly_connected_components(G)
+    3
+
+    See Also
+    --------
+    strongly_connected_components
+    number_connected_components
+    number_weakly_connected_components
+
+    Notes
+    -----
+    For directed graphs only.
+    """
+    return sum(1 for scc in strongly_connected_components(G))
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def is_strongly_connected(G):
+    """Test directed graph for strong connectivity.
+
+    A directed graph is strongly connected if and only if every vertex in
+    the graph is reachable from every other vertex.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+       A directed graph.
+
+    Returns
+    -------
+    connected : bool
+      True if the graph is strongly connected, False otherwise.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(0, 1), (1, 2), (2, 3), (3, 0), (2, 4), (4, 2)])
+    >>> nx.is_strongly_connected(G)
+    True
+    >>> G.remove_edge(2, 3)
+    >>> nx.is_strongly_connected(G)
+    False
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    See Also
+    --------
+    is_weakly_connected
+    is_semiconnected
+    is_connected
+    is_biconnected
+    strongly_connected_components
+
+    Notes
+    -----
+    For directed graphs only.
+    """
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept(
+            """Connectivity is undefined for the null graph."""
+        )
+
+    return len(next(strongly_connected_components(G))) == len(G)
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable(returns_graph=True)
+def condensation(G, scc=None):
+    """Returns the condensation of G.
+
+    The condensation of G is the graph with each of the strongly connected
+    components contracted into a single node.
+
+    Parameters
+    ----------
+    G : NetworkX DiGraph
+       A directed graph.
+
+    scc:  list or generator (optional, default=None)
+       Strongly connected components. If provided, the elements in
+       `scc` must partition the nodes in `G`. If not provided, it will be
+       calculated as scc=nx.strongly_connected_components(G).
+
+    Returns
+    -------
+    C : NetworkX DiGraph
+       The condensation graph C of G.  The node labels are integers
+       corresponding to the index of the component in the list of
+       strongly connected components of G.  C has a graph attribute named
+       'mapping' with a dictionary mapping the original nodes to the
+       nodes in C to which they belong.  Each node in C also has a node
+       attribute 'members' with the set of original nodes in G that
+       form the SCC that the node in C represents.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    Contracting two sets of strongly connected nodes into two distinct SCC
+    using the barbell graph.
+
+    >>> G = nx.barbell_graph(4, 0)
+    >>> G.remove_edge(3, 4)
+    >>> G = nx.DiGraph(G)
+    >>> H = nx.condensation(G)
+    >>> H.nodes.data()
+    NodeDataView({0: {'members': {0, 1, 2, 3}}, 1: {'members': {4, 5, 6, 7}}})
+    >>> H.graph["mapping"]
+    {0: 0, 1: 0, 2: 0, 3: 0, 4: 1, 5: 1, 6: 1, 7: 1}
+
+    Contracting a complete graph into one single SCC.
+
+    >>> G = nx.complete_graph(7, create_using=nx.DiGraph)
+    >>> H = nx.condensation(G)
+    >>> H.nodes
+    NodeView((0,))
+    >>> H.nodes.data()
+    NodeDataView({0: {'members': {0, 1, 2, 3, 4, 5, 6}}})
+
+    Notes
+    -----
+    After contracting all strongly connected components to a single node,
+    the resulting graph is a directed acyclic graph.
+
+    """
+    if scc is None:
+        scc = nx.strongly_connected_components(G)
+    mapping = {}
+    members = {}
+    C = nx.DiGraph()
+    # Add mapping dict as graph attribute
+    C.graph["mapping"] = mapping
+    if len(G) == 0:
+        return C
+    for i, component in enumerate(scc):
+        members[i] = component
+        mapping.update((n, i) for n in component)
+    number_of_components = i + 1
+    C.add_nodes_from(range(number_of_components))
+    C.add_edges_from(
+        (mapping[u], mapping[v]) for u, v in G.edges() if mapping[u] != mapping[v]
+    )
+    # Add a list of members (ie original nodes) to each node (ie scc) in C.
+    nx.set_node_attributes(C, members, "members")
+    return C

wemm/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_attracting.py

@@ -0,0 +1,70 @@
+import pytest
+
+import networkx as nx
+from networkx import NetworkXNotImplemented
+
+
+class TestAttractingComponents:
+    @classmethod
+    def setup_class(cls):
+        cls.G1 = nx.DiGraph()
+        cls.G1.add_edges_from(
+            [
+                (5, 11),
+                (11, 2),
+                (11, 9),
+                (11, 10),
+                (7, 11),
+                (7, 8),
+                (8, 9),
+                (3, 8),
+                (3, 10),
+            ]
+        )
+        cls.G2 = nx.DiGraph()
+        cls.G2.add_edges_from([(0, 1), (0, 2), (1, 1), (1, 2), (2, 1)])
+
+        cls.G3 = nx.DiGraph()
+        cls.G3.add_edges_from([(0, 1), (1, 2), (2, 1), (0, 3), (3, 4), (4, 3)])
+
+        cls.G4 = nx.DiGraph()
+
+    def test_attracting_components(self):
+        ac = list(nx.attracting_components(self.G1))
+        assert {2} in ac
+        assert {9} in ac
+        assert {10} in ac
+
+        ac = list(nx.attracting_components(self.G2))
+        ac = [tuple(sorted(x)) for x in ac]
+        assert ac == [(1, 2)]
+
+        ac = list(nx.attracting_components(self.G3))
+        ac = [tuple(sorted(x)) for x in ac]
+        assert (1, 2) in ac
+        assert (3, 4) in ac
+        assert len(ac) == 2
+
+        ac = list(nx.attracting_components(self.G4))
+        assert ac == []
+
+    def test_number_attacting_components(self):
+        assert nx.number_attracting_components(self.G1) == 3
+        assert nx.number_attracting_components(self.G2) == 1
+        assert nx.number_attracting_components(self.G3) == 2
+        assert nx.number_attracting_components(self.G4) == 0
+
+    def test_is_attracting_component(self):
+        assert not nx.is_attracting_component(self.G1)
+        assert not nx.is_attracting_component(self.G2)
+        assert not nx.is_attracting_component(self.G3)
+        g2 = self.G3.subgraph([1, 2])
+        assert nx.is_attracting_component(g2)
+        assert not nx.is_attracting_component(self.G4)
+
+    def test_connected_raise(self):
+        G = nx.Graph()
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.attracting_components(G))
+        pytest.raises(NetworkXNotImplemented, nx.number_attracting_components, G)
+        pytest.raises(NetworkXNotImplemented, nx.is_attracting_component, G)

wemm/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_semiconnected.py

@@ -0,0 +1,55 @@
+from itertools import chain
+
+import pytest
+
+import networkx as nx
+
+
+class TestIsSemiconnected:
+    def test_undirected(self):
+        pytest.raises(nx.NetworkXNotImplemented, nx.is_semiconnected, nx.Graph())
+        pytest.raises(nx.NetworkXNotImplemented, nx.is_semiconnected, nx.MultiGraph())
+
+    def test_empty(self):
+        pytest.raises(nx.NetworkXPointlessConcept, nx.is_semiconnected, nx.DiGraph())
+        pytest.raises(
+            nx.NetworkXPointlessConcept, nx.is_semiconnected, nx.MultiDiGraph()
+        )
+
+    def test_single_node_graph(self):
+        G = nx.DiGraph()
+        G.add_node(0)
+        assert nx.is_semiconnected(G)
+
+    def test_path(self):
+        G = nx.path_graph(100, create_using=nx.DiGraph())
+        assert nx.is_semiconnected(G)
+        G.add_edge(100, 99)
+        assert not nx.is_semiconnected(G)
+
+    def test_cycle(self):
+        G = nx.cycle_graph(100, create_using=nx.DiGraph())
+        assert nx.is_semiconnected(G)
+        G = nx.path_graph(100, create_using=nx.DiGraph())
+        G.add_edge(0, 99)
+        assert nx.is_semiconnected(G)
+
+    def test_tree(self):
+        G = nx.DiGraph()
+        G.add_edges_from(
+            chain.from_iterable([(i, 2 * i + 1), (i, 2 * i + 2)] for i in range(100))
+        )
+        assert not nx.is_semiconnected(G)
+
+    def test_dumbbell(self):
+        G = nx.cycle_graph(100, create_using=nx.DiGraph())
+        G.add_edges_from((i + 100, (i + 1) % 100 + 100) for i in range(100))
+        assert not nx.is_semiconnected(G)  # G is disconnected.
+        G.add_edge(100, 99)
+        assert nx.is_semiconnected(G)
+
+    def test_alternating_path(self):
+        G = nx.DiGraph(
+            chain.from_iterable([(i, i - 1), (i, i + 1)] for i in range(0, 100, 2))
+        )
+        assert not nx.is_semiconnected(G)

wemm/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_strongly_connected.py

@@ -0,0 +1,193 @@
+import pytest
+
+import networkx as nx
+from networkx import NetworkXNotImplemented
+
+
+class TestStronglyConnected:
+    @classmethod
+    def setup_class(cls):
+        cls.gc = []
+        G = nx.DiGraph()
+        G.add_edges_from(
+            [
+                (1, 2),
+                (2, 3),
+                (2, 8),
+                (3, 4),
+                (3, 7),
+                (4, 5),
+                (5, 3),
+                (5, 6),
+                (7, 4),
+                (7, 6),
+                (8, 1),
+                (8, 7),
+            ]
+        )
+        C = {frozenset([3, 4, 5, 7]), frozenset([1, 2, 8]), frozenset([6])}
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (1, 3), (1, 4), (4, 2), (3, 4), (2, 3)])
+        C = {frozenset([2, 3, 4]), frozenset([1])}
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (2, 3), (3, 2), (2, 1)])
+        C = {frozenset([1, 2, 3])}
+        cls.gc.append((G, C))
+
+        # Eppstein's tests
+        G = nx.DiGraph({0: [1], 1: [2, 3], 2: [4, 5], 3: [4, 5], 4: [6], 5: [], 6: []})
+        C = {
+            frozenset([0]),
+            frozenset([1]),
+            frozenset([2]),
+            frozenset([3]),
+            frozenset([4]),
+            frozenset([5]),
+            frozenset([6]),
+        }
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph({0: [1], 1: [2, 3, 4], 2: [0, 3], 3: [4], 4: [3]})
+        C = {frozenset([0, 1, 2]), frozenset([3, 4])}
+        cls.gc.append((G, C))
+
+    def test_tarjan(self):
+        scc = nx.strongly_connected_components
+        for G, C in self.gc:
+            assert {frozenset(g) for g in scc(G)} == C
+
+    def test_kosaraju(self):
+        scc = nx.kosaraju_strongly_connected_components
+        for G, C in self.gc:
+            assert {frozenset(g) for g in scc(G)} == C
+
+    def test_number_strongly_connected_components(self):
+        ncc = nx.number_strongly_connected_components
+        for G, C in self.gc:
+            assert ncc(G) == len(C)
+
+    def test_is_strongly_connected(self):
+        for G, C in self.gc:
+            if len(C) == 1:
+                assert nx.is_strongly_connected(G)
+            else:
+                assert not nx.is_strongly_connected(G)
+
+    def test_contract_scc1(self):
+        G = nx.DiGraph()
+        G.add_edges_from(
+            [
+                (1, 2),
+                (2, 3),
+                (2, 11),
+                (2, 12),
+                (3, 4),
+                (4, 3),
+                (4, 5),
+                (5, 6),
+                (6, 5),
+                (6, 7),
+                (7, 8),
+                (7, 9),
+                (7, 10),
+                (8, 9),
+                (9, 7),
+                (10, 6),
+                (11, 2),
+                (11, 4),
+                (11, 6),
+                (12, 6),
+                (12, 11),
+            ]
+        )
+        scc = list(nx.strongly_connected_components(G))
+        cG = nx.condensation(G, scc)
+        # DAG
+        assert nx.is_directed_acyclic_graph(cG)
+        # nodes
+        assert sorted(cG.nodes()) == [0, 1, 2, 3]
+        # edges
+        mapping = {}
+        for i, component in enumerate(scc):
+            for n in component:
+                mapping[n] = i
+        edge = (mapping[2], mapping[3])
+        assert cG.has_edge(*edge)
+        edge = (mapping[2], mapping[5])
+        assert cG.has_edge(*edge)
+        edge = (mapping[3], mapping[5])
+        assert cG.has_edge(*edge)
+
+    def test_contract_scc_isolate(self):
+        # Bug found and fixed in [1687].
+        G = nx.DiGraph()
+        G.add_edge(1, 2)
+        G.add_edge(2, 1)
+        scc = list(nx.strongly_connected_components(G))
+        cG = nx.condensation(G, scc)
+        assert list(cG.nodes()) == [0]
+        assert list(cG.edges()) == []
+
+    def test_contract_scc_edge(self):
+        G = nx.DiGraph()
+        G.add_edge(1, 2)
+        G.add_edge(2, 1)
+        G.add_edge(2, 3)
+        G.add_edge(3, 4)
+        G.add_edge(4, 3)
+        scc = list(nx.strongly_connected_components(G))
+        cG = nx.condensation(G, scc)
+        assert sorted(cG.nodes()) == [0, 1]
+        if 1 in scc[0]:
+            edge = (0, 1)
+        else:
+            edge = (1, 0)
+        assert list(cG.edges()) == [edge]
+
+    def test_condensation_mapping_and_members(self):
+        G, C = self.gc[1]
+        C = sorted(C, key=len, reverse=True)
+        cG = nx.condensation(G)
+        mapping = cG.graph["mapping"]
+        assert all(n in G for n in mapping)
+        assert all(0 == cN for n, cN in mapping.items() if n in C[0])
+        assert all(1 == cN for n, cN in mapping.items() if n in C[1])
+        for n, d in cG.nodes(data=True):
+            assert set(C[n]) == cG.nodes[n]["members"]
+
+    def test_null_graph(self):
+        G = nx.DiGraph()
+        assert list(nx.strongly_connected_components(G)) == []
+        assert list(nx.kosaraju_strongly_connected_components(G)) == []
+        assert len(nx.condensation(G)) == 0
+        pytest.raises(
+            nx.NetworkXPointlessConcept, nx.is_strongly_connected, nx.DiGraph()
+        )
+
+    def test_connected_raise(self):
+        G = nx.Graph()
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.strongly_connected_components(G))
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.kosaraju_strongly_connected_components(G))
+        pytest.raises(NetworkXNotImplemented, nx.is_strongly_connected, G)
+        pytest.raises(NetworkXNotImplemented, nx.condensation, G)
+
+    strong_cc_methods = (
+        nx.strongly_connected_components,
+        nx.kosaraju_strongly_connected_components,
+    )
+
+    @pytest.mark.parametrize("get_components", strong_cc_methods)
+    def test_connected_mutability(self, get_components):
+        DG = nx.path_graph(5, create_using=nx.DiGraph)
+        G = nx.disjoint_union(DG, DG)
+        seen = set()
+        for component in get_components(G):
+            assert len(seen & component) == 0
+            seen.update(component)
+            component.clear()

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

@@ -0,0 +1,197 @@
+"""Weakly connected components."""
+
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = [
+    "number_weakly_connected_components",
+    "weakly_connected_components",
+    "is_weakly_connected",
+]
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def weakly_connected_components(G):
+    """Generate weakly connected components of G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A directed graph
+
+    Returns
+    -------
+    comp : generator of sets
+        A generator of sets of nodes, one for each weakly connected
+        component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    Generate a sorted list of weakly connected components, largest first.
+
+    >>> G = nx.path_graph(4, create_using=nx.DiGraph())
+    >>> nx.add_path(G, [10, 11, 12])
+    >>> [
+    ...     len(c)
+    ...     for c in sorted(nx.weakly_connected_components(G), key=len, reverse=True)
+    ... ]
+    [4, 3]
+
+    If you only want the largest component, it's more efficient to
+    use max instead of sort:
+
+    >>> largest_cc = max(nx.weakly_connected_components(G), key=len)
+
+    See Also
+    --------
+    connected_components
+    strongly_connected_components
+
+    Notes
+    -----
+    For directed graphs only.
+
+    """
+    seen = set()
+    n = len(G)  # must be outside the loop to avoid performance hit with graph views
+    for v in G:
+        if v not in seen:
+            c = set(_plain_bfs(G, n, v))
+            seen.update(c)
+            yield c
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def number_weakly_connected_components(G):
+    """Returns the number of weakly connected components in G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A directed graph.
+
+    Returns
+    -------
+    n : integer
+        Number of weakly connected components
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(0, 1), (2, 1), (3, 4)])
+    >>> nx.number_weakly_connected_components(G)
+    2
+
+    See Also
+    --------
+    weakly_connected_components
+    number_connected_components
+    number_strongly_connected_components
+
+    Notes
+    -----
+    For directed graphs only.
+
+    """
+    return sum(1 for wcc in weakly_connected_components(G))
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def is_weakly_connected(G):
+    """Test directed graph for weak connectivity.
+
+    A directed graph is weakly connected if and only if the graph
+    is connected when the direction of the edge between nodes is ignored.
+
+    Note that if a graph is strongly connected (i.e. the graph is connected
+    even when we account for directionality), it is by definition weakly
+    connected as well.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        A directed graph.
+
+    Returns
+    -------
+    connected : bool
+        True if the graph is weakly connected, False otherwise.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(0, 1), (2, 1)])
+    >>> G.add_node(3)
+    >>> nx.is_weakly_connected(G)  # node 3 is not connected to the graph
+    False
+    >>> G.add_edge(2, 3)
+    >>> nx.is_weakly_connected(G)
+    True
+
+    See Also
+    --------
+    is_strongly_connected
+    is_semiconnected
+    is_connected
+    is_biconnected
+    weakly_connected_components
+
+    Notes
+    -----
+    For directed graphs only.
+
+    """
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept(
+            """Connectivity is undefined for the null graph."""
+        )
+
+    return len(next(weakly_connected_components(G))) == len(G)
+
+
+def _plain_bfs(G, n, source):
+    """A fast BFS node generator
+
+    The direction of the edge between nodes is ignored.
+
+    For directed graphs only.
+
+    """
+    Gsucc = G._succ
+    Gpred = G._pred
+    seen = {source}
+    nextlevel = [source]
+
+    yield source
+    while nextlevel:
+        thislevel = nextlevel
+        nextlevel = []
+        for v in thislevel:
+            for w in Gsucc[v]:
+                if w not in seen:
+                    seen.add(w)
+                    nextlevel.append(w)
+                    yield w
+            for w in Gpred[v]:
+                if w not in seen:
+                    seen.add(w)
+                    nextlevel.append(w)
+                    yield w
+            if len(seen) == n:
+                return