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.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/tests/test_basic.py

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

.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/tests/test_centrality.py

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

.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/tests/test_cluster.py

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

.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/tests/test_covering.py

@@ -0,0 +1,33 @@
+import networkx as nx
+from networkx.algorithms import bipartite
+
+
+class TestMinEdgeCover:
+    """Tests for :func:`networkx.algorithms.bipartite.min_edge_cover`"""
+
+    def test_empty_graph(self):
+        G = nx.Graph()
+        assert bipartite.min_edge_cover(G) == set()
+
+    def test_graph_single_edge(self):
+        G = nx.Graph()
+        G.add_edge(0, 1)
+        assert bipartite.min_edge_cover(G) == {(0, 1), (1, 0)}
+
+    def test_bipartite_default(self):
+        G = nx.Graph()
+        G.add_nodes_from([1, 2, 3, 4], bipartite=0)
+        G.add_nodes_from(["a", "b", "c"], bipartite=1)
+        G.add_edges_from([(1, "a"), (1, "b"), (2, "b"), (2, "c"), (3, "c"), (4, "a")])
+        min_cover = bipartite.min_edge_cover(G)
+        assert nx.is_edge_cover(G, min_cover)
+        assert len(min_cover) == 8
+
+    def test_bipartite_explicit(self):
+        G = nx.Graph()
+        G.add_nodes_from([1, 2, 3, 4], bipartite=0)
+        G.add_nodes_from(["a", "b", "c"], bipartite=1)
+        G.add_edges_from([(1, "a"), (1, "b"), (2, "b"), (2, "c"), (3, "c"), (4, "a")])
+        min_cover = bipartite.min_edge_cover(G, bipartite.eppstein_matching)
+        assert nx.is_edge_cover(G, min_cover)
+        assert len(min_cover) == 8

.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/tests/test_edgelist.py

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

.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/tests/test_extendability.py

@@ -0,0 +1,334 @@
+import pytest
+
+import networkx as nx
+
+
+def test_selfloops_raises():
+    G = nx.ladder_graph(3)
+    G.add_edge(0, 0)
+    with pytest.raises(nx.NetworkXError, match=".*not bipartite"):
+        nx.bipartite.maximal_extendability(G)
+
+
+def test_disconnected_raises():
+    G = nx.ladder_graph(3)
+    G.add_node("a")
+    with pytest.raises(nx.NetworkXError, match=".*not connected"):
+        nx.bipartite.maximal_extendability(G)
+
+
+def test_not_bipartite_raises():
+    G = nx.complete_graph(5)
+    with pytest.raises(nx.NetworkXError, match=".*not bipartite"):
+        nx.bipartite.maximal_extendability(G)
+
+
+def test_no_perfect_matching_raises():
+    G = nx.Graph([(0, 1), (0, 2)])
+    with pytest.raises(nx.NetworkXError, match=".*not contain a perfect matching"):
+        nx.bipartite.maximal_extendability(G)
+
+
+def test_residual_graph_not_strongly_connected_raises():
+    G = nx.Graph([(1, 2), (2, 3), (3, 4)])
+    with pytest.raises(
+        nx.NetworkXError, match="The residual graph of G is not strongly connected"
+    ):
+        nx.bipartite.maximal_extendability(G)
+
+
+def test_ladder_graph_is_1():
+    G = nx.ladder_graph(3)
+    assert nx.bipartite.maximal_extendability(G) == 1
+
+
+def test_cubical_graph_is_2():
+    G = nx.cubical_graph()
+    assert nx.bipartite.maximal_extendability(G) == 2
+
+
+def test_k_is_3():
+    G = nx.Graph(
+        [
+            (1, 6),
+            (1, 7),
+            (1, 8),
+            (1, 9),
+            (2, 6),
+            (2, 7),
+            (2, 8),
+            (2, 10),
+            (3, 6),
+            (3, 8),
+            (3, 9),
+            (3, 10),
+            (4, 7),
+            (4, 8),
+            (4, 9),
+            (4, 10),
+            (5, 6),
+            (5, 7),
+            (5, 9),
+            (5, 10),
+        ]
+    )
+    assert nx.bipartite.maximal_extendability(G) == 3
+
+
+def test_k_is_4():
+    G = nx.Graph(
+        [
+            (8, 1),
+            (8, 2),
+            (8, 3),
+            (8, 4),
+            (8, 5),
+            (9, 1),
+            (9, 2),
+            (9, 3),
+            (9, 4),
+            (9, 7),
+            (10, 1),
+            (10, 2),
+            (10, 3),
+            (10, 4),
+            (10, 6),
+            (11, 1),
+            (11, 2),
+            (11, 5),
+            (11, 6),
+            (11, 7),
+            (12, 1),
+            (12, 3),
+            (12, 5),
+            (12, 6),
+            (12, 7),
+            (13, 2),
+            (13, 4),
+            (13, 5),
+            (13, 6),
+            (13, 7),
+            (14, 3),
+            (14, 4),
+            (14, 5),
+            (14, 6),
+            (14, 7),
+        ]
+    )
+    assert nx.bipartite.maximal_extendability(G) == 4
+
+
+def test_k_is_5():
+    G = nx.Graph(
+        [
+            (8, 1),
+            (8, 2),
+            (8, 3),
+            (8, 4),
+            (8, 5),
+            (8, 6),
+            (9, 1),
+            (9, 2),
+            (9, 3),
+            (9, 4),
+            (9, 5),
+            (9, 7),
+            (10, 1),
+            (10, 2),
+            (10, 3),
+            (10, 4),
+            (10, 6),
+            (10, 7),
+            (11, 1),
+            (11, 2),
+            (11, 3),
+            (11, 5),
+            (11, 6),
+            (11, 7),
+            (12, 1),
+            (12, 2),
+            (12, 4),
+            (12, 5),
+            (12, 6),
+            (12, 7),
+            (13, 1),
+            (13, 3),
+            (13, 4),
+            (13, 5),
+            (13, 6),
+            (13, 7),
+            (14, 2),
+            (14, 3),
+            (14, 4),
+            (14, 5),
+            (14, 6),
+            (14, 7),
+        ]
+    )
+    assert nx.bipartite.maximal_extendability(G) == 5
+
+
+def test_k_is_6():
+    G = nx.Graph(
+        [
+            (9, 1),
+            (9, 2),
+            (9, 3),
+            (9, 4),
+            (9, 5),
+            (9, 6),
+            (9, 7),
+            (10, 1),
+            (10, 2),
+            (10, 3),
+            (10, 4),
+            (10, 5),
+            (10, 6),
+            (10, 8),
+            (11, 1),
+            (11, 2),
+            (11, 3),
+            (11, 4),
+            (11, 5),
+            (11, 7),
+            (11, 8),
+            (12, 1),
+            (12, 2),
+            (12, 3),
+            (12, 4),
+            (12, 6),
+            (12, 7),
+            (12, 8),
+            (13, 1),
+            (13, 2),
+            (13, 3),
+            (13, 5),
+            (13, 6),
+            (13, 7),
+            (13, 8),
+            (14, 1),
+            (14, 2),
+            (14, 4),
+            (14, 5),
+            (14, 6),
+            (14, 7),
+            (14, 8),
+            (15, 1),
+            (15, 3),
+            (15, 4),
+            (15, 5),
+            (15, 6),
+            (15, 7),
+            (15, 8),
+            (16, 2),
+            (16, 3),
+            (16, 4),
+            (16, 5),
+            (16, 6),
+            (16, 7),
+            (16, 8),
+        ]
+    )
+    assert nx.bipartite.maximal_extendability(G) == 6
+
+
+def test_k_is_7():
+    G = nx.Graph(
+        [
+            (1, 11),
+            (1, 12),
+            (1, 13),
+            (1, 14),
+            (1, 15),
+            (1, 16),
+            (1, 17),
+            (1, 18),
+            (2, 11),
+            (2, 12),
+            (2, 13),
+            (2, 14),
+            (2, 15),
+            (2, 16),
+            (2, 17),
+            (2, 19),
+            (3, 11),
+            (3, 12),
+            (3, 13),
+            (3, 14),
+            (3, 15),
+            (3, 16),
+            (3, 17),
+            (3, 20),
+            (4, 11),
+            (4, 12),
+            (4, 13),
+            (4, 14),
+            (4, 15),
+            (4, 16),
+            (4, 17),
+            (4, 18),
+            (4, 19),
+            (4, 20),
+            (5, 11),
+            (5, 12),
+            (5, 13),
+            (5, 14),
+            (5, 15),
+            (5, 16),
+            (5, 17),
+            (5, 18),
+            (5, 19),
+            (5, 20),
+            (6, 11),
+            (6, 12),
+            (6, 13),
+            (6, 14),
+            (6, 15),
+            (6, 16),
+            (6, 17),
+            (6, 18),
+            (6, 19),
+            (6, 20),
+            (7, 11),
+            (7, 12),
+            (7, 13),
+            (7, 14),
+            (7, 15),
+            (7, 16),
+            (7, 17),
+            (7, 18),
+            (7, 19),
+            (7, 20),
+            (8, 11),
+            (8, 12),
+            (8, 13),
+            (8, 14),
+            (8, 15),
+            (8, 16),
+            (8, 17),
+            (8, 18),
+            (8, 19),
+            (8, 20),
+            (9, 11),
+            (9, 12),
+            (9, 13),
+            (9, 14),
+            (9, 15),
+            (9, 16),
+            (9, 17),
+            (9, 18),
+            (9, 19),
+            (9, 20),
+            (10, 11),
+            (10, 12),
+            (10, 13),
+            (10, 14),
+            (10, 15),
+            (10, 16),
+            (10, 17),
+            (10, 18),
+            (10, 19),
+            (10, 20),
+        ]
+    )
+    assert nx.bipartite.maximal_extendability(G) == 7

.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/tests/test_generators.py

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

.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/tests/test_matching.py

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

.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/tests/test_matrix.py

@@ -0,0 +1,84 @@
+import pytest
+
+np = pytest.importorskip("numpy")
+sp = pytest.importorskip("scipy")
+sparse = pytest.importorskip("scipy.sparse")
+
+
+import networkx as nx
+from networkx.algorithms import bipartite
+from networkx.utils import edges_equal
+
+
+class TestBiadjacencyMatrix:
+    def test_biadjacency_matrix_weight(self):
+        G = nx.path_graph(5)
+        G.add_edge(0, 1, weight=2, other=4)
+        X = [1, 3]
+        Y = [0, 2, 4]
+        M = bipartite.biadjacency_matrix(G, X, weight="weight")
+        assert M[0, 0] == 2
+        M = bipartite.biadjacency_matrix(G, X, weight="other")
+        assert M[0, 0] == 4
+
+    def test_biadjacency_matrix(self):
+        tops = [2, 5, 10]
+        bots = [5, 10, 15]
+        for i in range(len(tops)):
+            G = bipartite.random_graph(tops[i], bots[i], 0.2)
+            top = [n for n, d in G.nodes(data=True) if d["bipartite"] == 0]
+            M = bipartite.biadjacency_matrix(G, top)
+            assert M.shape[0] == tops[i]
+            assert M.shape[1] == bots[i]
+
+    def test_biadjacency_matrix_order(self):
+        G = nx.path_graph(5)
+        G.add_edge(0, 1, weight=2)
+        X = [3, 1]
+        Y = [4, 2, 0]
+        M = bipartite.biadjacency_matrix(G, X, Y, weight="weight")
+        assert M[1, 2] == 2
+
+    def test_biadjacency_matrix_empty_graph(self):
+        G = nx.empty_graph(2)
+        M = nx.bipartite.biadjacency_matrix(G, [0])
+        assert np.array_equal(M.toarray(), np.array([[0]]))
+
+    def test_null_graph(self):
+        with pytest.raises(nx.NetworkXError):
+            bipartite.biadjacency_matrix(nx.Graph(), [])
+
+    def test_empty_graph(self):
+        with pytest.raises(nx.NetworkXError):
+            bipartite.biadjacency_matrix(nx.Graph([(1, 0)]), [])
+
+    def test_duplicate_row(self):
+        with pytest.raises(nx.NetworkXError):
+            bipartite.biadjacency_matrix(nx.Graph([(1, 0)]), [1, 1])
+
+    def test_duplicate_col(self):
+        with pytest.raises(nx.NetworkXError):
+            bipartite.biadjacency_matrix(nx.Graph([(1, 0)]), [0], [1, 1])
+
+    def test_format_keyword(self):
+        with pytest.raises(nx.NetworkXError):
+            bipartite.biadjacency_matrix(nx.Graph([(1, 0)]), [0], format="foo")
+
+    def test_from_biadjacency_roundtrip(self):
+        B1 = nx.path_graph(5)
+        M = bipartite.biadjacency_matrix(B1, [0, 2, 4])
+        B2 = bipartite.from_biadjacency_matrix(M)
+        assert nx.is_isomorphic(B1, B2)
+
+    def test_from_biadjacency_weight(self):
+        M = sparse.csc_matrix([[1, 2], [0, 3]])
+        B = bipartite.from_biadjacency_matrix(M)
+        assert edges_equal(B.edges(), [(0, 2), (0, 3), (1, 3)])
+        B = bipartite.from_biadjacency_matrix(M, edge_attribute="weight")
+        e = [(0, 2, {"weight": 1}), (0, 3, {"weight": 2}), (1, 3, {"weight": 3})]
+        assert edges_equal(B.edges(data=True), e)
+
+    def test_from_biadjacency_multigraph(self):
+        M = sparse.csc_matrix([[1, 2], [0, 3]])
+        B = bipartite.from_biadjacency_matrix(M, create_using=nx.MultiGraph())
+        assert edges_equal(B.edges(), [(0, 2), (0, 3), (0, 3), (1, 3), (1, 3), (1, 3)])

.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/tests/test_project.py

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

.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/tests/test_redundancy.py

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

.venv/lib/python3.11/site-packages/networkx/algorithms/bipartite/tests/test_spectral_bipartivity.py

@@ -0,0 +1,80 @@
+import pytest
+
+pytest.importorskip("scipy")
+
+import networkx as nx
+from networkx.algorithms.bipartite import spectral_bipartivity as sb
+
+# Examples from Figure 1
+# E. Estrada and J. A. Rodríguez-Velázquez, "Spectral measures of
+# bipartivity in complex networks", PhysRev E 72, 046105 (2005)
+
+
+class TestSpectralBipartivity:
+    def test_star_like(self):
+        # star-like
+
+        G = nx.star_graph(2)
+        G.add_edge(1, 2)
+        assert sb(G) == pytest.approx(0.843, abs=1e-3)
+
+        G = nx.star_graph(3)
+        G.add_edge(1, 2)
+        assert sb(G) == pytest.approx(0.871, abs=1e-3)
+
+        G = nx.star_graph(4)
+        G.add_edge(1, 2)
+        assert sb(G) == pytest.approx(0.890, abs=1e-3)
+
+    def test_k23_like(self):
+        # K2,3-like
+        G = nx.complete_bipartite_graph(2, 3)
+        G.add_edge(0, 1)
+        assert sb(G) == pytest.approx(0.769, abs=1e-3)
+
+        G = nx.complete_bipartite_graph(2, 3)
+        G.add_edge(2, 4)
+        assert sb(G) == pytest.approx(0.829, abs=1e-3)
+
+        G = nx.complete_bipartite_graph(2, 3)
+        G.add_edge(2, 4)
+        G.add_edge(3, 4)
+        assert sb(G) == pytest.approx(0.731, abs=1e-3)
+
+        G = nx.complete_bipartite_graph(2, 3)
+        G.add_edge(0, 1)
+        G.add_edge(2, 4)
+        assert sb(G) == pytest.approx(0.692, abs=1e-3)
+
+        G = nx.complete_bipartite_graph(2, 3)
+        G.add_edge(2, 4)
+        G.add_edge(3, 4)
+        G.add_edge(0, 1)
+        assert sb(G) == pytest.approx(0.645, abs=1e-3)
+
+        G = nx.complete_bipartite_graph(2, 3)
+        G.add_edge(2, 4)
+        G.add_edge(3, 4)
+        G.add_edge(2, 3)
+        assert sb(G) == pytest.approx(0.645, abs=1e-3)
+
+        G = nx.complete_bipartite_graph(2, 3)
+        G.add_edge(2, 4)
+        G.add_edge(3, 4)
+        G.add_edge(2, 3)
+        G.add_edge(0, 1)
+        assert sb(G) == pytest.approx(0.597, abs=1e-3)
+
+    def test_single_nodes(self):
+        # single nodes
+        G = nx.complete_bipartite_graph(2, 3)
+        G.add_edge(2, 4)
+        sbn = sb(G, nodes=[1, 2])
+        assert sbn[1] == pytest.approx(0.85, abs=1e-2)
+        assert sbn[2] == pytest.approx(0.77, abs=1e-2)
+
+        G = nx.complete_bipartite_graph(2, 3)
+        G.add_edge(0, 1)
+        sbn = sb(G, nodes=[1, 2])
+        assert sbn[1] == pytest.approx(0.73, abs=1e-2)
+        assert sbn[2] == pytest.approx(0.82, abs=1e-2)

.venv/lib/python3.11/site-packages/networkx/generators/__init__.py

@@ -0,0 +1,34 @@
+"""
+A package for generating various graphs in networkx.
+
+"""
+
+from networkx.generators.atlas import *
+from networkx.generators.classic import *
+from networkx.generators.cographs import *
+from networkx.generators.community import *
+from networkx.generators.degree_seq import *
+from networkx.generators.directed import *
+from networkx.generators.duplication import *
+from networkx.generators.ego import *
+from networkx.generators.expanders import *
+from networkx.generators.geometric import *
+from networkx.generators.harary_graph import *
+from networkx.generators.internet_as_graphs import *
+from networkx.generators.intersection import *
+from networkx.generators.interval_graph import *
+from networkx.generators.joint_degree_seq import *
+from networkx.generators.lattice import *
+from networkx.generators.line import *
+from networkx.generators.mycielski import *
+from networkx.generators.nonisomorphic_trees import *
+from networkx.generators.random_clustered import *
+from networkx.generators.random_graphs import *
+from networkx.generators.small import *
+from networkx.generators.social import *
+from networkx.generators.spectral_graph_forge import *
+from networkx.generators.stochastic import *
+from networkx.generators.sudoku import *
+from networkx.generators.time_series import *
+from networkx.generators.trees import *
+from networkx.generators.triads import *

.venv/lib/python3.11/site-packages/networkx/generators/atlas.py

@@ -0,0 +1,180 @@
+"""
+Generators for the small graph atlas.
+"""
+
+import gzip
+import importlib.resources
+import os
+import os.path
+from itertools import islice
+
+import networkx as nx
+
+__all__ = ["graph_atlas", "graph_atlas_g"]
+
+#: The total number of graphs in the atlas.
+#:
+#: The graphs are labeled starting from 0 and extending to (but not
+#: including) this number.
+NUM_GRAPHS = 1253
+
+#: The path to the data file containing the graph edge lists.
+#:
+#: This is the absolute path of the gzipped text file containing the
+#: edge list for each graph in the atlas. The file contains one entry
+#: per graph in the atlas, in sequential order, starting from graph
+#: number 0 and extending through graph number 1252 (see
+#: :data:`NUM_GRAPHS`). Each entry looks like
+#:
+#: .. sourcecode:: text
+#:
+#:    GRAPH 6
+#:    NODES 3
+#:    0 1
+#:    0 2
+#:
+#: where the first two lines are the graph's index in the atlas and the
+#: number of nodes in the graph, and the remaining lines are the edge
+#: list.
+#:
+#: This file was generated from a Python list of graphs via code like
+#: the following::
+#:
+#:     import gzip
+#:     from networkx.generators.atlas import graph_atlas_g
+#:     from networkx.readwrite.edgelist import write_edgelist
+#:
+#:     with gzip.open('atlas.dat.gz', 'wb') as f:
+#:         for i, G in enumerate(graph_atlas_g()):
+#:             f.write(bytes(f'GRAPH {i}\n', encoding='utf-8'))
+#:             f.write(bytes(f'NODES {len(G)}\n', encoding='utf-8'))
+#:             write_edgelist(G, f, data=False)
+#:
+
+# Path to the atlas file
+ATLAS_FILE = importlib.resources.files("networkx.generators") / "atlas.dat.gz"
+
+
+def _generate_graphs():
+    """Sequentially read the file containing the edge list data for the
+    graphs in the atlas and generate the graphs one at a time.
+
+    This function reads the file given in :data:`.ATLAS_FILE`.
+
+    """
+    with gzip.open(ATLAS_FILE, "rb") as f:
+        line = f.readline()
+        while line and line.startswith(b"GRAPH"):
+            # The first two lines of each entry tell us the index of the
+            # graph in the list and the number of nodes in the graph.
+            # They look like this:
+            #
+            #     GRAPH 3
+            #     NODES 2
+            #
+            graph_index = int(line[6:].rstrip())
+            line = f.readline()
+            num_nodes = int(line[6:].rstrip())
+            # The remaining lines contain the edge list, until the next
+            # GRAPH line (or until the end of the file).
+            edgelist = []
+            line = f.readline()
+            while line and not line.startswith(b"GRAPH"):
+                edgelist.append(line.rstrip())
+                line = f.readline()
+            G = nx.Graph()
+            G.name = f"G{graph_index}"
+            G.add_nodes_from(range(num_nodes))
+            G.add_edges_from(tuple(map(int, e.split())) for e in edgelist)
+            yield G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def graph_atlas(i):
+    """Returns graph number `i` from the Graph Atlas.
+
+    For more information, see :func:`.graph_atlas_g`.
+
+    Parameters
+    ----------
+    i : int
+        The index of the graph from the atlas to get. The graph at index
+        0 is assumed to be the null graph.
+
+    Returns
+    -------
+    list
+        A list of :class:`~networkx.Graph` objects, the one at index *i*
+        corresponding to the graph *i* in the Graph Atlas.
+
+    See also
+    --------
+    graph_atlas_g
+
+    Notes
+    -----
+    The time required by this function increases linearly with the
+    argument `i`, since it reads a large file sequentially in order to
+    generate the graph [1]_.
+
+    References
+    ----------
+    .. [1] Ronald C. Read and Robin J. Wilson, *An Atlas of Graphs*.
+           Oxford University Press, 1998.
+
+    """
+    if not (0 <= i < NUM_GRAPHS):
+        raise ValueError(f"index must be between 0 and {NUM_GRAPHS}")
+    return next(islice(_generate_graphs(), i, None))
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def graph_atlas_g():
+    """Returns the list of all graphs with up to seven nodes named in the
+    Graph Atlas.
+
+    The graphs are listed in increasing order by
+
+    1. number of nodes,
+    2. number of edges,
+    3. degree sequence (for example 111223 < 112222),
+    4. number of automorphisms,
+
+    in that order, with three exceptions as described in the *Notes*
+    section below. This causes the list to correspond with the index of
+    the graphs in the Graph Atlas [atlas]_, with the first graph,
+    ``G[0]``, being the null graph.
+
+    Returns
+    -------
+    list
+        A list of :class:`~networkx.Graph` objects, the one at index *i*
+        corresponding to the graph *i* in the Graph Atlas.
+
+    See also
+    --------
+    graph_atlas
+
+    Notes
+    -----
+    This function may be expensive in both time and space, since it
+    reads a large file sequentially in order to populate the list.
+
+    Although the NetworkX atlas functions match the order of graphs
+    given in the "Atlas of Graphs" book, there are (at least) three
+    errors in the ordering described in the book. The following three
+    pairs of nodes violate the lexicographically nondecreasing sorted
+    degree sequence rule:
+
+    - graphs 55 and 56 with degree sequences 001111 and 000112,
+    - graphs 1007 and 1008 with degree sequences 3333444 and 3333336,
+    - graphs 1012 and 1213 with degree sequences 1244555 and 1244456.
+
+    References
+    ----------
+    .. [atlas] Ronald C. Read and Robin J. Wilson,
+               *An Atlas of Graphs*.
+               Oxford University Press, 1998.
+
+    """
+    return list(_generate_graphs())

.venv/lib/python3.11/site-packages/networkx/generators/classic.py

@@ -0,0 +1,1068 @@
+"""Generators for some classic graphs.
+
+The typical graph builder function is called as follows:
+
+>>> G = nx.complete_graph(100)
+
+returning the complete graph on n nodes labeled 0, .., 99
+as a simple graph. Except for `empty_graph`, all the functions
+in this module return a Graph class (i.e. a simple, undirected graph).
+
+"""
+
+import itertools
+import numbers
+
+import networkx as nx
+from networkx.classes import Graph
+from networkx.exception import NetworkXError
+from networkx.utils import nodes_or_number, pairwise
+
+__all__ = [
+    "balanced_tree",
+    "barbell_graph",
+    "binomial_tree",
+    "complete_graph",
+    "complete_multipartite_graph",
+    "circular_ladder_graph",
+    "circulant_graph",
+    "cycle_graph",
+    "dorogovtsev_goltsev_mendes_graph",
+    "empty_graph",
+    "full_rary_tree",
+    "kneser_graph",
+    "ladder_graph",
+    "lollipop_graph",
+    "null_graph",
+    "path_graph",
+    "star_graph",
+    "tadpole_graph",
+    "trivial_graph",
+    "turan_graph",
+    "wheel_graph",
+]
+
+
+# -------------------------------------------------------------------
+#   Some Classic Graphs
+# -------------------------------------------------------------------
+
+
+def _tree_edges(n, r):
+    if n == 0:
+        return
+    # helper function for trees
+    # yields edges in rooted tree at 0 with n nodes and branching ratio r
+    nodes = iter(range(n))
+    parents = [next(nodes)]  # stack of max length r
+    while parents:
+        source = parents.pop(0)
+        for i in range(r):
+            try:
+                target = next(nodes)
+                parents.append(target)
+                yield source, target
+            except StopIteration:
+                break
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def full_rary_tree(r, n, create_using=None):
+    """Creates a full r-ary tree of `n` nodes.
+
+    Sometimes called a k-ary, n-ary, or m-ary tree.
+    "... all non-leaf nodes have exactly r children and all levels
+    are full except for some rightmost position of the bottom level
+    (if a leaf at the bottom level is missing, then so are all of the
+    leaves to its right." [1]_
+
+    .. plot::
+
+        >>> nx.draw(nx.full_rary_tree(2, 10))
+
+    Parameters
+    ----------
+    r : int
+        branching factor of the tree
+    n : int
+        Number of nodes in the tree
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    G : networkx Graph
+        An r-ary tree with n nodes
+
+    References
+    ----------
+    .. [1] An introduction to data structures and algorithms,
+           James Andrew Storer,  Birkhauser Boston 2001, (page 225).
+    """
+    G = empty_graph(n, create_using)
+    G.add_edges_from(_tree_edges(n, r))
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def kneser_graph(n, k):
+    """Returns the Kneser Graph with parameters `n` and `k`.
+
+    The Kneser Graph has nodes that are k-tuples (subsets) of the integers
+    between 0 and ``n-1``. Nodes are adjacent if their corresponding sets are disjoint.
+
+    Parameters
+    ----------
+    n: int
+        Number of integers from which to make node subsets.
+        Subsets are drawn from ``set(range(n))``.
+    k: int
+        Size of the subsets.
+
+    Returns
+    -------
+    G : NetworkX Graph
+
+    Examples
+    --------
+    >>> G = nx.kneser_graph(5, 2)
+    >>> G.number_of_nodes()
+    10
+    >>> G.number_of_edges()
+    15
+    >>> nx.is_isomorphic(G, nx.petersen_graph())
+    True
+    """
+    if n <= 0:
+        raise NetworkXError("n should be greater than zero")
+    if k <= 0 or k > n:
+        raise NetworkXError("k should be greater than zero and smaller than n")
+
+    G = nx.Graph()
+    # Create all k-subsets of [0, 1, ..., n-1]
+    subsets = list(itertools.combinations(range(n), k))
+
+    if 2 * k > n:
+        G.add_nodes_from(subsets)
+
+    universe = set(range(n))
+    comb = itertools.combinations  # only to make it all fit on one line
+    G.add_edges_from((s, t) for s in subsets for t in comb(universe - set(s), k))
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def balanced_tree(r, h, create_using=None):
+    """Returns the perfectly balanced `r`-ary tree of height `h`.
+
+    .. plot::
+
+        >>> nx.draw(nx.balanced_tree(2, 3))
+
+    Parameters
+    ----------
+    r : int
+        Branching factor of the tree; each node will have `r`
+        children.
+
+    h : int
+        Height of the tree.
+
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    G : NetworkX graph
+        A balanced `r`-ary tree of height `h`.
+
+    Notes
+    -----
+    This is the rooted tree where all leaves are at distance `h` from
+    the root. The root has degree `r` and all other internal nodes
+    have degree `r + 1`.
+
+    Node labels are integers, starting from zero.
+
+    A balanced tree is also known as a *complete r-ary tree*.
+
+    """
+    # The number of nodes in the balanced tree is `1 + r + ... + r^h`,
+    # which is computed by using the closed-form formula for a geometric
+    # sum with ratio `r`. In the special case that `r` is 1, the number
+    # of nodes is simply `h + 1` (since the tree is actually a path
+    # graph).
+    if r == 1:
+        n = h + 1
+    else:
+        # This must be an integer if both `r` and `h` are integers. If
+        # they are not, we force integer division anyway.
+        n = (1 - r ** (h + 1)) // (1 - r)
+    return full_rary_tree(r, n, create_using=create_using)
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def barbell_graph(m1, m2, create_using=None):
+    """Returns the Barbell Graph: two complete graphs connected by a path.
+
+    .. plot::
+
+        >>> nx.draw(nx.barbell_graph(4, 2))
+
+    Parameters
+    ----------
+    m1 : int
+        Size of the left and right barbells, must be greater than 2.
+
+    m2 : int
+        Length of the path connecting the barbells.
+
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+       Only undirected Graphs are supported.
+
+    Returns
+    -------
+    G : NetworkX graph
+        A barbell graph.
+
+    Notes
+    -----
+
+
+    Two identical complete graphs $K_{m1}$ form the left and right bells,
+    and are connected by a path $P_{m2}$.
+
+    The `2*m1+m2`  nodes are numbered
+        `0, ..., m1-1` for the left barbell,
+        `m1, ..., m1+m2-1` for the path,
+        and `m1+m2, ..., 2*m1+m2-1` for the right barbell.
+
+    The 3 subgraphs are joined via the edges `(m1-1, m1)` and
+    `(m1+m2-1, m1+m2)`. If `m2=0`, this is merely two complete
+    graphs joined together.
+
+    This graph is an extremal example in David Aldous
+    and Jim Fill's e-text on Random Walks on Graphs.
+
+    """
+    if m1 < 2:
+        raise NetworkXError("Invalid graph description, m1 should be >=2")
+    if m2 < 0:
+        raise NetworkXError("Invalid graph description, m2 should be >=0")
+
+    # left barbell
+    G = complete_graph(m1, create_using)
+    if G.is_directed():
+        raise NetworkXError("Directed Graph not supported")
+
+    # connecting path
+    G.add_nodes_from(range(m1, m1 + m2 - 1))
+    if m2 > 1:
+        G.add_edges_from(pairwise(range(m1, m1 + m2)))
+
+    # right barbell
+    G.add_edges_from(
+        (u, v) for u in range(m1 + m2, 2 * m1 + m2) for v in range(u + 1, 2 * m1 + m2)
+    )
+
+    # connect it up
+    G.add_edge(m1 - 1, m1)
+    if m2 > 0:
+        G.add_edge(m1 + m2 - 1, m1 + m2)
+
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def binomial_tree(n, create_using=None):
+    """Returns the Binomial Tree of order n.
+
+    The binomial tree of order 0 consists of a single node. A binomial tree of order k
+    is defined recursively by linking two binomial trees of order k-1: the root of one is
+    the leftmost child of the root of the other.
+
+    .. plot::
+
+        >>> nx.draw(nx.binomial_tree(3))
+
+    Parameters
+    ----------
+    n : int
+        Order of the binomial tree.
+
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    G : NetworkX graph
+        A binomial tree of $2^n$ nodes and $2^n - 1$ edges.
+
+    """
+    G = nx.empty_graph(1, create_using)
+
+    N = 1
+    for i in range(n):
+        # Use G.edges() to ensure 2-tuples. G.edges is 3-tuple for MultiGraph
+        edges = [(u + N, v + N) for (u, v) in G.edges()]
+        G.add_edges_from(edges)
+        G.add_edge(0, N)
+        N *= 2
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number(0)
+def complete_graph(n, create_using=None):
+    """Return the complete graph `K_n` with n nodes.
+
+    A complete graph on `n` nodes means that all pairs
+    of distinct nodes have an edge connecting them.
+
+    .. plot::
+
+        >>> nx.draw(nx.complete_graph(5))
+
+    Parameters
+    ----------
+    n : int or iterable container of nodes
+        If n is an integer, nodes are from range(n).
+        If n is a container of nodes, those nodes appear in the graph.
+        Warning: n is not checked for duplicates and if present the
+        resulting graph may not be as desired. Make sure you have no duplicates.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Examples
+    --------
+    >>> G = nx.complete_graph(9)
+    >>> len(G)
+    9
+    >>> G.size()
+    36
+    >>> G = nx.complete_graph(range(11, 14))
+    >>> list(G.nodes())
+    [11, 12, 13]
+    >>> G = nx.complete_graph(4, nx.DiGraph())
+    >>> G.is_directed()
+    True
+
+    """
+    _, nodes = n
+    G = empty_graph(nodes, create_using)
+    if len(nodes) > 1:
+        if G.is_directed():
+            edges = itertools.permutations(nodes, 2)
+        else:
+            edges = itertools.combinations(nodes, 2)
+        G.add_edges_from(edges)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def circular_ladder_graph(n, create_using=None):
+    """Returns the circular ladder graph $CL_n$ of length n.
+
+    $CL_n$ consists of two concentric n-cycles in which
+    each of the n pairs of concentric nodes are joined by an edge.
+
+    Node labels are the integers 0 to n-1
+
+    .. plot::
+
+        >>> nx.draw(nx.circular_ladder_graph(5))
+
+    """
+    G = ladder_graph(n, create_using)
+    G.add_edge(0, n - 1)
+    G.add_edge(n, 2 * n - 1)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def circulant_graph(n, offsets, create_using=None):
+    r"""Returns the circulant graph $Ci_n(x_1, x_2, ..., x_m)$ with $n$ nodes.
+
+    The circulant graph $Ci_n(x_1, ..., x_m)$ consists of $n$ nodes $0, ..., n-1$
+    such that node $i$ is connected to nodes $(i + x) \mod n$ and $(i - x) \mod n$
+    for all $x$ in $x_1, ..., x_m$. Thus $Ci_n(1)$ is a cycle graph.
+
+    .. plot::
+
+        >>> nx.draw(nx.circulant_graph(10, [1]))
+
+    Parameters
+    ----------
+    n : integer
+        The number of nodes in the graph.
+    offsets : list of integers
+        A list of node offsets, $x_1$ up to $x_m$, as described above.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    NetworkX Graph of type create_using
+
+    Examples
+    --------
+    Many well-known graph families are subfamilies of the circulant graphs;
+    for example, to create the cycle graph on n points, we connect every
+    node to nodes on either side (with offset plus or minus one). For n = 10,
+
+    >>> G = nx.circulant_graph(10, [1])
+    >>> edges = [
+    ...     (0, 9),
+    ...     (0, 1),
+    ...     (1, 2),
+    ...     (2, 3),
+    ...     (3, 4),
+    ...     (4, 5),
+    ...     (5, 6),
+    ...     (6, 7),
+    ...     (7, 8),
+    ...     (8, 9),
+    ... ]
+    >>> sorted(edges) == sorted(G.edges())
+    True
+
+    Similarly, we can create the complete graph
+    on 5 points with the set of offsets [1, 2]:
+
+    >>> G = nx.circulant_graph(5, [1, 2])
+    >>> edges = [
+    ...     (0, 1),
+    ...     (0, 2),
+    ...     (0, 3),
+    ...     (0, 4),
+    ...     (1, 2),
+    ...     (1, 3),
+    ...     (1, 4),
+    ...     (2, 3),
+    ...     (2, 4),
+    ...     (3, 4),
+    ... ]
+    >>> sorted(edges) == sorted(G.edges())
+    True
+
+    """
+    G = empty_graph(n, create_using)
+    for i in range(n):
+        for j in offsets:
+            G.add_edge(i, (i - j) % n)
+            G.add_edge(i, (i + j) % n)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number(0)
+def cycle_graph(n, create_using=None):
+    """Returns the cycle graph $C_n$ of cyclically connected nodes.
+
+    $C_n$ is a path with its two end-nodes connected.
+
+    .. plot::
+
+        >>> nx.draw(nx.cycle_graph(5))
+
+    Parameters
+    ----------
+    n : int or iterable container of nodes
+        If n is an integer, nodes are from `range(n)`.
+        If n is a container of nodes, those nodes appear in the graph.
+        Warning: n is not checked for duplicates and if present the
+        resulting graph may not be as desired. Make sure you have no duplicates.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Notes
+    -----
+    If create_using is directed, the direction is in increasing order.
+
+    """
+    _, nodes = n
+    G = empty_graph(nodes, create_using)
+    G.add_edges_from(pairwise(nodes, cyclic=True))
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def dorogovtsev_goltsev_mendes_graph(n, create_using=None):
+    """Returns the hierarchically constructed Dorogovtsev--Goltsev--Mendes graph.
+
+    The Dorogovtsev--Goltsev--Mendes [1]_ procedure deterministically produces a
+    scale-free graph with ``3/2 * (3**(n-1) + 1)`` nodes
+    and ``3**n`` edges for a given `n`.
+
+    Note that `n` denotes the number of times the state transition is applied,
+    starting from the base graph with ``n = 0`` (no transitions), as in [2]_.
+    This is different from the parameter ``t = n - 1`` in [1]_.
+
+    .. plot::
+
+        >>> nx.draw(nx.dorogovtsev_goltsev_mendes_graph(3))
+
+    Parameters
+    ----------
+    n : integer
+        The generation number.
+
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+        Graph type to create. Directed graphs and multigraphs are not supported.
+
+    Returns
+    -------
+    G : NetworkX `Graph`
+
+    Raises
+    ------
+    NetworkXError
+        If `n` is less than zero.
+
+        If `create_using` is a directed graph or multigraph.
+
+    Examples
+    --------
+    >>> G = nx.dorogovtsev_goltsev_mendes_graph(3)
+    >>> G.number_of_nodes()
+    15
+    >>> G.number_of_edges()
+    27
+    >>> nx.is_planar(G)
+    True
+
+    References
+    ----------
+    .. [1] S. N. Dorogovtsev, A. V. Goltsev and J. F. F. Mendes,
+        "Pseudofractal scale-free web", Physical Review E 65, 066122, 2002.
+        https://arxiv.org/pdf/cond-mat/0112143.pdf
+    .. [2] Weisstein, Eric W. "Dorogovtsev--Goltsev--Mendes Graph".
+        From MathWorld--A Wolfram Web Resource.
+        https://mathworld.wolfram.com/Dorogovtsev-Goltsev-MendesGraph.html
+    """
+    if n < 0:
+        raise NetworkXError("n must be greater than or equal to 0")
+
+    G = empty_graph(0, create_using)
+    if G.is_directed():
+        raise NetworkXError("directed graph not supported")
+    if G.is_multigraph():
+        raise NetworkXError("multigraph not supported")
+
+    G.add_edge(0, 1)
+    new_node = 2  # next node to be added
+    for _ in range(n):  # iterate over number of generations.
+        new_edges = []
+        for u, v in G.edges():
+            new_edges.append((u, new_node))
+            new_edges.append((v, new_node))
+            new_node += 1
+
+        G.add_edges_from(new_edges)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number(0)
+def empty_graph(n=0, create_using=None, default=Graph):
+    """Returns the empty graph with n nodes and zero edges.
+
+    .. plot::
+
+        >>> nx.draw(nx.empty_graph(5))
+
+    Parameters
+    ----------
+    n : int or iterable container of nodes (default = 0)
+        If n is an integer, nodes are from `range(n)`.
+        If n is a container of nodes, those nodes appear in the graph.
+    create_using : Graph Instance, Constructor or None
+        Indicator of type of graph to return.
+        If a Graph-type instance, then clear and use it.
+        If None, use the `default` constructor.
+        If a constructor, call it to create an empty graph.
+    default : Graph constructor (optional, default = nx.Graph)
+        The constructor to use if create_using is None.
+        If None, then nx.Graph is used.
+        This is used when passing an unknown `create_using` value
+        through your home-grown function to `empty_graph` and
+        you want a default constructor other than nx.Graph.
+
+    Examples
+    --------
+    >>> G = nx.empty_graph(10)
+    >>> G.number_of_nodes()
+    10
+    >>> G.number_of_edges()
+    0
+    >>> G = nx.empty_graph("ABC")
+    >>> G.number_of_nodes()
+    3
+    >>> sorted(G)
+    ['A', 'B', 'C']
+
+    Notes
+    -----
+    The variable create_using should be a Graph Constructor or a
+    "graph"-like object. Constructors, e.g. `nx.Graph` or `nx.MultiGraph`
+    will be used to create the returned graph. "graph"-like objects
+    will be cleared (nodes and edges will be removed) and refitted as
+    an empty "graph" with nodes specified in n. This capability
+    is useful for specifying the class-nature of the resulting empty
+    "graph" (i.e. Graph, DiGraph, MyWeirdGraphClass, etc.).
+
+    The variable create_using has three main uses:
+    Firstly, the variable create_using can be used to create an
+    empty digraph, multigraph, etc.  For example,
+
+    >>> n = 10
+    >>> G = nx.empty_graph(n, create_using=nx.DiGraph)
+
+    will create an empty digraph on n nodes.
+
+    Secondly, one can pass an existing graph (digraph, multigraph,
+    etc.) via create_using. For example, if G is an existing graph
+    (resp. digraph, multigraph, etc.), then empty_graph(n, create_using=G)
+    will empty G (i.e. delete all nodes and edges using G.clear())
+    and then add n nodes and zero edges, and return the modified graph.
+
+    Thirdly, when constructing your home-grown graph creation function
+    you can use empty_graph to construct the graph by passing a user
+    defined create_using to empty_graph. In this case, if you want the
+    default constructor to be other than nx.Graph, specify `default`.
+
+    >>> def mygraph(n, create_using=None):
+    ...     G = nx.empty_graph(n, create_using, nx.MultiGraph)
+    ...     G.add_edges_from([(0, 1), (0, 1)])
+    ...     return G
+    >>> G = mygraph(3)
+    >>> G.is_multigraph()
+    True
+    >>> G = mygraph(3, nx.Graph)
+    >>> G.is_multigraph()
+    False
+
+    See also create_empty_copy(G).
+
+    """
+    if create_using is None:
+        G = default()
+    elif isinstance(create_using, type):
+        G = create_using()
+    elif not hasattr(create_using, "adj"):
+        raise TypeError("create_using is not a valid NetworkX graph type or instance")
+    else:
+        # create_using is a NetworkX style Graph
+        create_using.clear()
+        G = create_using
+
+    _, nodes = n
+    G.add_nodes_from(nodes)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def ladder_graph(n, create_using=None):
+    """Returns the Ladder graph of length n.
+
+    This is two paths of n nodes, with
+    each pair connected by a single edge.
+
+    Node labels are the integers 0 to 2*n - 1.
+
+    .. plot::
+
+        >>> nx.draw(nx.ladder_graph(5))
+
+    """
+    G = empty_graph(2 * n, create_using)
+    if G.is_directed():
+        raise NetworkXError("Directed Graph not supported")
+    G.add_edges_from(pairwise(range(n)))
+    G.add_edges_from(pairwise(range(n, 2 * n)))
+    G.add_edges_from((v, v + n) for v in range(n))
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number([0, 1])
+def lollipop_graph(m, n, create_using=None):
+    """Returns the Lollipop Graph; ``K_m`` connected to ``P_n``.
+
+    This is the Barbell Graph without the right barbell.
+
+    .. plot::
+
+        >>> nx.draw(nx.lollipop_graph(3, 4))
+
+    Parameters
+    ----------
+    m, n : int or iterable container of nodes
+        If an integer, nodes are from ``range(m)`` and ``range(m, m+n)``.
+        If a container of nodes, those nodes appear in the graph.
+        Warning: `m` and `n` are not checked for duplicates and if present the
+        resulting graph may not be as desired. Make sure you have no duplicates.
+
+        The nodes for `m` appear in the complete graph $K_m$ and the nodes
+        for `n` appear in the path $P_n$
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    Networkx graph
+       A complete graph with `m` nodes connected to a path of length `n`.
+
+    Notes
+    -----
+    The 2 subgraphs are joined via an edge ``(m-1, m)``.
+    If ``n=0``, this is merely a complete graph.
+
+    (This graph is an extremal example in David Aldous and Jim
+    Fill's etext on Random Walks on Graphs.)
+
+    """
+    m, m_nodes = m
+    M = len(m_nodes)
+    if M < 2:
+        raise NetworkXError("Invalid description: m should indicate at least 2 nodes")
+
+    n, n_nodes = n
+    if isinstance(m, numbers.Integral) and isinstance(n, numbers.Integral):
+        n_nodes = list(range(M, M + n))
+    N = len(n_nodes)
+
+    # the ball
+    G = complete_graph(m_nodes, create_using)
+    if G.is_directed():
+        raise NetworkXError("Directed Graph not supported")
+
+    # the stick
+    G.add_nodes_from(n_nodes)
+    if N > 1:
+        G.add_edges_from(pairwise(n_nodes))
+
+    if len(G) != M + N:
+        raise NetworkXError("Nodes must be distinct in containers m and n")
+
+    # connect ball to stick
+    if M > 0 and N > 0:
+        G.add_edge(m_nodes[-1], n_nodes[0])
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def null_graph(create_using=None):
+    """Returns the Null graph with no nodes or edges.
+
+    See empty_graph for the use of create_using.
+
+    """
+    G = empty_graph(0, create_using)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number(0)
+def path_graph(n, create_using=None):
+    """Returns the Path graph `P_n` of linearly connected nodes.
+
+    .. plot::
+
+        >>> nx.draw(nx.path_graph(5))
+
+    Parameters
+    ----------
+    n : int or iterable
+        If an integer, nodes are 0 to n - 1.
+        If an iterable of nodes, in the order they appear in the path.
+        Warning: n is not checked for duplicates and if present the
+        resulting graph may not be as desired. Make sure you have no duplicates.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    """
+    _, nodes = n
+    G = empty_graph(nodes, create_using)
+    G.add_edges_from(pairwise(nodes))
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number(0)
+def star_graph(n, create_using=None):
+    """Return the star graph
+
+    The star graph consists of one center node connected to n outer nodes.
+
+    .. plot::
+
+        >>> nx.draw(nx.star_graph(6))
+
+    Parameters
+    ----------
+    n : int or iterable
+        If an integer, node labels are 0 to n with center 0.
+        If an iterable of nodes, the center is the first.
+        Warning: n is not checked for duplicates and if present the
+        resulting graph may not be as desired. Make sure you have no duplicates.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Notes
+    -----
+    The graph has n+1 nodes for integer n.
+    So star_graph(3) is the same as star_graph(range(4)).
+    """
+    n, nodes = n
+    if isinstance(n, numbers.Integral):
+        nodes.append(int(n))  # there should be n+1 nodes
+    G = empty_graph(nodes, create_using)
+    if G.is_directed():
+        raise NetworkXError("Directed Graph not supported")
+
+    if len(nodes) > 1:
+        hub, *spokes = nodes
+        G.add_edges_from((hub, node) for node in spokes)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number([0, 1])
+def tadpole_graph(m, n, create_using=None):
+    """Returns the (m,n)-tadpole graph; ``C_m`` connected to ``P_n``.
+
+    This graph on m+n nodes connects a cycle of size `m` to a path of length `n`.
+    It looks like a tadpole. It is also called a kite graph or a dragon graph.
+
+    .. plot::
+
+        >>> nx.draw(nx.tadpole_graph(3, 5))
+
+    Parameters
+    ----------
+    m, n : int or iterable container of nodes
+        If an integer, nodes are from ``range(m)`` and ``range(m,m+n)``.
+        If a container of nodes, those nodes appear in the graph.
+        Warning: `m` and `n` are not checked for duplicates and if present the
+        resulting graph may not be as desired.
+
+        The nodes for `m` appear in the cycle graph $C_m$ and the nodes
+        for `n` appear in the path $P_n$.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    Networkx graph
+       A cycle of size `m` connected to a path of length `n`.
+
+    Raises
+    ------
+    NetworkXError
+        If ``m < 2``. The tadpole graph is undefined for ``m<2``.
+
+    Notes
+    -----
+    The 2 subgraphs are joined via an edge ``(m-1, m)``.
+    If ``n=0``, this is a cycle graph.
+    `m` and/or `n` can be a container of nodes instead of an integer.
+
+    """
+    m, m_nodes = m
+    M = len(m_nodes)
+    if M < 2:
+        raise NetworkXError("Invalid description: m should indicate at least 2 nodes")
+
+    n, n_nodes = n
+    if isinstance(m, numbers.Integral) and isinstance(n, numbers.Integral):
+        n_nodes = list(range(M, M + n))
+
+    # the circle
+    G = cycle_graph(m_nodes, create_using)
+    if G.is_directed():
+        raise NetworkXError("Directed Graph not supported")
+
+    # the stick
+    nx.add_path(G, [m_nodes[-1]] + list(n_nodes))
+
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def trivial_graph(create_using=None):
+    """Return the Trivial graph with one node (with label 0) and no edges.
+
+    .. plot::
+
+        >>> nx.draw(nx.trivial_graph(), with_labels=True)
+
+    """
+    G = empty_graph(1, create_using)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def turan_graph(n, r):
+    r"""Return the Turan Graph
+
+    The Turan Graph is a complete multipartite graph on $n$ nodes
+    with $r$ disjoint subsets. That is, edges connect each node to
+    every node not in its subset.
+
+    Given $n$ and $r$, we create a complete multipartite graph with
+    $r-(n \mod r)$ partitions of size $n/r$, rounded down, and
+    $n \mod r$ partitions of size $n/r+1$, rounded down.
+
+    .. plot::
+
+        >>> nx.draw(nx.turan_graph(6, 2))
+
+    Parameters
+    ----------
+    n : int
+        The number of nodes.
+    r : int
+        The number of partitions.
+        Must be less than or equal to n.
+
+    Notes
+    -----
+    Must satisfy $1 <= r <= n$.
+    The graph has $(r-1)(n^2)/(2r)$ edges, rounded down.
+    """
+
+    if not 1 <= r <= n:
+        raise NetworkXError("Must satisfy 1 <= r <= n")
+
+    partitions = [n // r] * (r - (n % r)) + [n // r + 1] * (n % r)
+    G = complete_multipartite_graph(*partitions)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number(0)
+def wheel_graph(n, create_using=None):
+    """Return the wheel graph
+
+    The wheel graph consists of a hub node connected to a cycle of (n-1) nodes.
+
+    .. plot::
+
+        >>> nx.draw(nx.wheel_graph(5))
+
+    Parameters
+    ----------
+    n : int or iterable
+        If an integer, node labels are 0 to n with center 0.
+        If an iterable of nodes, the center is the first.
+        Warning: n is not checked for duplicates and if present the
+        resulting graph may not be as desired. Make sure you have no duplicates.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Node labels are the integers 0 to n - 1.
+    """
+    _, nodes = n
+    G = empty_graph(nodes, create_using)
+    if G.is_directed():
+        raise NetworkXError("Directed Graph not supported")
+
+    if len(nodes) > 1:
+        hub, *rim = nodes
+        G.add_edges_from((hub, node) for node in rim)
+        if len(rim) > 1:
+            G.add_edges_from(pairwise(rim, cyclic=True))
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def complete_multipartite_graph(*subset_sizes):
+    """Returns the complete multipartite graph with the specified subset sizes.
+
+    .. plot::
+
+        >>> nx.draw(nx.complete_multipartite_graph(1, 2, 3))
+
+    Parameters
+    ----------
+    subset_sizes : tuple of integers or tuple of node iterables
+       The arguments can either all be integer number of nodes or they
+       can all be iterables of nodes. If integers, they represent the
+       number of nodes in each subset of the multipartite graph.
+       If iterables, each is used to create the nodes for that subset.
+       The length of subset_sizes is the number of subsets.
+
+    Returns
+    -------
+    G : NetworkX Graph
+       Returns the complete multipartite graph with the specified subsets.
+
+       For each node, the node attribute 'subset' is an integer
+       indicating which subset contains the node.
+
+    Examples
+    --------
+    Creating a complete tripartite graph, with subsets of one, two, and three
+    nodes, respectively.
+
+        >>> G = nx.complete_multipartite_graph(1, 2, 3)
+        >>> [G.nodes[u]["subset"] for u in G]
+        [0, 1, 1, 2, 2, 2]
+        >>> list(G.edges(0))
+        [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)]
+        >>> list(G.edges(2))
+        [(2, 0), (2, 3), (2, 4), (2, 5)]
+        >>> list(G.edges(4))
+        [(4, 0), (4, 1), (4, 2)]
+
+        >>> G = nx.complete_multipartite_graph("a", "bc", "def")
+        >>> [G.nodes[u]["subset"] for u in sorted(G)]
+        [0, 1, 1, 2, 2, 2]
+
+    Notes
+    -----
+    This function generalizes several other graph builder functions.
+
+    - If no subset sizes are given, this returns the null graph.
+    - If a single subset size `n` is given, this returns the empty graph on
+      `n` nodes.
+    - If two subset sizes `m` and `n` are given, this returns the complete
+      bipartite graph on `m + n` nodes.
+    - If subset sizes `1` and `n` are given, this returns the star graph on
+      `n + 1` nodes.
+
+    See also
+    --------
+    complete_bipartite_graph
+    """
+    # The complete multipartite graph is an undirected simple graph.
+    G = Graph()
+
+    if len(subset_sizes) == 0:
+        return G
+
+    # set up subsets of nodes
+    try:
+        extents = pairwise(itertools.accumulate((0,) + subset_sizes))
+        subsets = [range(start, end) for start, end in extents]
+    except TypeError:
+        subsets = subset_sizes
+    else:
+        if any(size < 0 for size in subset_sizes):
+            raise NetworkXError(f"Negative number of nodes not valid: {subset_sizes}")
+
+    # add nodes with subset attribute
+    # while checking that ints are not mixed with iterables
+    try:
+        for i, subset in enumerate(subsets):
+            G.add_nodes_from(subset, subset=i)
+    except TypeError as err:
+        raise NetworkXError("Arguments must be all ints or all iterables") from err
+
+    # Across subsets, all nodes should be adjacent.
+    # We can use itertools.combinations() because undirected.
+    for subset1, subset2 in itertools.combinations(subsets, 2):
+        G.add_edges_from(itertools.product(subset1, subset2))
+    return G

.venv/lib/python3.11/site-packages/networkx/generators/cographs.py

@@ -0,0 +1,68 @@
+r"""Generators for cographs
+
+A cograph is a graph containing no path on four vertices.
+Cographs or $P_4$-free graphs can be obtained from a single vertex
+by disjoint union and complementation operations.
+
+References
+----------
+.. [0] D.G. Corneil, H. Lerchs, L.Stewart Burlingham,
+    "Complement reducible graphs",
+    Discrete Applied Mathematics, Volume 3, Issue 3, 1981, Pages 163-174,
+    ISSN 0166-218X.
+"""
+
+import networkx as nx
+from networkx.utils import py_random_state
+
+__all__ = ["random_cograph"]
+
+
+@py_random_state(1)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def random_cograph(n, seed=None):
+    r"""Returns a random cograph with $2 ^ n$ nodes.
+
+    A cograph is a graph containing no path on four vertices.
+    Cographs or $P_4$-free graphs can be obtained from a single vertex
+    by disjoint union and complementation operations.
+
+    This generator starts off from a single vertex and performs disjoint
+    union and full join operations on itself.
+    The decision on which operation will take place is random.
+
+    Parameters
+    ----------
+    n : int
+        The order of the cograph.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    G : A random graph containing no path on four vertices.
+
+    See Also
+    --------
+    full_join
+    union
+
+    References
+    ----------
+    .. [1] D.G. Corneil, H. Lerchs, L.Stewart Burlingham,
+       "Complement reducible graphs",
+       Discrete Applied Mathematics, Volume 3, Issue 3, 1981, Pages 163-174,
+       ISSN 0166-218X.
+    """
+    R = nx.empty_graph(1)
+
+    for i in range(n):
+        RR = nx.relabel_nodes(R.copy(), lambda x: x + len(R))
+
+        if seed.randint(0, 1) == 0:
+            R = nx.full_join(R, RR)
+        else:
+            R = nx.disjoint_union(R, RR)
+
+    return R

.venv/lib/python3.11/site-packages/networkx/generators/community.py

@@ -0,0 +1,1070 @@
+"""Generators for classes of graphs used in studying social networks."""
+
+import itertools
+import math
+
+import networkx as nx
+from networkx.utils import py_random_state
+
+__all__ = [
+    "caveman_graph",
+    "connected_caveman_graph",
+    "relaxed_caveman_graph",
+    "random_partition_graph",
+    "planted_partition_graph",
+    "gaussian_random_partition_graph",
+    "ring_of_cliques",
+    "windmill_graph",
+    "stochastic_block_model",
+    "LFR_benchmark_graph",
+]
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def caveman_graph(l, k):
+    """Returns a caveman graph of `l` cliques of size `k`.
+
+    Parameters
+    ----------
+    l : int
+      Number of cliques
+    k : int
+      Size of cliques
+
+    Returns
+    -------
+    G : NetworkX Graph
+      caveman graph
+
+    Notes
+    -----
+    This returns an undirected graph, it can be converted to a directed
+    graph using :func:`nx.to_directed`, or a multigraph using
+    ``nx.MultiGraph(nx.caveman_graph(l, k))``. Only the undirected version is
+    described in [1]_ and it is unclear which of the directed
+    generalizations is most useful.
+
+    Examples
+    --------
+    >>> G = nx.caveman_graph(3, 3)
+
+    See also
+    --------
+
+    connected_caveman_graph
+
+    References
+    ----------
+    .. [1] Watts, D. J. 'Networks, Dynamics, and the Small-World Phenomenon.'
+       Amer. J. Soc. 105, 493-527, 1999.
+    """
+    # l disjoint cliques of size k
+    G = nx.empty_graph(l * k)
+    if k > 1:
+        for start in range(0, l * k, k):
+            edges = itertools.combinations(range(start, start + k), 2)
+            G.add_edges_from(edges)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def connected_caveman_graph(l, k):
+    """Returns a connected caveman graph of `l` cliques of size `k`.
+
+    The connected caveman graph is formed by creating `n` cliques of size
+    `k`, then a single edge in each clique is rewired to a node in an
+    adjacent clique.
+
+    Parameters
+    ----------
+    l : int
+      number of cliques
+    k : int
+      size of cliques (k at least 2 or NetworkXError is raised)
+
+    Returns
+    -------
+    G : NetworkX Graph
+      connected caveman graph
+
+    Raises
+    ------
+    NetworkXError
+        If the size of cliques `k` is smaller than 2.
+
+    Notes
+    -----
+    This returns an undirected graph, it can be converted to a directed
+    graph using :func:`nx.to_directed`, or a multigraph using
+    ``nx.MultiGraph(nx.caveman_graph(l, k))``. Only the undirected version is
+    described in [1]_ and it is unclear which of the directed
+    generalizations is most useful.
+
+    Examples
+    --------
+    >>> G = nx.connected_caveman_graph(3, 3)
+
+    References
+    ----------
+    .. [1] Watts, D. J. 'Networks, Dynamics, and the Small-World Phenomenon.'
+       Amer. J. Soc. 105, 493-527, 1999.
+    """
+    if k < 2:
+        raise nx.NetworkXError(
+            "The size of cliques in a connected caveman graph must be at least 2."
+        )
+
+    G = nx.caveman_graph(l, k)
+    for start in range(0, l * k, k):
+        G.remove_edge(start, start + 1)
+        G.add_edge(start, (start - 1) % (l * k))
+    return G
+
+
+@py_random_state(3)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def relaxed_caveman_graph(l, k, p, seed=None):
+    """Returns a relaxed caveman graph.
+
+    A relaxed caveman graph starts with `l` cliques of size `k`.  Edges are
+    then randomly rewired with probability `p` to link different cliques.
+
+    Parameters
+    ----------
+    l : int
+      Number of groups
+    k : int
+      Size of cliques
+    p : float
+      Probability of rewiring each edge.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    G : NetworkX Graph
+      Relaxed Caveman Graph
+
+    Raises
+    ------
+    NetworkXError
+     If p is not in [0,1]
+
+    Examples
+    --------
+    >>> G = nx.relaxed_caveman_graph(2, 3, 0.1, seed=42)
+
+    References
+    ----------
+    .. [1] Santo Fortunato, Community Detection in Graphs,
+       Physics Reports Volume 486, Issues 3-5, February 2010, Pages 75-174.
+       https://arxiv.org/abs/0906.0612
+    """
+    G = nx.caveman_graph(l, k)
+    nodes = list(G)
+    for u, v in G.edges():
+        if seed.random() < p:  # rewire the edge
+            x = seed.choice(nodes)
+            if G.has_edge(u, x):
+                continue
+            G.remove_edge(u, v)
+            G.add_edge(u, x)
+    return G
+
+
+@py_random_state(3)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def random_partition_graph(sizes, p_in, p_out, seed=None, directed=False):
+    """Returns the random partition graph with a partition of sizes.
+
+    A partition graph is a graph of communities with sizes defined by
+    s in sizes. Nodes in the same group are connected with probability
+    p_in and nodes of different groups are connected with probability
+    p_out.
+
+    Parameters
+    ----------
+    sizes : list of ints
+      Sizes of groups
+    p_in : float
+      probability of edges with in groups
+    p_out : float
+      probability of edges between groups
+    directed : boolean optional, default=False
+      Whether to create a directed graph
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    G : NetworkX Graph or DiGraph
+      random partition graph of size sum(gs)
+
+    Raises
+    ------
+    NetworkXError
+      If p_in or p_out is not in [0,1]
+
+    Examples
+    --------
+    >>> G = nx.random_partition_graph([10, 10, 10], 0.25, 0.01)
+    >>> len(G)
+    30
+    >>> partition = G.graph["partition"]
+    >>> len(partition)
+    3
+
+    Notes
+    -----
+    This is a generalization of the planted-l-partition described in
+    [1]_.  It allows for the creation of groups of any size.
+
+    The partition is store as a graph attribute 'partition'.
+
+    References
+    ----------
+    .. [1] Santo Fortunato 'Community Detection in Graphs' Physical Reports
+       Volume 486, Issue 3-5 p. 75-174. https://arxiv.org/abs/0906.0612
+    """
+    # Use geometric method for O(n+m) complexity algorithm
+    # partition = nx.community_sets(nx.get_node_attributes(G, 'affiliation'))
+    if not 0.0 <= p_in <= 1.0:
+        raise nx.NetworkXError("p_in must be in [0,1]")
+    if not 0.0 <= p_out <= 1.0:
+        raise nx.NetworkXError("p_out must be in [0,1]")
+
+    # create connection matrix
+    num_blocks = len(sizes)
+    p = [[p_out for s in range(num_blocks)] for r in range(num_blocks)]
+    for r in range(num_blocks):
+        p[r][r] = p_in
+
+    return stochastic_block_model(
+        sizes,
+        p,
+        nodelist=None,
+        seed=seed,
+        directed=directed,
+        selfloops=False,
+        sparse=True,
+    )
+
+
+@py_random_state(4)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def planted_partition_graph(l, k, p_in, p_out, seed=None, directed=False):
+    """Returns the planted l-partition graph.
+
+    This model partitions a graph with n=l*k vertices in
+    l groups with k vertices each. Vertices of the same
+    group are linked with a probability p_in, and vertices
+    of different groups are linked with probability p_out.
+
+    Parameters
+    ----------
+    l : int
+      Number of groups
+    k : int
+      Number of vertices in each group
+    p_in : float
+      probability of connecting vertices within a group
+    p_out : float
+      probability of connected vertices between groups
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+    directed : bool,optional (default=False)
+      If True return a directed graph
+
+    Returns
+    -------
+    G : NetworkX Graph or DiGraph
+      planted l-partition graph
+
+    Raises
+    ------
+    NetworkXError
+      If `p_in`, `p_out` are not in `[0, 1]`
+
+    Examples
+    --------
+    >>> G = nx.planted_partition_graph(4, 3, 0.5, 0.1, seed=42)
+
+    See Also
+    --------
+    random_partition_model
+
+    References
+    ----------
+    .. [1] A. Condon, R.M. Karp, Algorithms for graph partitioning
+        on the planted partition model,
+        Random Struct. Algor. 18 (2001) 116-140.
+
+    .. [2] Santo Fortunato 'Community Detection in Graphs' Physical Reports
+       Volume 486, Issue 3-5 p. 75-174. https://arxiv.org/abs/0906.0612
+    """
+    return random_partition_graph([k] * l, p_in, p_out, seed=seed, directed=directed)
+
+
+@py_random_state(6)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def gaussian_random_partition_graph(n, s, v, p_in, p_out, directed=False, seed=None):
+    """Generate a Gaussian random partition graph.
+
+    A Gaussian random partition graph is created by creating k partitions
+    each with a size drawn from a normal distribution with mean s and variance
+    s/v. Nodes are connected within clusters with probability p_in and
+    between clusters with probability p_out[1]
+
+    Parameters
+    ----------
+    n : int
+      Number of nodes in the graph
+    s : float
+      Mean cluster size
+    v : float
+      Shape parameter. The variance of cluster size distribution is s/v.
+    p_in : float
+      Probability of intra cluster connection.
+    p_out : float
+      Probability of inter cluster connection.
+    directed : boolean, optional default=False
+      Whether to create a directed graph or not
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    G : NetworkX Graph or DiGraph
+      gaussian random partition graph
+
+    Raises
+    ------
+    NetworkXError
+      If s is > n
+      If p_in or p_out is not in [0,1]
+
+    Notes
+    -----
+    Note the number of partitions is dependent on s,v and n, and that the
+    last partition may be considerably smaller, as it is sized to simply
+    fill out the nodes [1]
+
+    See Also
+    --------
+    random_partition_graph
+
+    Examples
+    --------
+    >>> G = nx.gaussian_random_partition_graph(100, 10, 10, 0.25, 0.1)
+    >>> len(G)
+    100
+
+    References
+    ----------
+    .. [1] Ulrik Brandes, Marco Gaertler, Dorothea Wagner,
+       Experiments on Graph Clustering Algorithms,
+       In the proceedings of the 11th Europ. Symp. Algorithms, 2003.
+    """
+    if s > n:
+        raise nx.NetworkXError("s must be <= n")
+    assigned = 0
+    sizes = []
+    while True:
+        size = int(seed.gauss(s, s / v + 0.5))
+        if size < 1:  # how to handle 0 or negative sizes?
+            continue
+        if assigned + size >= n:
+            sizes.append(n - assigned)
+            break
+        assigned += size
+        sizes.append(size)
+    return random_partition_graph(sizes, p_in, p_out, seed=seed, directed=directed)
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def ring_of_cliques(num_cliques, clique_size):
+    """Defines a "ring of cliques" graph.
+
+    A ring of cliques graph is consisting of cliques, connected through single
+    links. Each clique is a complete graph.
+
+    Parameters
+    ----------
+    num_cliques : int
+        Number of cliques
+    clique_size : int
+        Size of cliques
+
+    Returns
+    -------
+    G : NetworkX Graph
+        ring of cliques graph
+
+    Raises
+    ------
+    NetworkXError
+        If the number of cliques is lower than 2 or
+        if the size of cliques is smaller than 2.
+
+    Examples
+    --------
+    >>> G = nx.ring_of_cliques(8, 4)
+
+    See Also
+    --------
+    connected_caveman_graph
+
+    Notes
+    -----
+    The `connected_caveman_graph` graph removes a link from each clique to
+    connect it with the next clique. Instead, the `ring_of_cliques` graph
+    simply adds the link without removing any link from the cliques.
+    """
+    if num_cliques < 2:
+        raise nx.NetworkXError("A ring of cliques must have at least two cliques")
+    if clique_size < 2:
+        raise nx.NetworkXError("The cliques must have at least two nodes")
+
+    G = nx.Graph()
+    for i in range(num_cliques):
+        edges = itertools.combinations(
+            range(i * clique_size, i * clique_size + clique_size), 2
+        )
+        G.add_edges_from(edges)
+        G.add_edge(
+            i * clique_size + 1, (i + 1) * clique_size % (num_cliques * clique_size)
+        )
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def windmill_graph(n, k):
+    """Generate a windmill graph.
+    A windmill graph is a graph of `n` cliques each of size `k` that are all
+    joined at one node.
+    It can be thought of as taking a disjoint union of `n` cliques of size `k`,
+    selecting one point from each, and contracting all of the selected points.
+    Alternatively, one could generate `n` cliques of size `k-1` and one node
+    that is connected to all other nodes in the graph.
+
+    Parameters
+    ----------
+    n : int
+        Number of cliques
+    k : int
+        Size of cliques
+
+    Returns
+    -------
+    G : NetworkX Graph
+        windmill graph with n cliques of size k
+
+    Raises
+    ------
+    NetworkXError
+        If the number of cliques is less than two
+        If the size of the cliques are less than two
+
+    Examples
+    --------
+    >>> G = nx.windmill_graph(4, 5)
+
+    Notes
+    -----
+    The node labeled `0` will be the node connected to all other nodes.
+    Note that windmill graphs are usually denoted `Wd(k,n)`, so the parameters
+    are in the opposite order as the parameters of this method.
+    """
+    if n < 2:
+        msg = "A windmill graph must have at least two cliques"
+        raise nx.NetworkXError(msg)
+    if k < 2:
+        raise nx.NetworkXError("The cliques must have at least two nodes")
+
+    G = nx.disjoint_union_all(
+        itertools.chain(
+            [nx.complete_graph(k)], (nx.complete_graph(k - 1) for _ in range(n - 1))
+        )
+    )
+    G.add_edges_from((0, i) for i in range(k, G.number_of_nodes()))
+    return G
+
+
+@py_random_state(3)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def stochastic_block_model(
+    sizes, p, nodelist=None, seed=None, directed=False, selfloops=False, sparse=True
+):
+    """Returns a stochastic block model graph.
+
+    This model partitions the nodes in blocks of arbitrary sizes, and places
+    edges between pairs of nodes independently, with a probability that depends
+    on the blocks.
+
+    Parameters
+    ----------
+    sizes : list of ints
+        Sizes of blocks
+    p : list of list of floats
+        Element (r,s) gives the density of edges going from the nodes
+        of group r to nodes of group s.
+        p must match the number of groups (len(sizes) == len(p)),
+        and it must be symmetric if the graph is undirected.
+    nodelist : list, optional
+        The block tags are assigned according to the node identifiers
+        in nodelist. If nodelist is None, then the ordering is the
+        range [0,sum(sizes)-1].
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+    directed : boolean optional, default=False
+        Whether to create a directed graph or not.
+    selfloops : boolean optional, default=False
+        Whether to include self-loops or not.
+    sparse: boolean optional, default=True
+        Use the sparse heuristic to speed up the generator.
+
+    Returns
+    -------
+    g : NetworkX Graph or DiGraph
+        Stochastic block model graph of size sum(sizes)
+
+    Raises
+    ------
+    NetworkXError
+      If probabilities are not in [0,1].
+      If the probability matrix is not square (directed case).
+      If the probability matrix is not symmetric (undirected case).
+      If the sizes list does not match nodelist or the probability matrix.
+      If nodelist contains duplicate.
+
+    Examples
+    --------
+    >>> sizes = [75, 75, 300]
+    >>> probs = [[0.25, 0.05, 0.02], [0.05, 0.35, 0.07], [0.02, 0.07, 0.40]]
+    >>> g = nx.stochastic_block_model(sizes, probs, seed=0)
+    >>> len(g)
+    450
+    >>> H = nx.quotient_graph(g, g.graph["partition"], relabel=True)
+    >>> for v in H.nodes(data=True):
+    ...     print(round(v[1]["density"], 3))
+    0.245
+    0.348
+    0.405
+    >>> for v in H.edges(data=True):
+    ...     print(round(1.0 * v[2]["weight"] / (sizes[v[0]] * sizes[v[1]]), 3))
+    0.051
+    0.022
+    0.07
+
+    See Also
+    --------
+    random_partition_graph
+    planted_partition_graph
+    gaussian_random_partition_graph
+    gnp_random_graph
+
+    References
+    ----------
+    .. [1] Holland, P. W., Laskey, K. B., & Leinhardt, S.,
+           "Stochastic blockmodels: First steps",
+           Social networks, 5(2), 109-137, 1983.
+    """
+    # Check if dimensions match
+    if len(sizes) != len(p):
+        raise nx.NetworkXException("'sizes' and 'p' do not match.")
+    # Check for probability symmetry (undirected) and shape (directed)
+    for row in p:
+        if len(p) != len(row):
+            raise nx.NetworkXException("'p' must be a square matrix.")
+    if not directed:
+        p_transpose = [list(i) for i in zip(*p)]
+        for i in zip(p, p_transpose):
+            for j in zip(i[0], i[1]):
+                if abs(j[0] - j[1]) > 1e-08:
+                    raise nx.NetworkXException("'p' must be symmetric.")
+    # Check for probability range
+    for row in p:
+        for prob in row:
+            if prob < 0 or prob > 1:
+                raise nx.NetworkXException("Entries of 'p' not in [0,1].")
+    # Check for nodelist consistency
+    if nodelist is not None:
+        if len(nodelist) != sum(sizes):
+            raise nx.NetworkXException("'nodelist' and 'sizes' do not match.")
+        if len(nodelist) != len(set(nodelist)):
+            raise nx.NetworkXException("nodelist contains duplicate.")
+    else:
+        nodelist = range(sum(sizes))
+
+    # Setup the graph conditionally to the directed switch.
+    block_range = range(len(sizes))
+    if directed:
+        g = nx.DiGraph()
+        block_iter = itertools.product(block_range, block_range)
+    else:
+        g = nx.Graph()
+        block_iter = itertools.combinations_with_replacement(block_range, 2)
+    # Split nodelist in a partition (list of sets).
+    size_cumsum = [sum(sizes[0:x]) for x in range(len(sizes) + 1)]
+    g.graph["partition"] = [
+        set(nodelist[size_cumsum[x] : size_cumsum[x + 1]])
+        for x in range(len(size_cumsum) - 1)
+    ]
+    # Setup nodes and graph name
+    for block_id, nodes in enumerate(g.graph["partition"]):
+        for node in nodes:
+            g.add_node(node, block=block_id)
+
+    g.name = "stochastic_block_model"
+
+    # Test for edge existence
+    parts = g.graph["partition"]
+    for i, j in block_iter:
+        if i == j:
+            if directed:
+                if selfloops:
+                    edges = itertools.product(parts[i], parts[i])
+                else:
+                    edges = itertools.permutations(parts[i], 2)
+            else:
+                edges = itertools.combinations(parts[i], 2)
+                if selfloops:
+                    edges = itertools.chain(edges, zip(parts[i], parts[i]))
+            for e in edges:
+                if seed.random() < p[i][j]:
+                    g.add_edge(*e)
+        else:
+            edges = itertools.product(parts[i], parts[j])
+        if sparse:
+            if p[i][j] == 1:  # Test edges cases p_ij = 0 or 1
+                for e in edges:
+                    g.add_edge(*e)
+            elif p[i][j] > 0:
+                while True:
+                    try:
+                        logrand = math.log(seed.random())
+                        skip = math.floor(logrand / math.log(1 - p[i][j]))
+                        # consume "skip" edges
+                        next(itertools.islice(edges, skip, skip), None)
+                        e = next(edges)
+                        g.add_edge(*e)  # __safe
+                    except StopIteration:
+                        break
+        else:
+            for e in edges:
+                if seed.random() < p[i][j]:
+                    g.add_edge(*e)  # __safe
+    return g
+
+
+def _zipf_rv_below(gamma, xmin, threshold, seed):
+    """Returns a random value chosen from the bounded Zipf distribution.
+
+    Repeatedly draws values from the Zipf distribution until the
+    threshold is met, then returns that value.
+    """
+    result = nx.utils.zipf_rv(gamma, xmin, seed)
+    while result > threshold:
+        result = nx.utils.zipf_rv(gamma, xmin, seed)
+    return result
+
+
+def _powerlaw_sequence(gamma, low, high, condition, length, max_iters, seed):
+    """Returns a list of numbers obeying a constrained power law distribution.
+
+    ``gamma`` and ``low`` are the parameters for the Zipf distribution.
+
+    ``high`` is the maximum allowed value for values draw from the Zipf
+    distribution. For more information, see :func:`_zipf_rv_below`.
+
+    ``condition`` and ``length`` are Boolean-valued functions on
+    lists. While generating the list, random values are drawn and
+    appended to the list until ``length`` is satisfied by the created
+    list. Once ``condition`` is satisfied, the sequence generated in
+    this way is returned.
+
+    ``max_iters`` indicates the number of times to generate a list
+    satisfying ``length``. If the number of iterations exceeds this
+    value, :exc:`~networkx.exception.ExceededMaxIterations` is raised.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+    """
+    for i in range(max_iters):
+        seq = []
+        while not length(seq):
+            seq.append(_zipf_rv_below(gamma, low, high, seed))
+        if condition(seq):
+            return seq
+    raise nx.ExceededMaxIterations("Could not create power law sequence")
+
+
+def _hurwitz_zeta(x, q, tolerance):
+    """The Hurwitz zeta function, or the Riemann zeta function of two arguments.
+
+    ``x`` must be greater than one and ``q`` must be positive.
+
+    This function repeatedly computes subsequent partial sums until
+    convergence, as decided by ``tolerance``.
+    """
+    z = 0
+    z_prev = -float("inf")
+    k = 0
+    while abs(z - z_prev) > tolerance:
+        z_prev = z
+        z += 1 / ((k + q) ** x)
+        k += 1
+    return z
+
+
+def _generate_min_degree(gamma, average_degree, max_degree, tolerance, max_iters):
+    """Returns a minimum degree from the given average degree."""
+    # Defines zeta function whether or not Scipy is available
+    try:
+        from scipy.special import zeta
+    except ImportError:
+
+        def zeta(x, q):
+            return _hurwitz_zeta(x, q, tolerance)
+
+    min_deg_top = max_degree
+    min_deg_bot = 1
+    min_deg_mid = (min_deg_top - min_deg_bot) / 2 + min_deg_bot
+    itrs = 0
+    mid_avg_deg = 0
+    while abs(mid_avg_deg - average_degree) > tolerance:
+        if itrs > max_iters:
+            raise nx.ExceededMaxIterations("Could not match average_degree")
+        mid_avg_deg = 0
+        for x in range(int(min_deg_mid), max_degree + 1):
+            mid_avg_deg += (x ** (-gamma + 1)) / zeta(gamma, min_deg_mid)
+        if mid_avg_deg > average_degree:
+            min_deg_top = min_deg_mid
+            min_deg_mid = (min_deg_top - min_deg_bot) / 2 + min_deg_bot
+        else:
+            min_deg_bot = min_deg_mid
+            min_deg_mid = (min_deg_top - min_deg_bot) / 2 + min_deg_bot
+        itrs += 1
+    # return int(min_deg_mid + 0.5)
+    return round(min_deg_mid)
+
+
+def _generate_communities(degree_seq, community_sizes, mu, max_iters, seed):
+    """Returns a list of sets, each of which represents a community.
+
+    ``degree_seq`` is the degree sequence that must be met by the
+    graph.
+
+    ``community_sizes`` is the community size distribution that must be
+    met by the generated list of sets.
+
+    ``mu`` is a float in the interval [0, 1] indicating the fraction of
+    intra-community edges incident to each node.
+
+    ``max_iters`` is the number of times to try to add a node to a
+    community. This must be greater than the length of
+    ``degree_seq``, otherwise this function will always fail. If
+    the number of iterations exceeds this value,
+    :exc:`~networkx.exception.ExceededMaxIterations` is raised.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    The communities returned by this are sets of integers in the set {0,
+    ..., *n* - 1}, where *n* is the length of ``degree_seq``.
+
+    """
+    # This assumes the nodes in the graph will be natural numbers.
+    result = [set() for _ in community_sizes]
+    n = len(degree_seq)
+    free = list(range(n))
+    for i in range(max_iters):
+        v = free.pop()
+        c = seed.choice(range(len(community_sizes)))
+        # s = int(degree_seq[v] * (1 - mu) + 0.5)
+        s = round(degree_seq[v] * (1 - mu))
+        # If the community is large enough, add the node to the chosen
+        # community. Otherwise, return it to the list of unaffiliated
+        # nodes.
+        if s < community_sizes[c]:
+            result[c].add(v)
+        else:
+            free.append(v)
+        # If the community is too big, remove a node from it.
+        if len(result[c]) > community_sizes[c]:
+            free.append(result[c].pop())
+        if not free:
+            return result
+    msg = "Could not assign communities; try increasing min_community"
+    raise nx.ExceededMaxIterations(msg)
+
+
+@py_random_state(11)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def LFR_benchmark_graph(
+    n,
+    tau1,
+    tau2,
+    mu,
+    average_degree=None,
+    min_degree=None,
+    max_degree=None,
+    min_community=None,
+    max_community=None,
+    tol=1.0e-7,
+    max_iters=500,
+    seed=None,
+):
+    r"""Returns the LFR benchmark graph.
+
+    This algorithm proceeds as follows:
+
+    1) Find a degree sequence with a power law distribution, and minimum
+       value ``min_degree``, which has approximate average degree
+       ``average_degree``. This is accomplished by either
+
+       a) specifying ``min_degree`` and not ``average_degree``,
+       b) specifying ``average_degree`` and not ``min_degree``, in which
+          case a suitable minimum degree will be found.
+
+       ``max_degree`` can also be specified, otherwise it will be set to
+       ``n``. Each node *u* will have $\mu \mathrm{deg}(u)$ edges
+       joining it to nodes in communities other than its own and $(1 -
+       \mu) \mathrm{deg}(u)$ edges joining it to nodes in its own
+       community.
+    2) Generate community sizes according to a power law distribution
+       with exponent ``tau2``. If ``min_community`` and
+       ``max_community`` are not specified they will be selected to be
+       ``min_degree`` and ``max_degree``, respectively.  Community sizes
+       are generated until the sum of their sizes equals ``n``.
+    3) Each node will be randomly assigned a community with the
+       condition that the community is large enough for the node's
+       intra-community degree, $(1 - \mu) \mathrm{deg}(u)$ as
+       described in step 2. If a community grows too large, a random node
+       will be selected for reassignment to a new community, until all
+       nodes have been assigned a community.
+    4) Each node *u* then adds $(1 - \mu) \mathrm{deg}(u)$
+       intra-community edges and $\mu \mathrm{deg}(u)$ inter-community
+       edges.
+
+    Parameters
+    ----------
+    n : int
+        Number of nodes in the created graph.
+
+    tau1 : float
+        Power law exponent for the degree distribution of the created
+        graph. This value must be strictly greater than one.
+
+    tau2 : float
+        Power law exponent for the community size distribution in the
+        created graph. This value must be strictly greater than one.
+
+    mu : float
+        Fraction of inter-community edges incident to each node. This
+        value must be in the interval [0, 1].
+
+    average_degree : float
+        Desired average degree of nodes in the created graph. This value
+        must be in the interval [0, *n*]. Exactly one of this and
+        ``min_degree`` must be specified, otherwise a
+        :exc:`NetworkXError` is raised.
+
+    min_degree : int
+        Minimum degree of nodes in the created graph. This value must be
+        in the interval [0, *n*]. Exactly one of this and
+        ``average_degree`` must be specified, otherwise a
+        :exc:`NetworkXError` is raised.
+
+    max_degree : int
+        Maximum degree of nodes in the created graph. If not specified,
+        this is set to ``n``, the total number of nodes in the graph.
+
+    min_community : int
+        Minimum size of communities in the graph. If not specified, this
+        is set to ``min_degree``.
+
+    max_community : int
+        Maximum size of communities in the graph. If not specified, this
+        is set to ``n``, the total number of nodes in the graph.
+
+    tol : float
+        Tolerance when comparing floats, specifically when comparing
+        average degree values.
+
+    max_iters : int
+        Maximum number of iterations to try to create the community sizes,
+        degree distribution, and community affiliations.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    G : NetworkX graph
+        The LFR benchmark graph generated according to the specified
+        parameters.
+
+        Each node in the graph has a node attribute ``'community'`` that
+        stores the community (that is, the set of nodes) that includes
+        it.
+
+    Raises
+    ------
+    NetworkXError
+        If any of the parameters do not meet their upper and lower bounds:
+
+        - ``tau1`` and ``tau2`` must be strictly greater than 1.
+        - ``mu`` must be in [0, 1].
+        - ``max_degree`` must be in {1, ..., *n*}.
+        - ``min_community`` and ``max_community`` must be in {0, ...,
+          *n*}.
+
+        If not exactly one of ``average_degree`` and ``min_degree`` is
+        specified.
+
+        If ``min_degree`` is not specified and a suitable ``min_degree``
+        cannot be found.
+
+    ExceededMaxIterations
+        If a valid degree sequence cannot be created within
+        ``max_iters`` number of iterations.
+
+        If a valid set of community sizes cannot be created within
+        ``max_iters`` number of iterations.
+
+        If a valid community assignment cannot be created within ``10 *
+        n * max_iters`` number of iterations.
+
+    Examples
+    --------
+    Basic usage::
+
+        >>> from networkx.generators.community import LFR_benchmark_graph
+        >>> n = 250
+        >>> tau1 = 3
+        >>> tau2 = 1.5
+        >>> mu = 0.1
+        >>> G = LFR_benchmark_graph(
+        ...     n, tau1, tau2, mu, average_degree=5, min_community=20, seed=10
+        ... )
+
+    Continuing the example above, you can get the communities from the
+    node attributes of the graph::
+
+        >>> communities = {frozenset(G.nodes[v]["community"]) for v in G}
+
+    Notes
+    -----
+    This algorithm differs slightly from the original way it was
+    presented in [1].
+
+    1) Rather than connecting the graph via a configuration model then
+       rewiring to match the intra-community and inter-community
+       degrees, we do this wiring explicitly at the end, which should be
+       equivalent.
+    2) The code posted on the author's website [2] calculates the random
+       power law distributed variables and their average using
+       continuous approximations, whereas we use the discrete
+       distributions here as both degree and community size are
+       discrete.
+
+    Though the authors describe the algorithm as quite robust, testing
+    during development indicates that a somewhat narrower parameter set
+    is likely to successfully produce a graph. Some suggestions have
+    been provided in the event of exceptions.
+
+    References
+    ----------
+    .. [1] "Benchmark graphs for testing community detection algorithms",
+           Andrea Lancichinetti, Santo Fortunato, and Filippo Radicchi,
+           Phys. Rev. E 78, 046110 2008
+    .. [2] https://www.santofortunato.net/resources
+
+    """
+    # Perform some basic parameter validation.
+    if not tau1 > 1:
+        raise nx.NetworkXError("tau1 must be greater than one")
+    if not tau2 > 1:
+        raise nx.NetworkXError("tau2 must be greater than one")
+    if not 0 <= mu <= 1:
+        raise nx.NetworkXError("mu must be in the interval [0, 1]")
+
+    # Validate parameters for generating the degree sequence.
+    if max_degree is None:
+        max_degree = n
+    elif not 0 < max_degree <= n:
+        raise nx.NetworkXError("max_degree must be in the interval (0, n]")
+    if not ((min_degree is None) ^ (average_degree is None)):
+        raise nx.NetworkXError(
+            "Must assign exactly one of min_degree and average_degree"
+        )
+    if min_degree is None:
+        min_degree = _generate_min_degree(
+            tau1, average_degree, max_degree, tol, max_iters
+        )
+
+    # Generate a degree sequence with a power law distribution.
+    low, high = min_degree, max_degree
+
+    def condition(seq):
+        return sum(seq) % 2 == 0
+
+    def length(seq):
+        return len(seq) >= n
+
+    deg_seq = _powerlaw_sequence(tau1, low, high, condition, length, max_iters, seed)
+
+    # Validate parameters for generating the community size sequence.
+    if min_community is None:
+        min_community = min(deg_seq)
+    if max_community is None:
+        max_community = max(deg_seq)
+
+    # Generate a community size sequence with a power law distribution.
+    #
+    # TODO The original code incremented the number of iterations each
+    # time a new Zipf random value was drawn from the distribution. This
+    # differed from the way the number of iterations was incremented in
+    # `_powerlaw_degree_sequence`, so this code was changed to match
+    # that one. As a result, this code is allowed many more chances to
+    # generate a valid community size sequence.
+    low, high = min_community, max_community
+
+    def condition(seq):
+        return sum(seq) == n
+
+    def length(seq):
+        return sum(seq) >= n
+
+    comms = _powerlaw_sequence(tau2, low, high, condition, length, max_iters, seed)
+
+    # Generate the communities based on the given degree sequence and
+    # community sizes.
+    max_iters *= 10 * n
+    communities = _generate_communities(deg_seq, comms, mu, max_iters, seed)
+
+    # Finally, generate the benchmark graph based on the given
+    # communities, joining nodes according to the intra- and
+    # inter-community degrees.
+    G = nx.Graph()
+    G.add_nodes_from(range(n))
+    for c in communities:
+        for u in c:
+            while G.degree(u) < round(deg_seq[u] * (1 - mu)):
+                v = seed.choice(list(c))
+                G.add_edge(u, v)
+            while G.degree(u) < deg_seq[u]:
+                v = seed.choice(range(n))
+                if v not in c:
+                    G.add_edge(u, v)
+            G.nodes[u]["community"] = c
+    return G