Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/networkx/algorithms/connectivity/tests/test_connectivity.py

@@ -0,0 +1,418 @@
+import itertools
+import pytest
+
+import networkx as nx
+from networkx.algorithms import flow
+from networkx.algorithms.connectivity import local_edge_connectivity
+from networkx.algorithms.connectivity import local_node_connectivity
+
+flow_funcs = [
+    flow.boykov_kolmogorov,
+    flow.dinitz,
+    flow.edmonds_karp,
+    flow.preflow_push,
+    flow.shortest_augmenting_path,
+]
+
+
+# helper functions for tests
+
+
+def _generate_no_biconnected(max_attempts=50):
+    attempts = 0
+    while True:
+        G = nx.fast_gnp_random_graph(100, 0.0575, seed=42)
+        if nx.is_connected(G) and not nx.is_biconnected(G):
+            attempts = 0
+            yield G
+        else:
+            if attempts >= max_attempts:
+                msg = f"Tried {max_attempts} times: no suitable Graph."
+                raise Exception(msg)
+            else:
+                attempts += 1
+
+
+def test_average_connectivity():
+    # figure 1 from:
+    # Beineke, L., O. Oellermann, and R. Pippert (2002). The average
+    # connectivity of a graph. Discrete mathematics 252(1-3), 31-45
+    # http://www.sciencedirect.com/science/article/pii/S0012365X01001807
+    G1 = nx.path_graph(3)
+    G1.add_edges_from([(1, 3), (1, 4)])
+    G2 = nx.path_graph(3)
+    G2.add_edges_from([(1, 3), (1, 4), (0, 3), (0, 4), (3, 4)])
+    G3 = nx.Graph()
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert nx.average_node_connectivity(G1, **kwargs) == 1, errmsg
+        assert nx.average_node_connectivity(G2, **kwargs) == 2.2, errmsg
+        assert nx.average_node_connectivity(G3, **kwargs) == 0, errmsg
+
+
+def test_average_connectivity_directed():
+    G = nx.DiGraph([(1, 3), (1, 4), (1, 5)])
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert nx.average_node_connectivity(G) == 0.25, errmsg
+
+
+def test_articulation_points():
+    Ggen = _generate_no_biconnected()
+    for flow_func in flow_funcs:
+        for i in range(3):
+            G = next(Ggen)
+            errmsg = f"Assertion failed in function: {flow_func.__name__}"
+            assert nx.node_connectivity(G, flow_func=flow_func) == 1, errmsg
+
+
+def test_brandes_erlebach():
+    # Figure 1 chapter 7: Connectivity
+    # http://www.informatik.uni-augsburg.de/thi/personen/kammer/Graph_Connectivity.pdf
+    G = nx.Graph()
+    G.add_edges_from(
+        [
+            (1, 2),
+            (1, 3),
+            (1, 4),
+            (1, 5),
+            (2, 3),
+            (2, 6),
+            (3, 4),
+            (3, 6),
+            (4, 6),
+            (4, 7),
+            (5, 7),
+            (6, 8),
+            (6, 9),
+            (7, 8),
+            (7, 10),
+            (8, 11),
+            (9, 10),
+            (9, 11),
+            (10, 11),
+        ]
+    )
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert 3 == local_edge_connectivity(G, 1, 11, **kwargs), errmsg
+        assert 3 == nx.edge_connectivity(G, 1, 11, **kwargs), errmsg
+        assert 2 == local_node_connectivity(G, 1, 11, **kwargs), errmsg
+        assert 2 == nx.node_connectivity(G, 1, 11, **kwargs), errmsg
+        assert 2 == nx.edge_connectivity(G, **kwargs), errmsg
+        assert 2 == nx.node_connectivity(G, **kwargs), errmsg
+        if flow_func is flow.preflow_push:
+            assert 3 == nx.edge_connectivity(G, 1, 11, cutoff=2, **kwargs), errmsg
+        else:
+            assert 2 == nx.edge_connectivity(G, 1, 11, cutoff=2, **kwargs), errmsg
+
+
+def test_white_harary_1():
+    # Figure 1b white and harary (2001)
+    # # http://eclectic.ss.uci.edu/~drwhite/sm-w23.PDF
+    # A graph with high adhesion (edge connectivity) and low cohesion
+    # (vertex connectivity)
+    G = nx.disjoint_union(nx.complete_graph(4), nx.complete_graph(4))
+    G.remove_node(7)
+    for i in range(4, 7):
+        G.add_edge(0, i)
+    G = nx.disjoint_union(G, nx.complete_graph(4))
+    G.remove_node(G.order() - 1)
+    for i in range(7, 10):
+        G.add_edge(0, i)
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert 1 == nx.node_connectivity(G, flow_func=flow_func), errmsg
+        assert 3 == nx.edge_connectivity(G, flow_func=flow_func), errmsg
+
+
+def test_white_harary_2():
+    # Figure 8 white and harary (2001)
+    # # http://eclectic.ss.uci.edu/~drwhite/sm-w23.PDF
+    G = nx.disjoint_union(nx.complete_graph(4), nx.complete_graph(4))
+    G.add_edge(0, 4)
+    # kappa <= lambda <= delta
+    assert 3 == min(nx.core_number(G).values())
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert 1 == nx.node_connectivity(G, flow_func=flow_func), errmsg
+        assert 1 == nx.edge_connectivity(G, flow_func=flow_func), errmsg
+
+
+def test_complete_graphs():
+    for n in range(5, 20, 5):
+        for flow_func in flow_funcs:
+            G = nx.complete_graph(n)
+            errmsg = f"Assertion failed in function: {flow_func.__name__}"
+            assert n - 1 == nx.node_connectivity(G, flow_func=flow_func), errmsg
+            assert n - 1 == nx.node_connectivity(
+                G.to_directed(), flow_func=flow_func
+            ), errmsg
+            assert n - 1 == nx.edge_connectivity(G, flow_func=flow_func), errmsg
+            assert n - 1 == nx.edge_connectivity(
+                G.to_directed(), flow_func=flow_func
+            ), errmsg
+
+
+def test_empty_graphs():
+    for k in range(5, 25, 5):
+        G = nx.empty_graph(k)
+        for flow_func in flow_funcs:
+            errmsg = f"Assertion failed in function: {flow_func.__name__}"
+            assert 0 == nx.node_connectivity(G, flow_func=flow_func), errmsg
+            assert 0 == nx.edge_connectivity(G, flow_func=flow_func), errmsg
+
+
+def test_petersen():
+    G = nx.petersen_graph()
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert 3 == nx.node_connectivity(G, flow_func=flow_func), errmsg
+        assert 3 == nx.edge_connectivity(G, flow_func=flow_func), errmsg
+
+
+def test_tutte():
+    G = nx.tutte_graph()
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert 3 == nx.node_connectivity(G, flow_func=flow_func), errmsg
+        assert 3 == nx.edge_connectivity(G, flow_func=flow_func), errmsg
+
+
+def test_dodecahedral():
+    G = nx.dodecahedral_graph()
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert 3 == nx.node_connectivity(G, flow_func=flow_func), errmsg
+        assert 3 == nx.edge_connectivity(G, flow_func=flow_func), errmsg
+
+
+def test_octahedral():
+    G = nx.octahedral_graph()
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert 4 == nx.node_connectivity(G, flow_func=flow_func), errmsg
+        assert 4 == nx.edge_connectivity(G, flow_func=flow_func), errmsg
+
+
+def test_icosahedral():
+    G = nx.icosahedral_graph()
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert 5 == nx.node_connectivity(G, flow_func=flow_func), errmsg
+        assert 5 == nx.edge_connectivity(G, flow_func=flow_func), errmsg
+
+
+def test_missing_source():
+    G = nx.path_graph(4)
+    for flow_func in flow_funcs:
+        pytest.raises(
+            nx.NetworkXError, nx.node_connectivity, G, 10, 1, flow_func=flow_func
+        )
+
+
+def test_missing_target():
+    G = nx.path_graph(4)
+    for flow_func in flow_funcs:
+        pytest.raises(
+            nx.NetworkXError, nx.node_connectivity, G, 1, 10, flow_func=flow_func
+        )
+
+
+def test_edge_missing_source():
+    G = nx.path_graph(4)
+    for flow_func in flow_funcs:
+        pytest.raises(
+            nx.NetworkXError, nx.edge_connectivity, G, 10, 1, flow_func=flow_func
+        )
+
+
+def test_edge_missing_target():
+    G = nx.path_graph(4)
+    for flow_func in flow_funcs:
+        pytest.raises(
+            nx.NetworkXError, nx.edge_connectivity, G, 1, 10, flow_func=flow_func
+        )
+
+
+def test_not_weakly_connected():
+    G = nx.DiGraph()
+    nx.add_path(G, [1, 2, 3])
+    nx.add_path(G, [4, 5])
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert nx.node_connectivity(G) == 0, errmsg
+        assert nx.edge_connectivity(G) == 0, errmsg
+
+
+def test_not_connected():
+    G = nx.Graph()
+    nx.add_path(G, [1, 2, 3])
+    nx.add_path(G, [4, 5])
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert nx.node_connectivity(G) == 0, errmsg
+        assert nx.edge_connectivity(G) == 0, errmsg
+
+
+def test_directed_edge_connectivity():
+    G = nx.cycle_graph(10, create_using=nx.DiGraph())  # only one direction
+    D = nx.cycle_graph(10).to_directed()  # 2 reciprocal edges
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        assert 1 == nx.edge_connectivity(G, flow_func=flow_func), errmsg
+        assert 1 == local_edge_connectivity(G, 1, 4, flow_func=flow_func), errmsg
+        assert 1 == nx.edge_connectivity(G, 1, 4, flow_func=flow_func), errmsg
+        assert 2 == nx.edge_connectivity(D, flow_func=flow_func), errmsg
+        assert 2 == local_edge_connectivity(D, 1, 4, flow_func=flow_func), errmsg
+        assert 2 == nx.edge_connectivity(D, 1, 4, flow_func=flow_func), errmsg
+
+
+def test_cutoff():
+    G = nx.complete_graph(5)
+    for local_func in [local_edge_connectivity, local_node_connectivity]:
+        for flow_func in flow_funcs:
+            if flow_func is flow.preflow_push:
+                # cutoff is not supported by preflow_push
+                continue
+            for cutoff in [3, 2, 1]:
+                result = local_func(G, 0, 4, flow_func=flow_func, cutoff=cutoff)
+                assert cutoff == result, f"cutoff error in {flow_func.__name__}"
+
+
+def test_invalid_auxiliary():
+    G = nx.complete_graph(5)
+    pytest.raises(nx.NetworkXError, local_node_connectivity, G, 0, 3, auxiliary=G)
+
+
+def test_interface_only_source():
+    G = nx.complete_graph(5)
+    for interface_func in [nx.node_connectivity, nx.edge_connectivity]:
+        pytest.raises(nx.NetworkXError, interface_func, G, s=0)
+
+
+def test_interface_only_target():
+    G = nx.complete_graph(5)
+    for interface_func in [nx.node_connectivity, nx.edge_connectivity]:
+        pytest.raises(nx.NetworkXError, interface_func, G, t=3)
+
+
+def test_edge_connectivity_flow_vs_stoer_wagner():
+    graph_funcs = [nx.icosahedral_graph, nx.octahedral_graph, nx.dodecahedral_graph]
+    for graph_func in graph_funcs:
+        G = graph_func()
+        assert nx.stoer_wagner(G)[0] == nx.edge_connectivity(G)
+
+
+class TestAllPairsNodeConnectivity:
+    @classmethod
+    def setup_class(cls):
+        cls.path = nx.path_graph(7)
+        cls.directed_path = nx.path_graph(7, create_using=nx.DiGraph())
+        cls.cycle = nx.cycle_graph(7)
+        cls.directed_cycle = nx.cycle_graph(7, create_using=nx.DiGraph())
+        cls.gnp = nx.gnp_random_graph(30, 0.1, seed=42)
+        cls.directed_gnp = nx.gnp_random_graph(30, 0.1, directed=True, seed=42)
+        cls.K20 = nx.complete_graph(20)
+        cls.K10 = nx.complete_graph(10)
+        cls.K5 = nx.complete_graph(5)
+        cls.G_list = [
+            cls.path,
+            cls.directed_path,
+            cls.cycle,
+            cls.directed_cycle,
+            cls.gnp,
+            cls.directed_gnp,
+            cls.K10,
+            cls.K5,
+            cls.K20,
+        ]
+
+    def test_cycles(self):
+        K_undir = nx.all_pairs_node_connectivity(self.cycle)
+        for source in K_undir:
+            for target, k in K_undir[source].items():
+                assert k == 2
+        K_dir = nx.all_pairs_node_connectivity(self.directed_cycle)
+        for source in K_dir:
+            for target, k in K_dir[source].items():
+                assert k == 1
+
+    def test_complete(self):
+        for G in [self.K10, self.K5, self.K20]:
+            K = nx.all_pairs_node_connectivity(G)
+            for source in K:
+                for target, k in K[source].items():
+                    assert k == len(G) - 1
+
+    def test_paths(self):
+        K_undir = nx.all_pairs_node_connectivity(self.path)
+        for source in K_undir:
+            for target, k in K_undir[source].items():
+                assert k == 1
+        K_dir = nx.all_pairs_node_connectivity(self.directed_path)
+        for source in K_dir:
+            for target, k in K_dir[source].items():
+                if source < target:
+                    assert k == 1
+                else:
+                    assert k == 0
+
+    def test_all_pairs_connectivity_nbunch(self):
+        G = nx.complete_graph(5)
+        nbunch = [0, 2, 3]
+        C = nx.all_pairs_node_connectivity(G, nbunch=nbunch)
+        assert len(C) == len(nbunch)
+
+    def test_all_pairs_connectivity_icosahedral(self):
+        G = nx.icosahedral_graph()
+        C = nx.all_pairs_node_connectivity(G)
+        assert all(5 == C[u][v] for u, v in itertools.combinations(G, 2))
+
+    def test_all_pairs_connectivity(self):
+        G = nx.Graph()
+        nodes = [0, 1, 2, 3]
+        nx.add_path(G, nodes)
+        A = {n: {} for n in G}
+        for u, v in itertools.combinations(nodes, 2):
+            A[u][v] = A[v][u] = nx.node_connectivity(G, u, v)
+        C = nx.all_pairs_node_connectivity(G)
+        assert sorted((k, sorted(v)) for k, v in A.items()) == sorted(
+            (k, sorted(v)) for k, v in C.items()
+        )
+
+    def test_all_pairs_connectivity_directed(self):
+        G = nx.DiGraph()
+        nodes = [0, 1, 2, 3]
+        nx.add_path(G, nodes)
+        A = {n: {} for n in G}
+        for u, v in itertools.permutations(nodes, 2):
+            A[u][v] = nx.node_connectivity(G, u, v)
+        C = nx.all_pairs_node_connectivity(G)
+        assert sorted((k, sorted(v)) for k, v in A.items()) == sorted(
+            (k, sorted(v)) for k, v in C.items()
+        )
+
+    def test_all_pairs_connectivity_nbunch_combinations(self):
+        G = nx.complete_graph(5)
+        nbunch = [0, 2, 3]
+        A = {n: {} for n in nbunch}
+        for u, v in itertools.combinations(nbunch, 2):
+            A[u][v] = A[v][u] = nx.node_connectivity(G, u, v)
+        C = nx.all_pairs_node_connectivity(G, nbunch=nbunch)
+        assert sorted((k, sorted(v)) for k, v in A.items()) == sorted(
+            (k, sorted(v)) for k, v in C.items()
+        )
+
+    def test_all_pairs_connectivity_nbunch_iter(self):
+        G = nx.complete_graph(5)
+        nbunch = [0, 2, 3]
+        A = {n: {} for n in nbunch}
+        for u, v in itertools.combinations(nbunch, 2):
+            A[u][v] = A[v][u] = nx.node_connectivity(G, u, v)
+        C = nx.all_pairs_node_connectivity(G, nbunch=iter(nbunch))
+        assert sorted((k, sorted(v)) for k, v in A.items()) == sorted(
+            (k, sorted(v)) for k, v in C.items()
+        )

venv/Lib/site-packages/networkx/algorithms/connectivity/tests/test_cuts.py

@@ -0,0 +1,310 @@
+import pytest
+
+import networkx as nx
+from networkx.algorithms import flow
+from networkx.algorithms.connectivity import minimum_st_edge_cut
+from networkx.algorithms.connectivity import minimum_st_node_cut
+from networkx.utils import arbitrary_element
+
+flow_funcs = [
+    flow.boykov_kolmogorov,
+    flow.dinitz,
+    flow.edmonds_karp,
+    flow.preflow_push,
+    flow.shortest_augmenting_path,
+]
+
+# Tests for node and edge cutsets
+
+
+def _generate_no_biconnected(max_attempts=50):
+    attempts = 0
+    while True:
+        G = nx.fast_gnp_random_graph(100, 0.0575, seed=42)
+        if nx.is_connected(G) and not nx.is_biconnected(G):
+            attempts = 0
+            yield G
+        else:
+            if attempts >= max_attempts:
+                msg = f"Tried {attempts} times: no suitable Graph."
+                raise Exception(msg)
+            else:
+                attempts += 1
+
+
+def test_articulation_points():
+    Ggen = _generate_no_biconnected()
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        for i in range(1):  # change 1 to 3 or more for more realizations.
+            G = next(Ggen)
+            cut = nx.minimum_node_cut(G, flow_func=flow_func)
+            assert len(cut) == 1, errmsg
+            assert cut.pop() in set(nx.articulation_points(G)), errmsg
+
+
+def test_brandes_erlebach_book():
+    # Figure 1 chapter 7: Connectivity
+    # http://www.informatik.uni-augsburg.de/thi/personen/kammer/Graph_Connectivity.pdf
+    G = nx.Graph()
+    G.add_edges_from(
+        [
+            (1, 2),
+            (1, 3),
+            (1, 4),
+            (1, 5),
+            (2, 3),
+            (2, 6),
+            (3, 4),
+            (3, 6),
+            (4, 6),
+            (4, 7),
+            (5, 7),
+            (6, 8),
+            (6, 9),
+            (7, 8),
+            (7, 10),
+            (8, 11),
+            (9, 10),
+            (9, 11),
+            (10, 11),
+        ]
+    )
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        # edge cutsets
+        assert 3 == len(nx.minimum_edge_cut(G, 1, 11, **kwargs)), errmsg
+        edge_cut = nx.minimum_edge_cut(G, **kwargs)
+        # Node 5 has only two edges
+        assert 2 == len(edge_cut), errmsg
+        H = G.copy()
+        H.remove_edges_from(edge_cut)
+        assert not nx.is_connected(H), errmsg
+        # node cuts
+        assert {6, 7} == minimum_st_node_cut(G, 1, 11, **kwargs), errmsg
+        assert {6, 7} == nx.minimum_node_cut(G, 1, 11, **kwargs), errmsg
+        node_cut = nx.minimum_node_cut(G, **kwargs)
+        assert 2 == len(node_cut), errmsg
+        H = G.copy()
+        H.remove_nodes_from(node_cut)
+        assert not nx.is_connected(H), errmsg
+
+
+def test_white_harary_paper():
+    # Figure 1b white and harary (2001)
+    # http://eclectic.ss.uci.edu/~drwhite/sm-w23.PDF
+    # A graph with high adhesion (edge connectivity) and low cohesion
+    # (node connectivity)
+    G = nx.disjoint_union(nx.complete_graph(4), nx.complete_graph(4))
+    G.remove_node(7)
+    for i in range(4, 7):
+        G.add_edge(0, i)
+    G = nx.disjoint_union(G, nx.complete_graph(4))
+    G.remove_node(G.order() - 1)
+    for i in range(7, 10):
+        G.add_edge(0, i)
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        # edge cuts
+        edge_cut = nx.minimum_edge_cut(G, **kwargs)
+        assert 3 == len(edge_cut), errmsg
+        H = G.copy()
+        H.remove_edges_from(edge_cut)
+        assert not nx.is_connected(H), errmsg
+        # node cuts
+        node_cut = nx.minimum_node_cut(G, **kwargs)
+        assert {0} == node_cut, errmsg
+        H = G.copy()
+        H.remove_nodes_from(node_cut)
+        assert not nx.is_connected(H), errmsg
+
+
+def test_petersen_cutset():
+    G = nx.petersen_graph()
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        # edge cuts
+        edge_cut = nx.minimum_edge_cut(G, **kwargs)
+        assert 3 == len(edge_cut), errmsg
+        H = G.copy()
+        H.remove_edges_from(edge_cut)
+        assert not nx.is_connected(H), errmsg
+        # node cuts
+        node_cut = nx.minimum_node_cut(G, **kwargs)
+        assert 3 == len(node_cut), errmsg
+        H = G.copy()
+        H.remove_nodes_from(node_cut)
+        assert not nx.is_connected(H), errmsg
+
+
+def test_octahedral_cutset():
+    G = nx.octahedral_graph()
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        # edge cuts
+        edge_cut = nx.minimum_edge_cut(G, **kwargs)
+        assert 4 == len(edge_cut), errmsg
+        H = G.copy()
+        H.remove_edges_from(edge_cut)
+        assert not nx.is_connected(H), errmsg
+        # node cuts
+        node_cut = nx.minimum_node_cut(G, **kwargs)
+        assert 4 == len(node_cut), errmsg
+        H = G.copy()
+        H.remove_nodes_from(node_cut)
+        assert not nx.is_connected(H), errmsg
+
+
+def test_icosahedral_cutset():
+    G = nx.icosahedral_graph()
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        # edge cuts
+        edge_cut = nx.minimum_edge_cut(G, **kwargs)
+        assert 5 == len(edge_cut), errmsg
+        H = G.copy()
+        H.remove_edges_from(edge_cut)
+        assert not nx.is_connected(H), errmsg
+        # node cuts
+        node_cut = nx.minimum_node_cut(G, **kwargs)
+        assert 5 == len(node_cut), errmsg
+        H = G.copy()
+        H.remove_nodes_from(node_cut)
+        assert not nx.is_connected(H), errmsg
+
+
+def test_node_cutset_exception():
+    G = nx.Graph()
+    G.add_edges_from([(1, 2), (3, 4)])
+    for flow_func in flow_funcs:
+        pytest.raises(nx.NetworkXError, nx.minimum_node_cut, G, flow_func=flow_func)
+
+
+def test_node_cutset_random_graphs():
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        for i in range(3):
+            G = nx.fast_gnp_random_graph(50, 0.25, seed=42)
+            if not nx.is_connected(G):
+                ccs = iter(nx.connected_components(G))
+                start = arbitrary_element(next(ccs))
+                G.add_edges_from((start, arbitrary_element(c)) for c in ccs)
+            cutset = nx.minimum_node_cut(G, flow_func=flow_func)
+            assert nx.node_connectivity(G) == len(cutset), errmsg
+            G.remove_nodes_from(cutset)
+            assert not nx.is_connected(G), errmsg
+
+
+def test_edge_cutset_random_graphs():
+    for flow_func in flow_funcs:
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        for i in range(3):
+            G = nx.fast_gnp_random_graph(50, 0.25, seed=42)
+            if not nx.is_connected(G):
+                ccs = iter(nx.connected_components(G))
+                start = arbitrary_element(next(ccs))
+                G.add_edges_from((start, arbitrary_element(c)) for c in ccs)
+            cutset = nx.minimum_edge_cut(G, flow_func=flow_func)
+            assert nx.edge_connectivity(G) == len(cutset), errmsg
+            G.remove_edges_from(cutset)
+            assert not nx.is_connected(G), errmsg
+
+
+def test_empty_graphs():
+    G = nx.Graph()
+    D = nx.DiGraph()
+    for interface_func in [nx.minimum_node_cut, nx.minimum_edge_cut]:
+        for flow_func in flow_funcs:
+            pytest.raises(
+                nx.NetworkXPointlessConcept, interface_func, G, flow_func=flow_func
+            )
+            pytest.raises(
+                nx.NetworkXPointlessConcept, interface_func, D, flow_func=flow_func
+            )
+
+
+def test_unbounded():
+    G = nx.complete_graph(5)
+    for flow_func in flow_funcs:
+        assert 4 == len(minimum_st_edge_cut(G, 1, 4, flow_func=flow_func))
+
+
+def test_missing_source():
+    G = nx.path_graph(4)
+    for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
+        for flow_func in flow_funcs:
+            pytest.raises(
+                nx.NetworkXError, interface_func, G, 10, 1, flow_func=flow_func
+            )
+
+
+def test_missing_target():
+    G = nx.path_graph(4)
+    for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
+        for flow_func in flow_funcs:
+            pytest.raises(
+                nx.NetworkXError, interface_func, G, 1, 10, flow_func=flow_func
+            )
+
+
+def test_not_weakly_connected():
+    G = nx.DiGraph()
+    nx.add_path(G, [1, 2, 3])
+    nx.add_path(G, [4, 5])
+    for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
+        for flow_func in flow_funcs:
+            pytest.raises(nx.NetworkXError, interface_func, G, flow_func=flow_func)
+
+
+def test_not_connected():
+    G = nx.Graph()
+    nx.add_path(G, [1, 2, 3])
+    nx.add_path(G, [4, 5])
+    for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
+        for flow_func in flow_funcs:
+            pytest.raises(nx.NetworkXError, interface_func, G, flow_func=flow_func)
+
+
+def tests_min_cut_complete():
+    G = nx.complete_graph(5)
+    for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
+        for flow_func in flow_funcs:
+            assert 4 == len(interface_func(G, flow_func=flow_func))
+
+
+def tests_min_cut_complete_directed():
+    G = nx.complete_graph(5)
+    G = G.to_directed()
+    for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
+        for flow_func in flow_funcs:
+            assert 4 == len(interface_func(G, flow_func=flow_func))
+
+
+def tests_minimum_st_node_cut():
+    G = nx.Graph()
+    G.add_nodes_from([0, 1, 2, 3, 7, 8, 11, 12])
+    G.add_edges_from([(7, 11), (1, 11), (1, 12), (12, 8), (0, 1)])
+    nodelist = minimum_st_node_cut(G, 7, 11)
+    assert nodelist == {}
+
+
+def test_invalid_auxiliary():
+    G = nx.complete_graph(5)
+    pytest.raises(nx.NetworkXError, minimum_st_node_cut, G, 0, 3, auxiliary=G)
+
+
+def test_interface_only_source():
+    G = nx.complete_graph(5)
+    for interface_func in [nx.minimum_node_cut, nx.minimum_edge_cut]:
+        pytest.raises(nx.NetworkXError, interface_func, G, s=0)
+
+
+def test_interface_only_target():
+    G = nx.complete_graph(5)
+    for interface_func in [nx.minimum_node_cut, nx.minimum_edge_cut]:
+        pytest.raises(nx.NetworkXError, interface_func, G, t=3)

venv/Lib/site-packages/networkx/algorithms/connectivity/tests/test_disjoint_paths.py

@@ -0,0 +1,249 @@
+import pytest
+
+import networkx as nx
+from networkx.algorithms import flow
+from networkx.utils import pairwise
+
+flow_funcs = [
+    flow.boykov_kolmogorov,
+    flow.edmonds_karp,
+    flow.dinitz,
+    flow.preflow_push,
+    flow.shortest_augmenting_path,
+]
+
+
+def is_path(G, path):
+    return all(v in G[u] for u, v in pairwise(path))
+
+
+def are_edge_disjoint_paths(G, paths):
+    if not paths:
+        return False
+    for path in paths:
+        assert is_path(G, path)
+    paths_edges = [list(pairwise(p)) for p in paths]
+    num_of_edges = sum(len(e) for e in paths_edges)
+    num_unique_edges = len(set.union(*[set(es) for es in paths_edges]))
+    if num_of_edges == num_unique_edges:
+        return True
+    return False
+
+
+def are_node_disjoint_paths(G, paths):
+    if not paths:
+        return False
+    for path in paths:
+        assert is_path(G, path)
+    # first and last nodes are source and target
+    st = {paths[0][0], paths[0][-1]}
+    num_of_nodes = len([n for path in paths for n in path if n not in st])
+    num_unique_nodes = len({n for path in paths for n in path if n not in st})
+    if num_of_nodes == num_unique_nodes:
+        return True
+    return False
+
+
+def test_graph_from_pr_2053():
+    G = nx.Graph()
+    G.add_edges_from(
+        [
+            ("A", "B"),
+            ("A", "D"),
+            ("A", "F"),
+            ("A", "G"),
+            ("B", "C"),
+            ("B", "D"),
+            ("B", "G"),
+            ("C", "D"),
+            ("C", "E"),
+            ("C", "Z"),
+            ("D", "E"),
+            ("D", "F"),
+            ("E", "F"),
+            ("E", "Z"),
+            ("F", "Z"),
+            ("G", "Z"),
+        ]
+    )
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        # edge disjoint paths
+        edge_paths = list(nx.edge_disjoint_paths(G, "A", "Z", **kwargs))
+        assert are_edge_disjoint_paths(G, edge_paths), errmsg
+        assert nx.edge_connectivity(G, "A", "Z") == len(edge_paths), errmsg
+        # node disjoint paths
+        node_paths = list(nx.node_disjoint_paths(G, "A", "Z", **kwargs))
+        assert are_node_disjoint_paths(G, node_paths), errmsg
+        assert nx.node_connectivity(G, "A", "Z") == len(node_paths), errmsg
+
+
+def test_florentine_families():
+    G = nx.florentine_families_graph()
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        # edge disjoint paths
+        edge_dpaths = list(nx.edge_disjoint_paths(G, "Medici", "Strozzi", **kwargs))
+        assert are_edge_disjoint_paths(G, edge_dpaths), errmsg
+        assert nx.edge_connectivity(G, "Medici", "Strozzi") == len(edge_dpaths), errmsg
+        # node disjoint paths
+        node_dpaths = list(nx.node_disjoint_paths(G, "Medici", "Strozzi", **kwargs))
+        assert are_node_disjoint_paths(G, node_dpaths), errmsg
+        assert nx.node_connectivity(G, "Medici", "Strozzi") == len(node_dpaths), errmsg
+
+
+def test_karate():
+    G = nx.karate_club_graph()
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        # edge disjoint paths
+        edge_dpaths = list(nx.edge_disjoint_paths(G, 0, 33, **kwargs))
+        assert are_edge_disjoint_paths(G, edge_dpaths), errmsg
+        assert nx.edge_connectivity(G, 0, 33) == len(edge_dpaths), errmsg
+        # node disjoint paths
+        node_dpaths = list(nx.node_disjoint_paths(G, 0, 33, **kwargs))
+        assert are_node_disjoint_paths(G, node_dpaths), errmsg
+        assert nx.node_connectivity(G, 0, 33) == len(node_dpaths), errmsg
+
+
+def test_petersen_disjoint_paths():
+    G = nx.petersen_graph()
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        # edge disjoint paths
+        edge_dpaths = list(nx.edge_disjoint_paths(G, 0, 6, **kwargs))
+        assert are_edge_disjoint_paths(G, edge_dpaths), errmsg
+        assert 3 == len(edge_dpaths), errmsg
+        # node disjoint paths
+        node_dpaths = list(nx.node_disjoint_paths(G, 0, 6, **kwargs))
+        assert are_node_disjoint_paths(G, node_dpaths), errmsg
+        assert 3 == len(node_dpaths), errmsg
+
+
+def test_octahedral_disjoint_paths():
+    G = nx.octahedral_graph()
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        # edge disjoint paths
+        edge_dpaths = list(nx.edge_disjoint_paths(G, 0, 5, **kwargs))
+        assert are_edge_disjoint_paths(G, edge_dpaths), errmsg
+        assert 4 == len(edge_dpaths), errmsg
+        # node disjoint paths
+        node_dpaths = list(nx.node_disjoint_paths(G, 0, 5, **kwargs))
+        assert are_node_disjoint_paths(G, node_dpaths), errmsg
+        assert 4 == len(node_dpaths), errmsg
+
+
+def test_icosahedral_disjoint_paths():
+    G = nx.icosahedral_graph()
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        # edge disjoint paths
+        edge_dpaths = list(nx.edge_disjoint_paths(G, 0, 6, **kwargs))
+        assert are_edge_disjoint_paths(G, edge_dpaths), errmsg
+        assert 5 == len(edge_dpaths), errmsg
+        # node disjoint paths
+        node_dpaths = list(nx.node_disjoint_paths(G, 0, 6, **kwargs))
+        assert are_node_disjoint_paths(G, node_dpaths), errmsg
+        assert 5 == len(node_dpaths), errmsg
+
+
+def test_cutoff_disjoint_paths():
+    G = nx.icosahedral_graph()
+    for flow_func in flow_funcs:
+        kwargs = dict(flow_func=flow_func)
+        errmsg = f"Assertion failed in function: {flow_func.__name__}"
+        for cutoff in [2, 4]:
+            kwargs["cutoff"] = cutoff
+            # edge disjoint paths
+            edge_dpaths = list(nx.edge_disjoint_paths(G, 0, 6, **kwargs))
+            assert are_edge_disjoint_paths(G, edge_dpaths), errmsg
+            assert cutoff == len(edge_dpaths), errmsg
+            # node disjoint paths
+            node_dpaths = list(nx.node_disjoint_paths(G, 0, 6, **kwargs))
+            assert are_node_disjoint_paths(G, node_dpaths), errmsg
+            assert cutoff == len(node_dpaths), errmsg
+
+
+def test_missing_source_edge_paths():
+    with pytest.raises(nx.NetworkXError):
+        G = nx.path_graph(4)
+        list(nx.edge_disjoint_paths(G, 10, 1))
+
+
+def test_missing_source_node_paths():
+    with pytest.raises(nx.NetworkXError):
+        G = nx.path_graph(4)
+        list(nx.node_disjoint_paths(G, 10, 1))
+
+
+def test_missing_target_edge_paths():
+    with pytest.raises(nx.NetworkXError):
+        G = nx.path_graph(4)
+        list(nx.edge_disjoint_paths(G, 1, 10))
+
+
+def test_missing_target_node_paths():
+    with pytest.raises(nx.NetworkXError):
+        G = nx.path_graph(4)
+        list(nx.node_disjoint_paths(G, 1, 10))
+
+
+def test_not_weakly_connected_edges():
+    with pytest.raises(nx.NetworkXNoPath):
+        G = nx.DiGraph()
+        nx.add_path(G, [1, 2, 3])
+        nx.add_path(G, [4, 5])
+        list(nx.edge_disjoint_paths(G, 1, 5))
+
+
+def test_not_weakly_connected_nodes():
+    with pytest.raises(nx.NetworkXNoPath):
+        G = nx.DiGraph()
+        nx.add_path(G, [1, 2, 3])
+        nx.add_path(G, [4, 5])
+        list(nx.node_disjoint_paths(G, 1, 5))
+
+
+def test_not_connected_edges():
+    with pytest.raises(nx.NetworkXNoPath):
+        G = nx.Graph()
+        nx.add_path(G, [1, 2, 3])
+        nx.add_path(G, [4, 5])
+        list(nx.edge_disjoint_paths(G, 1, 5))
+
+
+def test_not_connected_nodes():
+    with pytest.raises(nx.NetworkXNoPath):
+        G = nx.Graph()
+        nx.add_path(G, [1, 2, 3])
+        nx.add_path(G, [4, 5])
+        list(nx.node_disjoint_paths(G, 1, 5))
+
+
+def test_isolated_edges():
+    with pytest.raises(nx.NetworkXNoPath):
+        G = nx.Graph()
+        G.add_node(1)
+        nx.add_path(G, [4, 5])
+        list(nx.edge_disjoint_paths(G, 1, 5))
+
+
+def test_isolated_nodes():
+    with pytest.raises(nx.NetworkXNoPath):
+        G = nx.Graph()
+        G.add_node(1)
+        nx.add_path(G, [4, 5])
+        list(nx.node_disjoint_paths(G, 1, 5))
+
+
+def test_invalid_auxiliary():
+    with pytest.raises(nx.NetworkXError):
+        G = nx.complete_graph(5)
+        list(nx.node_disjoint_paths(G, 0, 3, auxiliary=G))

venv/Lib/site-packages/networkx/algorithms/connectivity/tests/test_edge_augmentation.py

@@ -0,0 +1,495 @@
+import random
+import networkx as nx
+import itertools as it
+from networkx.utils import pairwise
+import pytest
+from networkx.algorithms.connectivity import k_edge_augmentation
+from networkx.algorithms.connectivity.edge_augmentation import (
+    collapse,
+    complement_edges,
+    is_locally_k_edge_connected,
+    is_k_edge_connected,
+    _unpack_available_edges,
+)
+
+# This should be set to the largest k for which an efficient algorithm is
+# explicitly defined.
+MAX_EFFICIENT_K = 2
+
+
+def tarjan_bridge_graph():
+    # graph from tarjan paper
+    # RE Tarjan - "A note on finding the bridges of a graph"
+    # Information Processing Letters, 1974 - Elsevier
+    # doi:10.1016/0020-0190(74)90003-9.
+    # define 2-connected components and bridges
+    ccs = [
+        (1, 2, 4, 3, 1, 4),
+        (5, 6, 7, 5),
+        (8, 9, 10, 8),
+        (17, 18, 16, 15, 17),
+        (11, 12, 14, 13, 11, 14),
+    ]
+    bridges = [(4, 8), (3, 5), (3, 17)]
+    G = nx.Graph(it.chain(*(pairwise(path) for path in ccs + bridges)))
+    return G
+
+
+def test_weight_key():
+    G = nx.Graph()
+    G.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8, 9])
+    G.add_edges_from([(3, 8), (1, 2), (2, 3)])
+    impossible = {(3, 6), (3, 9)}
+    rng = random.Random(0)
+    avail_uv = list(set(complement_edges(G)) - impossible)
+    avail = [(u, v, {"cost": rng.random()}) for u, v in avail_uv]
+
+    _augment_and_check(G, k=1)
+    _augment_and_check(G, k=1, avail=avail_uv)
+    _augment_and_check(G, k=1, avail=avail, weight="cost")
+
+    _check_augmentations(G, avail, weight="cost")
+
+
+def test_is_locally_k_edge_connected_exceptions():
+    pytest.raises(nx.NetworkXNotImplemented, is_k_edge_connected, nx.DiGraph(), k=0)
+    pytest.raises(nx.NetworkXNotImplemented, is_k_edge_connected, nx.MultiGraph(), k=0)
+    pytest.raises(ValueError, is_k_edge_connected, nx.Graph(), k=0)
+
+
+def test_is_k_edge_connected():
+    G = nx.barbell_graph(10, 0)
+    assert is_k_edge_connected(G, k=1)
+    assert not is_k_edge_connected(G, k=2)
+
+    G = nx.Graph()
+    G.add_nodes_from([5, 15])
+    assert not is_k_edge_connected(G, k=1)
+    assert not is_k_edge_connected(G, k=2)
+
+    G = nx.complete_graph(5)
+    assert is_k_edge_connected(G, k=1)
+    assert is_k_edge_connected(G, k=2)
+    assert is_k_edge_connected(G, k=3)
+    assert is_k_edge_connected(G, k=4)
+
+
+def test_is_k_edge_connected_exceptions():
+    pytest.raises(
+        nx.NetworkXNotImplemented, is_locally_k_edge_connected, nx.DiGraph(), 1, 2, k=0
+    )
+    pytest.raises(
+        nx.NetworkXNotImplemented,
+        is_locally_k_edge_connected,
+        nx.MultiGraph(),
+        1,
+        2,
+        k=0,
+    )
+    pytest.raises(ValueError, is_locally_k_edge_connected, nx.Graph(), 1, 2, k=0)
+
+
+def test_is_locally_k_edge_connected():
+    G = nx.barbell_graph(10, 0)
+    assert is_locally_k_edge_connected(G, 5, 15, k=1)
+    assert not is_locally_k_edge_connected(G, 5, 15, k=2)
+
+    G = nx.Graph()
+    G.add_nodes_from([5, 15])
+    assert not is_locally_k_edge_connected(G, 5, 15, k=2)
+
+
+def test_null_graph():
+    G = nx.Graph()
+    _check_augmentations(G, max_k=MAX_EFFICIENT_K + 2)
+
+
+def test_cliques():
+    for n in range(1, 10):
+        G = nx.complete_graph(n)
+        _check_augmentations(G, max_k=MAX_EFFICIENT_K + 2)
+
+
+def test_clique_and_node():
+    for n in range(1, 10):
+        G = nx.complete_graph(n)
+        G.add_node(n + 1)
+        _check_augmentations(G, max_k=MAX_EFFICIENT_K + 2)
+
+
+def test_point_graph():
+    G = nx.Graph()
+    G.add_node(1)
+    _check_augmentations(G, max_k=MAX_EFFICIENT_K + 2)
+
+
+def test_edgeless_graph():
+    G = nx.Graph()
+    G.add_nodes_from([1, 2, 3, 4])
+    _check_augmentations(G)
+
+
+def test_invalid_k():
+    G = nx.Graph()
+    pytest.raises(ValueError, list, k_edge_augmentation(G, k=-1))
+    pytest.raises(ValueError, list, k_edge_augmentation(G, k=0))
+
+
+def test_unfeasible():
+    G = tarjan_bridge_graph()
+    pytest.raises(nx.NetworkXUnfeasible, list, k_edge_augmentation(G, k=1, avail=[]))
+
+    pytest.raises(nx.NetworkXUnfeasible, list, k_edge_augmentation(G, k=2, avail=[]))
+
+    pytest.raises(
+        nx.NetworkXUnfeasible, list, k_edge_augmentation(G, k=2, avail=[(7, 9)])
+    )
+
+    # partial solutions should not error if real solutions are infeasible
+    aug_edges = list(k_edge_augmentation(G, k=2, avail=[(7, 9)], partial=True))
+    assert aug_edges == [(7, 9)]
+
+    _check_augmentations(G, avail=[], max_k=MAX_EFFICIENT_K + 2)
+
+    _check_augmentations(G, avail=[(7, 9)], max_k=MAX_EFFICIENT_K + 2)
+
+
+def test_tarjan():
+    G = tarjan_bridge_graph()
+
+    aug_edges = set(_augment_and_check(G, k=2)[0])
+    print(f"aug_edges = {aug_edges!r}")
+    # can't assert edge exactly equality due to non-determinant edge order
+    # but we do know the size of the solution must be 3
+    assert len(aug_edges) == 3
+
+    avail = [
+        (9, 7),
+        (8, 5),
+        (2, 10),
+        (6, 13),
+        (11, 18),
+        (1, 17),
+        (2, 3),
+        (16, 17),
+        (18, 14),
+        (15, 14),
+    ]
+    aug_edges = set(_augment_and_check(G, avail=avail, k=2)[0])
+
+    # Can't assert exact length since approximation depends on the order of a
+    # dict traversal.
+    assert len(aug_edges) <= 3 * 2
+
+    _check_augmentations(G, avail)
+
+
+def test_configuration():
+    # seeds = [2718183590, 2470619828, 1694705158, 3001036531, 2401251497]
+    seeds = [1001, 1002, 1003, 1004]
+    for seed in seeds:
+        deg_seq = nx.random_powerlaw_tree_sequence(20, seed=seed, tries=5000)
+        G = nx.Graph(nx.configuration_model(deg_seq, seed=seed))
+        G.remove_edges_from(nx.selfloop_edges(G))
+        _check_augmentations(G)
+
+
+def test_shell():
+    # seeds = [2057382236, 3331169846, 1840105863, 476020778, 2247498425]
+    seeds = [18]
+    for seed in seeds:
+        constructor = [(12, 70, 0.8), (15, 40, 0.6)]
+        G = nx.random_shell_graph(constructor, seed=seed)
+        _check_augmentations(G)
+
+
+def test_karate():
+    G = nx.karate_club_graph()
+    _check_augmentations(G)
+
+
+def test_star():
+    G = nx.star_graph(3)
+    _check_augmentations(G)
+
+    G = nx.star_graph(5)
+    _check_augmentations(G)
+
+    G = nx.star_graph(10)
+    _check_augmentations(G)
+
+
+def test_barbell():
+    G = nx.barbell_graph(5, 0)
+    _check_augmentations(G)
+
+    G = nx.barbell_graph(5, 2)
+    _check_augmentations(G)
+
+    G = nx.barbell_graph(5, 3)
+    _check_augmentations(G)
+
+    G = nx.barbell_graph(5, 4)
+    _check_augmentations(G)
+
+
+def test_bridge():
+    G = nx.Graph([(2393, 2257), (2393, 2685), (2685, 2257), (1758, 2257)])
+    _check_augmentations(G)
+
+
+def test_gnp_augmentation():
+    rng = random.Random(0)
+    G = nx.gnp_random_graph(30, 0.005, seed=0)
+    # Randomly make edges available
+    avail = {
+        (u, v): 1 + rng.random() for u, v in complement_edges(G) if rng.random() < 0.25
+    }
+    _check_augmentations(G, avail)
+
+
+def _assert_solution_properties(G, aug_edges, avail_dict=None):
+    """ Checks that aug_edges are consistently formatted """
+    if avail_dict is not None:
+        assert all(
+            e in avail_dict for e in aug_edges
+        ), "when avail is specified aug-edges should be in avail"
+
+    unique_aug = set(map(tuple, map(sorted, aug_edges)))
+    unique_aug = list(map(tuple, map(sorted, aug_edges)))
+    assert len(aug_edges) == len(unique_aug), "edges should be unique"
+
+    assert not any(u == v for u, v in unique_aug), "should be no self-edges"
+
+    assert not any(
+        G.has_edge(u, v) for u, v in unique_aug
+    ), "aug edges and G.edges should be disjoint"
+
+
+def _augment_and_check(
+    G, k, avail=None, weight=None, verbose=False, orig_k=None, max_aug_k=None
+):
+    """
+    Does one specific augmentation and checks for properties of the result
+    """
+    if orig_k is None:
+        try:
+            orig_k = nx.edge_connectivity(G)
+        except nx.NetworkXPointlessConcept:
+            orig_k = 0
+    info = {}
+    try:
+        if avail is not None:
+            # ensure avail is in dict form
+            avail_dict = dict(zip(*_unpack_available_edges(avail, weight=weight)))
+        else:
+            avail_dict = None
+        try:
+            # Find the augmentation if possible
+            generator = nx.k_edge_augmentation(G, k=k, weight=weight, avail=avail)
+            assert not isinstance(generator, list), "should always return an iter"
+            aug_edges = []
+            for edge in generator:
+                aug_edges.append(edge)
+        except nx.NetworkXUnfeasible:
+            infeasible = True
+            info["infeasible"] = True
+            assert len(aug_edges) == 0, "should not generate anything if unfeasible"
+
+            if avail is None:
+                n_nodes = G.number_of_nodes()
+                assert n_nodes <= k, (
+                    "unconstrained cases are only unfeasible if |V| <= k. "
+                    f"Got |V|={n_nodes} and k={k}"
+                )
+            else:
+                if max_aug_k is None:
+                    G_aug_all = G.copy()
+                    G_aug_all.add_edges_from(avail_dict.keys())
+                    try:
+                        max_aug_k = nx.edge_connectivity(G_aug_all)
+                    except nx.NetworkXPointlessConcept:
+                        max_aug_k = 0
+
+                assert max_aug_k < k, (
+                    "avail should only be unfeasible if using all edges "
+                    "does not achieve k-edge-connectivity"
+                )
+
+            # Test for a partial solution
+            partial_edges = list(
+                nx.k_edge_augmentation(G, k=k, weight=weight, partial=True, avail=avail)
+            )
+
+            info["n_partial_edges"] = len(partial_edges)
+
+            if avail_dict is None:
+                assert set(partial_edges) == set(
+                    complement_edges(G)
+                ), "unweighted partial solutions should be the complement"
+            elif len(avail_dict) > 0:
+                H = G.copy()
+
+                # Find the partial / full augmented connectivity
+                H.add_edges_from(partial_edges)
+                partial_conn = nx.edge_connectivity(H)
+
+                H.add_edges_from(set(avail_dict.keys()))
+                full_conn = nx.edge_connectivity(H)
+
+                # Full connectivity should be no better than our partial
+                # solution.
+                assert (
+                    partial_conn == full_conn
+                ), "adding more edges should not increase k-conn"
+
+            # Find the new edge-connectivity after adding the augmenting edges
+            aug_edges = partial_edges
+        else:
+            infeasible = False
+
+        # Find the weight of the augmentation
+        num_edges = len(aug_edges)
+        if avail is not None:
+            total_weight = sum([avail_dict[e] for e in aug_edges])
+        else:
+            total_weight = num_edges
+
+        info["total_weight"] = total_weight
+        info["num_edges"] = num_edges
+
+        # Find the new edge-connectivity after adding the augmenting edges
+        G_aug = G.copy()
+        G_aug.add_edges_from(aug_edges)
+        try:
+            aug_k = nx.edge_connectivity(G_aug)
+        except nx.NetworkXPointlessConcept:
+            aug_k = 0
+        info["aug_k"] = aug_k
+
+        # Do checks
+        if not infeasible and orig_k < k:
+            assert info["aug_k"] >= k, f"connectivity should increase to k={k} or more"
+
+        assert info["aug_k"] >= orig_k, "augmenting should never reduce connectivity"
+
+        _assert_solution_properties(G, aug_edges, avail_dict)
+
+    except Exception:
+        info["failed"] = True
+        print(f"edges = {list(G.edges())}")
+        print(f"nodes = {list(G.nodes())}")
+        print(f"aug_edges = {list(aug_edges)}")
+        print(f"info  = {info}")
+        raise
+    else:
+        if verbose:
+            print(f"info  = {info}")
+
+    if infeasible:
+        aug_edges = None
+    return aug_edges, info
+
+
+def _check_augmentations(G, avail=None, max_k=None, weight=None, verbose=False):
+    """ Helper to check weighted/unweighted cases with multiple values of k """
+    # Using all available edges, find the maximum edge-connectivity
+    try:
+        orig_k = nx.edge_connectivity(G)
+    except nx.NetworkXPointlessConcept:
+        orig_k = 0
+
+    if avail is not None:
+        all_aug_edges = _unpack_available_edges(avail, weight=weight)[0]
+        G_aug_all = G.copy()
+        G_aug_all.add_edges_from(all_aug_edges)
+        try:
+            max_aug_k = nx.edge_connectivity(G_aug_all)
+        except nx.NetworkXPointlessConcept:
+            max_aug_k = 0
+    else:
+        max_aug_k = G.number_of_nodes() - 1
+
+    if max_k is None:
+        max_k = min(4, max_aug_k)
+
+    avail_uniform = {e: 1 for e in complement_edges(G)}
+
+    if verbose:
+        print("\n=== CHECK_AUGMENTATION ===")
+        print(f"G.number_of_nodes = {G.number_of_nodes()!r}")
+        print(f"G.number_of_edges = {G.number_of_edges()!r}")
+        print(f"max_k = {max_k!r}")
+        print(f"max_aug_k = {max_aug_k!r}")
+        print(f"orig_k = {orig_k!r}")
+
+    # check augmentation for multiple values of k
+    for k in range(1, max_k + 1):
+        if verbose:
+            print("---------------")
+            print(f"Checking k = {k}")
+
+        # Check the unweighted version
+        if verbose:
+            print("unweighted case")
+        aug_edges1, info1 = _augment_and_check(G, k=k, verbose=verbose, orig_k=orig_k)
+
+        # Check that the weighted version with all available edges and uniform
+        # weights gives a similar solution to the unweighted case.
+        if verbose:
+            print("weighted uniform case")
+        aug_edges2, info2 = _augment_and_check(
+            G,
+            k=k,
+            avail=avail_uniform,
+            verbose=verbose,
+            orig_k=orig_k,
+            max_aug_k=G.number_of_nodes() - 1,
+        )
+
+        # Check the weighted version
+        if avail is not None:
+            if verbose:
+                print("weighted case")
+            aug_edges3, info3 = _augment_and_check(
+                G,
+                k=k,
+                avail=avail,
+                weight=weight,
+                verbose=verbose,
+                max_aug_k=max_aug_k,
+                orig_k=orig_k,
+            )
+
+        if aug_edges1 is not None:
+            # Check approximation ratios
+            if k == 1:
+                # when k=1, both solutions should be optimal
+                assert info2["total_weight"] == info1["total_weight"]
+            if k == 2:
+                # when k=2, the weighted version is an approximation
+                if orig_k == 0:
+                    # the approximation ratio is 3 if G is not connected
+                    assert info2["total_weight"] <= info1["total_weight"] * 3
+                else:
+                    # the approximation ratio is 2 if G is was connected
+                    assert info2["total_weight"] <= info1["total_weight"] * 2
+                _check_unconstrained_bridge_property(G, info1)
+
+
+def _check_unconstrained_bridge_property(G, info1):
+    # Check Theorem 5 from Eswaran and Tarjan. (1975) Augmentation problems
+    import math
+
+    bridge_ccs = list(nx.connectivity.bridge_components(G))
+    # condense G into an forest C
+    C = collapse(G, bridge_ccs)
+
+    p = len([n for n, d in C.degree() if d == 1])  # leafs
+    q = len([n for n, d in C.degree() if d == 0])  # isolated
+    if p + q > 1:
+        size_target = int(math.ceil(p / 2.0)) + q
+        size_aug = info1["num_edges"]
+        assert (
+            size_aug == size_target
+        ), "augmentation size is different from what theory predicts"

venv/Lib/site-packages/networkx/algorithms/connectivity/tests/test_edge_kcomponents.py

@@ -0,0 +1,485 @@
+import networkx as nx
+import itertools as it
+import pytest
+from networkx.utils import pairwise
+from networkx.algorithms.connectivity import bridge_components, EdgeComponentAuxGraph
+from networkx.algorithms.connectivity.edge_kcomponents import general_k_edge_subgraphs
+
+
+# ----------------
+# Helper functions
+# ----------------
+
+
+def fset(list_of_sets):
+    """ allows == to be used for list of sets """
+    return set(map(frozenset, list_of_sets))
+
+
+def _assert_subgraph_edge_connectivity(G, ccs_subgraph, k):
+    """
+    tests properties of k-edge-connected subgraphs
+
+    the actual edge connectivity should be no less than k unless the cc is a
+    single node.
+    """
+    for cc in ccs_subgraph:
+        C = G.subgraph(cc)
+        if len(cc) > 1:
+            connectivity = nx.edge_connectivity(C)
+            assert connectivity >= k
+
+
+def _memo_connectivity(G, u, v, memo):
+    edge = (u, v)
+    if edge in memo:
+        return memo[edge]
+    if not G.is_directed():
+        redge = (v, u)
+        if redge in memo:
+            return memo[redge]
+    memo[edge] = nx.edge_connectivity(G, *edge)
+    return memo[edge]
+
+
+def _all_pairs_connectivity(G, cc, k, memo):
+    # Brute force check
+    for u, v in it.combinations(cc, 2):
+        # Use a memoization dict to save on computation
+        connectivity = _memo_connectivity(G, u, v, memo)
+        if G.is_directed():
+            connectivity = min(connectivity, _memo_connectivity(G, v, u, memo))
+        assert connectivity >= k
+
+
+def _assert_local_cc_edge_connectivity(G, ccs_local, k, memo):
+    """
+    tests properties of k-edge-connected components
+
+    the local edge connectivity between each pair of nodes in the the original
+    graph should be no less than k unless the cc is a single node.
+    """
+    for cc in ccs_local:
+        if len(cc) > 1:
+            # Strategy for testing a bit faster: If the subgraph has high edge
+            # connectivity then it must have local connectivity
+            C = G.subgraph(cc)
+            connectivity = nx.edge_connectivity(C)
+            if connectivity < k:
+                # Otherwise do the brute force (with memoization) check
+                _all_pairs_connectivity(G, cc, k, memo)
+
+
+# Helper function
+def _check_edge_connectivity(G):
+    """
+    Helper - generates all k-edge-components using the aux graph.  Checks the
+    both local and subgraph edge connectivity of each cc. Also checks that
+    alternate methods of computing the k-edge-ccs generate the same result.
+    """
+    # Construct the auxiliary graph that can be used to make each k-cc or k-sub
+    aux_graph = EdgeComponentAuxGraph.construct(G)
+
+    # memoize the local connectivity in this graph
+    memo = {}
+
+    for k in it.count(1):
+        # Test "local" k-edge-components and k-edge-subgraphs
+        ccs_local = fset(aux_graph.k_edge_components(k))
+        ccs_subgraph = fset(aux_graph.k_edge_subgraphs(k))
+
+        # Check connectivity properties that should be garuenteed by the
+        # algorithms.
+        _assert_local_cc_edge_connectivity(G, ccs_local, k, memo)
+        _assert_subgraph_edge_connectivity(G, ccs_subgraph, k)
+
+        if k == 1 or k == 2 and not G.is_directed():
+            assert (
+                ccs_local == ccs_subgraph
+            ), "Subgraphs and components should be the same when k == 1 or (k == 2 and not G.directed())"
+
+        if G.is_directed():
+            # Test special case methods are the same as the aux graph
+            if k == 1:
+                alt_sccs = fset(nx.strongly_connected_components(G))
+                assert alt_sccs == ccs_local, "k=1 failed alt"
+                assert alt_sccs == ccs_subgraph, "k=1 failed alt"
+        else:
+            # Test special case methods are the same as the aux graph
+            if k == 1:
+                alt_ccs = fset(nx.connected_components(G))
+                assert alt_ccs == ccs_local, "k=1 failed alt"
+                assert alt_ccs == ccs_subgraph, "k=1 failed alt"
+            elif k == 2:
+                alt_bridge_ccs = fset(bridge_components(G))
+                assert alt_bridge_ccs == ccs_local, "k=2 failed alt"
+                assert alt_bridge_ccs == ccs_subgraph, "k=2 failed alt"
+            # if new methods for k == 3 or k == 4 are implemented add them here
+
+        # Check the general subgraph method works by itself
+        alt_subgraph_ccs = fset(
+            [set(C.nodes()) for C in general_k_edge_subgraphs(G, k=k)]
+        )
+        assert alt_subgraph_ccs == ccs_subgraph, "alt subgraph method failed"
+
+        # Stop once k is larger than all special case methods
+        # and we cannot break down ccs any further.
+        if k > 2 and all(len(cc) == 1 for cc in ccs_local):
+            break
+
+
+# ----------------
+# Misc tests
+# ----------------
+
+
+def test_zero_k_exception():
+    G = nx.Graph()
+    # functions that return generators error immediately
+    pytest.raises(ValueError, nx.k_edge_components, G, k=0)
+    pytest.raises(ValueError, nx.k_edge_subgraphs, G, k=0)
+
+    # actual generators only error when you get the first item
+    aux_graph = EdgeComponentAuxGraph.construct(G)
+    pytest.raises(ValueError, list, aux_graph.k_edge_components(k=0))
+    pytest.raises(ValueError, list, aux_graph.k_edge_subgraphs(k=0))
+
+    pytest.raises(ValueError, list, general_k_edge_subgraphs(G, k=0))
+
+
+def test_empty_input():
+    G = nx.Graph()
+    assert [] == list(nx.k_edge_components(G, k=5))
+    assert [] == list(nx.k_edge_subgraphs(G, k=5))
+
+    G = nx.DiGraph()
+    assert [] == list(nx.k_edge_components(G, k=5))
+    assert [] == list(nx.k_edge_subgraphs(G, k=5))
+
+
+def test_not_implemented():
+    G = nx.MultiGraph()
+    pytest.raises(nx.NetworkXNotImplemented, EdgeComponentAuxGraph.construct, G)
+    pytest.raises(nx.NetworkXNotImplemented, nx.k_edge_components, G, k=2)
+    pytest.raises(nx.NetworkXNotImplemented, nx.k_edge_subgraphs, G, k=2)
+    pytest.raises(nx.NetworkXNotImplemented, bridge_components, G)
+    pytest.raises(nx.NetworkXNotImplemented, bridge_components, nx.DiGraph())
+
+
+def test_general_k_edge_subgraph_quick_return():
+    # tests quick return optimization
+    G = nx.Graph()
+    G.add_node(0)
+    subgraphs = list(general_k_edge_subgraphs(G, k=1))
+    assert len(subgraphs) == 1
+    for subgraph in subgraphs:
+        assert subgraph.number_of_nodes() == 1
+
+    G.add_node(1)
+    subgraphs = list(general_k_edge_subgraphs(G, k=1))
+    assert len(subgraphs) == 2
+    for subgraph in subgraphs:
+        assert subgraph.number_of_nodes() == 1
+
+
+# ----------------
+# Undirected tests
+# ----------------
+
+
+def test_random_gnp():
+    # seeds = [1550709854, 1309423156, 4208992358, 2785630813, 1915069929]
+    seeds = [12, 13]
+
+    for seed in seeds:
+        G = nx.gnp_random_graph(20, 0.2, seed=seed)
+        _check_edge_connectivity(G)
+
+
+def test_configuration():
+    # seeds = [2718183590, 2470619828, 1694705158, 3001036531, 2401251497]
+    seeds = [14, 15]
+    for seed in seeds:
+        deg_seq = nx.random_powerlaw_tree_sequence(20, seed=seed, tries=5000)
+        G = nx.Graph(nx.configuration_model(deg_seq, seed=seed))
+        G.remove_edges_from(nx.selfloop_edges(G))
+        _check_edge_connectivity(G)
+
+
+def test_shell():
+    # seeds = [2057382236, 3331169846, 1840105863, 476020778, 2247498425]
+    seeds = [20]
+    for seed in seeds:
+        constructor = [(12, 70, 0.8), (15, 40, 0.6)]
+        G = nx.random_shell_graph(constructor, seed=seed)
+        _check_edge_connectivity(G)
+
+
+def test_karate():
+    G = nx.karate_club_graph()
+    _check_edge_connectivity(G)
+
+
+def test_tarjan_bridge():
+    # graph from tarjan paper
+    # RE Tarjan - "A note on finding the bridges of a graph"
+    # Information Processing Letters, 1974 - Elsevier
+    # doi:10.1016/0020-0190(74)90003-9.
+    # define 2-connected components and bridges
+    ccs = [
+        (1, 2, 4, 3, 1, 4),
+        (5, 6, 7, 5),
+        (8, 9, 10, 8),
+        (17, 18, 16, 15, 17),
+        (11, 12, 14, 13, 11, 14),
+    ]
+    bridges = [(4, 8), (3, 5), (3, 17)]
+    G = nx.Graph(it.chain(*(pairwise(path) for path in ccs + bridges)))
+    _check_edge_connectivity(G)
+
+
+def test_bridge_cc():
+    # define 2-connected components and bridges
+    cc2 = [(1, 2, 4, 3, 1, 4), (8, 9, 10, 8), (11, 12, 13, 11)]
+    bridges = [(4, 8), (3, 5), (20, 21), (22, 23, 24)]
+    G = nx.Graph(it.chain(*(pairwise(path) for path in cc2 + bridges)))
+    bridge_ccs = fset(bridge_components(G))
+    target_ccs = fset(
+        [{1, 2, 3, 4}, {5}, {8, 9, 10}, {11, 12, 13}, {20}, {21}, {22}, {23}, {24}]
+    )
+    assert bridge_ccs == target_ccs
+    _check_edge_connectivity(G)
+
+
+def test_undirected_aux_graph():
+    # Graph similar to the one in
+    # http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0136264
+    a, b, c, d, e, f, g, h, i = "abcdefghi"
+    paths = [
+        (a, d, b, f, c),
+        (a, e, b),
+        (a, e, b, c, g, b, a),
+        (c, b),
+        (f, g, f),
+        (h, i),
+    ]
+    G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
+    aux_graph = EdgeComponentAuxGraph.construct(G)
+
+    components_1 = fset(aux_graph.k_edge_subgraphs(k=1))
+    target_1 = fset([{a, b, c, d, e, f, g}, {h, i}])
+    assert target_1 == components_1
+
+    # Check that the undirected case for k=1 agrees with CCs
+    alt_1 = fset(nx.k_edge_subgraphs(G, k=1))
+    assert alt_1 == components_1
+
+    components_2 = fset(aux_graph.k_edge_subgraphs(k=2))
+    target_2 = fset([{a, b, c, d, e, f, g}, {h}, {i}])
+    assert target_2 == components_2
+
+    # Check that the undirected case for k=2 agrees with bridge components
+    alt_2 = fset(nx.k_edge_subgraphs(G, k=2))
+    assert alt_2 == components_2
+
+    components_3 = fset(aux_graph.k_edge_subgraphs(k=3))
+    target_3 = fset([{a}, {b, c, f, g}, {d}, {e}, {h}, {i}])
+    assert target_3 == components_3
+
+    components_4 = fset(aux_graph.k_edge_subgraphs(k=4))
+    target_4 = fset([{a}, {b}, {c}, {d}, {e}, {f}, {g}, {h}, {i}])
+    assert target_4 == components_4
+
+    _check_edge_connectivity(G)
+
+
+def test_local_subgraph_difference():
+    paths = [
+        (11, 12, 13, 14, 11, 13, 14, 12),  # first 4-clique
+        (21, 22, 23, 24, 21, 23, 24, 22),  # second 4-clique
+        # paths connecting each node of the 4 cliques
+        (11, 101, 21),
+        (12, 102, 22),
+        (13, 103, 23),
+        (14, 104, 24),
+    ]
+    G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
+    aux_graph = EdgeComponentAuxGraph.construct(G)
+
+    # Each clique is returned separately in k-edge-subgraphs
+    subgraph_ccs = fset(aux_graph.k_edge_subgraphs(3))
+    subgraph_target = fset(
+        [{101}, {102}, {103}, {104}, {21, 22, 23, 24}, {11, 12, 13, 14}]
+    )
+    assert subgraph_ccs == subgraph_target
+
+    # But in k-edge-ccs they are returned together
+    # because they are locally 3-edge-connected
+    local_ccs = fset(aux_graph.k_edge_components(3))
+    local_target = fset([{101}, {102}, {103}, {104}, {11, 12, 13, 14, 21, 22, 23, 24}])
+    assert local_ccs == local_target
+
+
+def test_local_subgraph_difference_directed():
+    dipaths = [(1, 2, 3, 4, 1), (1, 3, 1)]
+    G = nx.DiGraph(it.chain(*[pairwise(path) for path in dipaths]))
+
+    assert fset(nx.k_edge_components(G, k=1)) == fset(nx.k_edge_subgraphs(G, k=1))
+
+    # Unlike undirected graphs, when k=2, for directed graphs there is a case
+    # where the k-edge-ccs are not the same as the k-edge-subgraphs.
+    # (in directed graphs ccs and subgraphs are the same when k=2)
+    assert fset(nx.k_edge_components(G, k=2)) != fset(nx.k_edge_subgraphs(G, k=2))
+
+    assert fset(nx.k_edge_components(G, k=3)) == fset(nx.k_edge_subgraphs(G, k=3))
+
+    _check_edge_connectivity(G)
+
+
+def test_triangles():
+    paths = [
+        (11, 12, 13, 11),  # first 3-clique
+        (21, 22, 23, 21),  # second 3-clique
+        (11, 21),  # connected by an edge
+    ]
+    G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
+
+    # subgraph and ccs are the same in all cases here
+    assert fset(nx.k_edge_components(G, k=1)) == fset(nx.k_edge_subgraphs(G, k=1))
+
+    assert fset(nx.k_edge_components(G, k=2)) == fset(nx.k_edge_subgraphs(G, k=2))
+
+    assert fset(nx.k_edge_components(G, k=3)) == fset(nx.k_edge_subgraphs(G, k=3))
+
+    _check_edge_connectivity(G)
+
+
+def test_four_clique():
+    paths = [
+        (11, 12, 13, 14, 11, 13, 14, 12),  # first 4-clique
+        (21, 22, 23, 24, 21, 23, 24, 22),  # second 4-clique
+        # paths connecting the 4 cliques such that they are
+        # 3-connected in G, but not in the subgraph.
+        # Case where the nodes bridging them do not have degree less than 3.
+        (100, 13),
+        (12, 100, 22),
+        (13, 200, 23),
+        (14, 300, 24),
+    ]
+    G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
+
+    # The subgraphs and ccs are different for k=3
+    local_ccs = fset(nx.k_edge_components(G, k=3))
+    subgraphs = fset(nx.k_edge_subgraphs(G, k=3))
+    assert local_ccs != subgraphs
+
+    # The cliques ares in the same cc
+    clique1 = frozenset(paths[0])
+    clique2 = frozenset(paths[1])
+    assert clique1.union(clique2).union({100}) in local_ccs
+
+    # but different subgraphs
+    assert clique1 in subgraphs
+    assert clique2 in subgraphs
+
+    assert G.degree(100) == 3
+
+    _check_edge_connectivity(G)
+
+
+def test_five_clique():
+    # Make a graph that can be disconnected less than 4 edges, but no node has
+    # degree less than 4.
+    G = nx.disjoint_union(nx.complete_graph(5), nx.complete_graph(5))
+    paths = [
+        # add aux-connections
+        (1, 100, 6),
+        (2, 100, 7),
+        (3, 200, 8),
+        (4, 200, 100),
+    ]
+    G.add_edges_from(it.chain(*[pairwise(path) for path in paths]))
+    assert min(dict(nx.degree(G)).values()) == 4
+
+    # For k=3 they are the same
+    assert fset(nx.k_edge_components(G, k=3)) == fset(nx.k_edge_subgraphs(G, k=3))
+
+    # For k=4 they are the different
+    # the aux nodes are in the same CC as clique 1 but no the same subgraph
+    assert fset(nx.k_edge_components(G, k=4)) != fset(nx.k_edge_subgraphs(G, k=4))
+
+    # For k=5 they are not the same
+    assert fset(nx.k_edge_components(G, k=5)) != fset(nx.k_edge_subgraphs(G, k=5))
+
+    # For k=6 they are the same
+    assert fset(nx.k_edge_components(G, k=6)) == fset(nx.k_edge_subgraphs(G, k=6))
+    _check_edge_connectivity(G)
+
+
+# ----------------
+# Undirected tests
+# ----------------
+
+
+def test_directed_aux_graph():
+    # Graph similar to the one in
+    # http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0136264
+    a, b, c, d, e, f, g, h, i = "abcdefghi"
+    dipaths = [
+        (a, d, b, f, c),
+        (a, e, b),
+        (a, e, b, c, g, b, a),
+        (c, b),
+        (f, g, f),
+        (h, i),
+    ]
+    G = nx.DiGraph(it.chain(*[pairwise(path) for path in dipaths]))
+    aux_graph = EdgeComponentAuxGraph.construct(G)
+
+    components_1 = fset(aux_graph.k_edge_subgraphs(k=1))
+    target_1 = fset([{a, b, c, d, e, f, g}, {h}, {i}])
+    assert target_1 == components_1
+
+    # Check that the directed case for k=1 agrees with SCCs
+    alt_1 = fset(nx.strongly_connected_components(G))
+    assert alt_1 == components_1
+
+    components_2 = fset(aux_graph.k_edge_subgraphs(k=2))
+    target_2 = fset([{i}, {e}, {d}, {b, c, f, g}, {h}, {a}])
+    assert target_2 == components_2
+
+    components_3 = fset(aux_graph.k_edge_subgraphs(k=3))
+    target_3 = fset([{a}, {b}, {c}, {d}, {e}, {f}, {g}, {h}, {i}])
+    assert target_3 == components_3
+
+
+def test_random_gnp_directed():
+    # seeds = [3894723670, 500186844, 267231174, 2181982262, 1116750056]
+    seeds = [21]
+    for seed in seeds:
+        G = nx.gnp_random_graph(20, 0.2, directed=True, seed=seed)
+        _check_edge_connectivity(G)
+
+
+def test_configuration_directed():
+    # seeds = [671221681, 2403749451, 124433910, 672335939, 1193127215]
+    seeds = [67]
+    for seed in seeds:
+        deg_seq = nx.random_powerlaw_tree_sequence(20, seed=seed, tries=5000)
+        G = nx.DiGraph(nx.configuration_model(deg_seq, seed=seed))
+        G.remove_edges_from(nx.selfloop_edges(G))
+        _check_edge_connectivity(G)
+
+
+def test_shell_directed():
+    # seeds = [3134027055, 4079264063, 1350769518, 1405643020, 530038094]
+    seeds = [31]
+    for seed in seeds:
+        constructor = [(12, 70, 0.8), (15, 40, 0.6)]
+        G = nx.random_shell_graph(constructor, seed=seed).to_directed()
+        _check_edge_connectivity(G)
+
+
+def test_karate_directed():
+    G = nx.karate_club_graph().to_directed()
+    _check_edge_connectivity(G)

venv/Lib/site-packages/networkx/algorithms/connectivity/tests/test_kcomponents.py

@@ -0,0 +1,295 @@
+# Test for Moody and White k-components algorithm
+import pytest
+import networkx as nx
+from networkx.algorithms.connectivity.kcomponents import (
+    build_k_number_dict,
+    _consolidate,
+)
+
+##
+# A nice synthetic graph
+##
+
+
+def torrents_and_ferraro_graph():
+    # Graph from https://arxiv.org/pdf/1503.04476v1 p.26
+    G = nx.convert_node_labels_to_integers(
+        nx.grid_graph([5, 5]), label_attribute="labels"
+    )
+    rlabels = nx.get_node_attributes(G, "labels")
+    labels = {v: k for k, v in rlabels.items()}
+
+    for nodes in [(labels[(0, 4)], labels[(1, 4)]), (labels[(3, 4)], labels[(4, 4)])]:
+        new_node = G.order() + 1
+        # Petersen graph is triconnected
+        P = nx.petersen_graph()
+        G = nx.disjoint_union(G, P)
+        # Add two edges between the grid and P
+        G.add_edge(new_node + 1, nodes[0])
+        G.add_edge(new_node, nodes[1])
+        # K5 is 4-connected
+        K = nx.complete_graph(5)
+        G = nx.disjoint_union(G, K)
+        # Add three edges between P and K5
+        G.add_edge(new_node + 2, new_node + 11)
+        G.add_edge(new_node + 3, new_node + 12)
+        G.add_edge(new_node + 4, new_node + 13)
+        # Add another K5 sharing a node
+        G = nx.disjoint_union(G, K)
+        nbrs = G[new_node + 10]
+        G.remove_node(new_node + 10)
+        for nbr in nbrs:
+            G.add_edge(new_node + 17, nbr)
+        # This edge makes the graph biconnected; it's
+        # needed because K5s share only one node.
+        G.add_edge(new_node + 16, new_node + 8)
+
+    for nodes in [(labels[(0, 0)], labels[(1, 0)]), (labels[(3, 0)], labels[(4, 0)])]:
+        new_node = G.order() + 1
+        # Petersen graph is triconnected
+        P = nx.petersen_graph()
+        G = nx.disjoint_union(G, P)
+        # Add two edges between the grid and P
+        G.add_edge(new_node + 1, nodes[0])
+        G.add_edge(new_node, nodes[1])
+        # K5 is 4-connected
+        K = nx.complete_graph(5)
+        G = nx.disjoint_union(G, K)
+        # Add three edges between P and K5
+        G.add_edge(new_node + 2, new_node + 11)
+        G.add_edge(new_node + 3, new_node + 12)
+        G.add_edge(new_node + 4, new_node + 13)
+        # Add another K5 sharing two nodes
+        G = nx.disjoint_union(G, K)
+        nbrs = G[new_node + 10]
+        G.remove_node(new_node + 10)
+        for nbr in nbrs:
+            G.add_edge(new_node + 17, nbr)
+        nbrs2 = G[new_node + 9]
+        G.remove_node(new_node + 9)
+        for nbr in nbrs2:
+            G.add_edge(new_node + 18, nbr)
+    return G
+
+
+def test_directed():
+    with pytest.raises(nx.NetworkXNotImplemented):
+        G = nx.gnp_random_graph(10, 0.2, directed=True, seed=42)
+        nx.k_components(G)
+
+
+# Helper function
+def _check_connectivity(G, k_components):
+    for k, components in k_components.items():
+        if k < 3:
+            continue
+        # check that k-components have node connectivity >= k.
+        for component in components:
+            C = G.subgraph(component)
+            K = nx.node_connectivity(C)
+            assert K >= k
+
+
+@pytest.mark.slow
+def test_torrents_and_ferraro_graph():
+    G = torrents_and_ferraro_graph()
+    result = nx.k_components(G)
+    _check_connectivity(G, result)
+
+    # In this example graph there are 8 3-components, 4 with 15 nodes
+    # and 4 with 5 nodes.
+    assert len(result[3]) == 8
+    assert len([c for c in result[3] if len(c) == 15]) == 4
+    assert len([c for c in result[3] if len(c) == 5]) == 4
+    # There are also 8 4-components all with 5 nodes.
+    assert len(result[4]) == 8
+    assert all(len(c) == 5 for c in result[4])
+
+
+@pytest.mark.slow
+def test_random_gnp():
+    G = nx.gnp_random_graph(50, 0.2, seed=42)
+    result = nx.k_components(G)
+    _check_connectivity(G, result)
+
+
+@pytest.mark.slow
+def test_shell():
+    constructor = [(20, 80, 0.8), (80, 180, 0.6)]
+    G = nx.random_shell_graph(constructor, seed=42)
+    result = nx.k_components(G)
+    _check_connectivity(G, result)
+
+
+def test_configuration():
+    deg_seq = nx.random_powerlaw_tree_sequence(100, tries=5, seed=72)
+    G = nx.Graph(nx.configuration_model(deg_seq))
+    G.remove_edges_from(nx.selfloop_edges(G))
+    result = nx.k_components(G)
+    _check_connectivity(G, result)
+
+
+def test_karate():
+    G = nx.karate_club_graph()
+    result = nx.k_components(G)
+    _check_connectivity(G, result)
+
+
+def test_karate_component_number():
+    karate_k_num = {
+        0: 4,
+        1: 4,
+        2: 4,
+        3: 4,
+        4: 3,
+        5: 3,
+        6: 3,
+        7: 4,
+        8: 4,
+        9: 2,
+        10: 3,
+        11: 1,
+        12: 2,
+        13: 4,
+        14: 2,
+        15: 2,
+        16: 2,
+        17: 2,
+        18: 2,
+        19: 3,
+        20: 2,
+        21: 2,
+        22: 2,
+        23: 3,
+        24: 3,
+        25: 3,
+        26: 2,
+        27: 3,
+        28: 3,
+        29: 3,
+        30: 4,
+        31: 3,
+        32: 4,
+        33: 4,
+    }
+    G = nx.karate_club_graph()
+    k_components = nx.k_components(G)
+    k_num = build_k_number_dict(k_components)
+    assert karate_k_num == k_num
+
+
+def test_davis_southern_women():
+    G = nx.davis_southern_women_graph()
+    result = nx.k_components(G)
+    _check_connectivity(G, result)
+
+
+def test_davis_southern_women_detail_3_and_4():
+    solution = {
+        3: [
+            {
+                "Nora Fayette",
+                "E10",
+                "Myra Liddel",
+                "E12",
+                "E14",
+                "Frances Anderson",
+                "Evelyn Jefferson",
+                "Ruth DeSand",
+                "Helen Lloyd",
+                "Eleanor Nye",
+                "E9",
+                "E8",
+                "E5",
+                "E4",
+                "E7",
+                "E6",
+                "E1",
+                "Verne Sanderson",
+                "E3",
+                "E2",
+                "Theresa Anderson",
+                "Pearl Oglethorpe",
+                "Katherina Rogers",
+                "Brenda Rogers",
+                "E13",
+                "Charlotte McDowd",
+                "Sylvia Avondale",
+                "Laura Mandeville",
+            }
+        ],
+        4: [
+            {
+                "Nora Fayette",
+                "E10",
+                "Verne Sanderson",
+                "E12",
+                "Frances Anderson",
+                "Evelyn Jefferson",
+                "Ruth DeSand",
+                "Helen Lloyd",
+                "Eleanor Nye",
+                "E9",
+                "E8",
+                "E5",
+                "E4",
+                "E7",
+                "E6",
+                "Myra Liddel",
+                "E3",
+                "Theresa Anderson",
+                "Katherina Rogers",
+                "Brenda Rogers",
+                "Charlotte McDowd",
+                "Sylvia Avondale",
+                "Laura Mandeville",
+            }
+        ],
+    }
+    G = nx.davis_southern_women_graph()
+    result = nx.k_components(G)
+    for k, components in result.items():
+        if k < 3:
+            continue
+        assert len(components) == len(solution[k])
+        for component in components:
+            assert component in solution[k]
+
+
+def test_set_consolidation_rosettacode():
+    # Tests from http://rosettacode.org/wiki/Set_consolidation
+    def list_of_sets_equal(result, solution):
+        assert {frozenset(s) for s in result} == {frozenset(s) for s in solution}
+
+    question = [{"A", "B"}, {"C", "D"}]
+    solution = [{"A", "B"}, {"C", "D"}]
+    list_of_sets_equal(_consolidate(question, 1), solution)
+    question = [{"A", "B"}, {"B", "C"}]
+    solution = [{"A", "B", "C"}]
+    list_of_sets_equal(_consolidate(question, 1), solution)
+    question = [{"A", "B"}, {"C", "D"}, {"D", "B"}]
+    solution = [{"A", "C", "B", "D"}]
+    list_of_sets_equal(_consolidate(question, 1), solution)
+    question = [{"H", "I", "K"}, {"A", "B"}, {"C", "D"}, {"D", "B"}, {"F", "G", "H"}]
+    solution = [{"A", "C", "B", "D"}, {"G", "F", "I", "H", "K"}]
+    list_of_sets_equal(_consolidate(question, 1), solution)
+    question = [
+        {"A", "H"},
+        {"H", "I", "K"},
+        {"A", "B"},
+        {"C", "D"},
+        {"D", "B"},
+        {"F", "G", "H"},
+    ]
+    solution = [{"A", "C", "B", "D", "G", "F", "I", "H", "K"}]
+    list_of_sets_equal(_consolidate(question, 1), solution)
+    question = [
+        {"H", "I", "K"},
+        {"A", "B"},
+        {"C", "D"},
+        {"D", "B"},
+        {"F", "G", "H"},
+        {"A", "H"},
+    ]
+    solution = [{"A", "C", "B", "D", "G", "F", "I", "H", "K"}]
+    list_of_sets_equal(_consolidate(question, 1), solution)

venv/Lib/site-packages/networkx/algorithms/connectivity/tests/test_kcutsets.py

@@ -0,0 +1,266 @@
+# Jordi Torrents
+# Test for k-cutsets
+import itertools
+import pytest
+
+import networkx as nx
+from networkx.algorithms import flow
+from networkx.algorithms.connectivity.kcutsets import _is_separating_set
+
+MAX_CUTSETS_TO_TEST = 4  # originally 100. cut to decrease testing time
+
+flow_funcs = [
+    flow.boykov_kolmogorov,
+    flow.dinitz,
+    flow.edmonds_karp,
+    flow.preflow_push,
+    flow.shortest_augmenting_path,
+]
+
+
+##
+# Some nice synthetic graphs
+##
+def graph_example_1():
+    G = nx.convert_node_labels_to_integers(
+        nx.grid_graph([5, 5]), label_attribute="labels"
+    )
+    rlabels = nx.get_node_attributes(G, "labels")
+    labels = {v: k for k, v in rlabels.items()}
+
+    for nodes in [
+        (labels[(0, 0)], labels[(1, 0)]),
+        (labels[(0, 4)], labels[(1, 4)]),
+        (labels[(3, 0)], labels[(4, 0)]),
+        (labels[(3, 4)], labels[(4, 4)]),
+    ]:
+        new_node = G.order() + 1
+        # Petersen graph is triconnected
+        P = nx.petersen_graph()
+        G = nx.disjoint_union(G, P)
+        # Add two edges between the grid and P
+        G.add_edge(new_node + 1, nodes[0])
+        G.add_edge(new_node, nodes[1])
+        # K5 is 4-connected
+        K = nx.complete_graph(5)
+        G = nx.disjoint_union(G, K)
+        # Add three edges between P and K5
+        G.add_edge(new_node + 2, new_node + 11)
+        G.add_edge(new_node + 3, new_node + 12)
+        G.add_edge(new_node + 4, new_node + 13)
+        # Add another K5 sharing a node
+        G = nx.disjoint_union(G, K)
+        nbrs = G[new_node + 10]
+        G.remove_node(new_node + 10)
+        for nbr in nbrs:
+            G.add_edge(new_node + 17, nbr)
+        G.add_edge(new_node + 16, new_node + 5)
+    return G
+
+
+def torrents_and_ferraro_graph():
+    G = nx.convert_node_labels_to_integers(
+        nx.grid_graph([5, 5]), label_attribute="labels"
+    )
+    rlabels = nx.get_node_attributes(G, "labels")
+    labels = {v: k for k, v in rlabels.items()}
+
+    for nodes in [(labels[(0, 4)], labels[(1, 4)]), (labels[(3, 4)], labels[(4, 4)])]:
+        new_node = G.order() + 1
+        # Petersen graph is triconnected
+        P = nx.petersen_graph()
+        G = nx.disjoint_union(G, P)
+        # Add two edges between the grid and P
+        G.add_edge(new_node + 1, nodes[0])
+        G.add_edge(new_node, nodes[1])
+        # K5 is 4-connected
+        K = nx.complete_graph(5)
+        G = nx.disjoint_union(G, K)
+        # Add three edges between P and K5
+        G.add_edge(new_node + 2, new_node + 11)
+        G.add_edge(new_node + 3, new_node + 12)
+        G.add_edge(new_node + 4, new_node + 13)
+        # Add another K5 sharing a node
+        G = nx.disjoint_union(G, K)
+        nbrs = G[new_node + 10]
+        G.remove_node(new_node + 10)
+        for nbr in nbrs:
+            G.add_edge(new_node + 17, nbr)
+        # Commenting this makes the graph not biconnected !!
+        # This stupid mistake make one reviewer very angry :P
+        G.add_edge(new_node + 16, new_node + 8)
+
+    for nodes in [(labels[(0, 0)], labels[(1, 0)]), (labels[(3, 0)], labels[(4, 0)])]:
+        new_node = G.order() + 1
+        # Petersen graph is triconnected
+        P = nx.petersen_graph()
+        G = nx.disjoint_union(G, P)
+        # Add two edges between the grid and P
+        G.add_edge(new_node + 1, nodes[0])
+        G.add_edge(new_node, nodes[1])
+        # K5 is 4-connected
+        K = nx.complete_graph(5)
+        G = nx.disjoint_union(G, K)
+        # Add three edges between P and K5
+        G.add_edge(new_node + 2, new_node + 11)
+        G.add_edge(new_node + 3, new_node + 12)
+        G.add_edge(new_node + 4, new_node + 13)
+        # Add another K5 sharing two nodes
+        G = nx.disjoint_union(G, K)
+        nbrs = G[new_node + 10]
+        G.remove_node(new_node + 10)
+        for nbr in nbrs:
+            G.add_edge(new_node + 17, nbr)
+        nbrs2 = G[new_node + 9]
+        G.remove_node(new_node + 9)
+        for nbr in nbrs2:
+            G.add_edge(new_node + 18, nbr)
+    return G
+
+
+# Helper function
+def _check_separating_sets(G):
+    for cc in nx.connected_components(G):
+        if len(cc) < 3:
+            continue
+        Gc = G.subgraph(cc)
+        node_conn = nx.node_connectivity(Gc)
+        all_cuts = nx.all_node_cuts(Gc)
+        # Only test a limited number of cut sets to reduce test time.
+        for cut in itertools.islice(all_cuts, MAX_CUTSETS_TO_TEST):
+            assert node_conn == len(cut)
+            assert not nx.is_connected(nx.restricted_view(G, cut, []))
+
+
+@pytest.mark.slow
+def test_torrents_and_ferraro_graph():
+    G = torrents_and_ferraro_graph()
+    _check_separating_sets(G)
+
+
+def test_example_1():
+    G = graph_example_1()
+    _check_separating_sets(G)
+
+
+def test_random_gnp():
+    G = nx.gnp_random_graph(100, 0.1, seed=42)
+    _check_separating_sets(G)
+
+
+def test_shell():
+    constructor = [(20, 80, 0.8), (80, 180, 0.6)]
+    G = nx.random_shell_graph(constructor, seed=42)
+    _check_separating_sets(G)
+
+
+def test_configuration():
+    deg_seq = nx.random_powerlaw_tree_sequence(100, tries=5, seed=72)
+    G = nx.Graph(nx.configuration_model(deg_seq))
+    G.remove_edges_from(nx.selfloop_edges(G))
+    _check_separating_sets(G)
+
+
+def test_karate():
+    G = nx.karate_club_graph()
+    _check_separating_sets(G)
+
+
+def _generate_no_biconnected(max_attempts=50):
+    attempts = 0
+    while True:
+        G = nx.fast_gnp_random_graph(100, 0.0575, seed=42)
+        if nx.is_connected(G) and not nx.is_biconnected(G):
+            attempts = 0
+            yield G
+        else:
+            if attempts >= max_attempts:
+                msg = f"Tried {attempts} times: no suitable Graph."
+                raise Exception(msg)
+            else:
+                attempts += 1
+
+
+def test_articulation_points():
+    Ggen = _generate_no_biconnected()
+    for i in range(1):  # change 1 to 3 or more for more realizations.
+        G = next(Ggen)
+        articulation_points = list({a} for a in nx.articulation_points(G))
+        for cut in nx.all_node_cuts(G):
+            assert cut in articulation_points
+
+
+def test_grid_2d_graph():
+    # All minimum node cuts of a 2d grid
+    # are the four pairs of nodes that are
+    # neighbors of the four corner nodes.
+    G = nx.grid_2d_graph(5, 5)
+    solution = [{(0, 1), (1, 0)}, {(3, 0), (4, 1)}, {(3, 4), (4, 3)}, {(0, 3), (1, 4)}]
+    for cut in nx.all_node_cuts(G):
+        assert cut in solution
+
+
+def test_disconnected_graph():
+    G = nx.fast_gnp_random_graph(100, 0.01, seed=42)
+    cuts = nx.all_node_cuts(G)
+    pytest.raises(nx.NetworkXError, next, cuts)
+
+
+@pytest.mark.slow
+def test_alternative_flow_functions():
+    graphs = [nx.grid_2d_graph(4, 4), nx.cycle_graph(5)]
+    for G in graphs:
+        node_conn = nx.node_connectivity(G)
+        for flow_func in flow_funcs:
+            all_cuts = nx.all_node_cuts(G, flow_func=flow_func)
+            # Only test a limited number of cut sets to reduce test time.
+            for cut in itertools.islice(all_cuts, MAX_CUTSETS_TO_TEST):
+                assert node_conn == len(cut)
+                assert not nx.is_connected(nx.restricted_view(G, cut, []))
+
+
+def test_is_separating_set_complete_graph():
+    G = nx.complete_graph(5)
+    assert _is_separating_set(G, {0, 1, 2, 3})
+
+
+def test_is_separating_set():
+    for i in [5, 10, 15]:
+        G = nx.star_graph(i)
+        max_degree_node = max(G, key=G.degree)
+        assert _is_separating_set(G, {max_degree_node})
+
+
+def test_non_repeated_cuts():
+    # The algorithm was repeating the cut {0, 1} for the giant biconnected
+    # component of the Karate club graph.
+    K = nx.karate_club_graph()
+    bcc = max(list(nx.biconnected_components(K)), key=len)
+    G = K.subgraph(bcc)
+    solution = [{32, 33}, {2, 33}, {0, 3}, {0, 1}, {29, 33}]
+    cuts = list(nx.all_node_cuts(G))
+    if len(solution) != len(cuts):
+        print(nx.info(G))
+        print(f"Solution: {solution}")
+        print(f"Result: {cuts}")
+    assert len(solution) == len(cuts)
+    for cut in cuts:
+        assert cut in solution
+
+
+def test_cycle_graph():
+    G = nx.cycle_graph(5)
+    solution = [{0, 2}, {0, 3}, {1, 3}, {1, 4}, {2, 4}]
+    cuts = list(nx.all_node_cuts(G))
+    assert len(solution) == len(cuts)
+    for cut in cuts:
+        assert cut in solution
+
+
+def test_complete_graph():
+    G = nx.complete_graph(5)
+    solution = [{0, 1, 2, 3}, {0, 1, 2, 4}, {0, 1, 3, 4}, {0, 2, 3, 4}, {1, 2, 3, 4}]
+    cuts = list(nx.all_node_cuts(G))
+    assert len(solution) == len(cuts)
+    for cut in cuts:
+        assert cut in solution

venv/Lib/site-packages/networkx/algorithms/connectivity/tests/test_stoer_wagner.py

@@ -0,0 +1,100 @@
+from itertools import chain
+import networkx as nx
+import pytest
+
+
+def _check_partition(G, cut_value, partition, weight):
+    assert isinstance(partition, tuple)
+    assert len(partition) == 2
+    assert isinstance(partition[0], list)
+    assert isinstance(partition[1], list)
+    assert len(partition[0]) > 0
+    assert len(partition[1]) > 0
+    assert sum(map(len, partition)) == len(G)
+    assert set(chain.from_iterable(partition)) == set(G)
+    partition = tuple(map(set, partition))
+    w = 0
+    for u, v, e in G.edges(data=True):
+        if (u in partition[0]) == (v in partition[1]):
+            w += e.get(weight, 1)
+    assert w == cut_value
+
+
+def _test_stoer_wagner(G, answer, weight="weight"):
+    cut_value, partition = nx.stoer_wagner(G, weight, heap=nx.utils.PairingHeap)
+    assert cut_value == answer
+    _check_partition(G, cut_value, partition, weight)
+    cut_value, partition = nx.stoer_wagner(G, weight, heap=nx.utils.BinaryHeap)
+    assert cut_value == answer
+    _check_partition(G, cut_value, partition, weight)
+
+
+def test_graph1():
+    G = nx.Graph()
+    G.add_edge("x", "a", weight=3)
+    G.add_edge("x", "b", weight=1)
+    G.add_edge("a", "c", weight=3)
+    G.add_edge("b", "c", weight=5)
+    G.add_edge("b", "d", weight=4)
+    G.add_edge("d", "e", weight=2)
+    G.add_edge("c", "y", weight=2)
+    G.add_edge("e", "y", weight=3)
+    _test_stoer_wagner(G, 4)
+
+
+def test_graph2():
+    G = nx.Graph()
+    G.add_edge("x", "a")
+    G.add_edge("x", "b")
+    G.add_edge("a", "c")
+    G.add_edge("b", "c")
+    G.add_edge("b", "d")
+    G.add_edge("d", "e")
+    G.add_edge("c", "y")
+    G.add_edge("e", "y")
+    _test_stoer_wagner(G, 2)
+
+
+def test_graph3():
+    # Source:
+    # Stoer, M. and Wagner, F. (1997). "A simple min-cut algorithm". Journal of
+    # the ACM 44 (4), 585-591.
+    G = nx.Graph()
+    G.add_edge(1, 2, weight=2)
+    G.add_edge(1, 5, weight=3)
+    G.add_edge(2, 3, weight=3)
+    G.add_edge(2, 5, weight=2)
+    G.add_edge(2, 6, weight=2)
+    G.add_edge(3, 4, weight=4)
+    G.add_edge(3, 7, weight=2)
+    G.add_edge(4, 7, weight=2)
+    G.add_edge(4, 8, weight=2)
+    G.add_edge(5, 6, weight=3)
+    G.add_edge(6, 7, weight=1)
+    G.add_edge(7, 8, weight=3)
+    _test_stoer_wagner(G, 4)
+
+
+def test_weight_name():
+    G = nx.Graph()
+    G.add_edge(1, 2, weight=1, cost=8)
+    G.add_edge(1, 3, cost=2)
+    G.add_edge(2, 3, cost=4)
+    _test_stoer_wagner(G, 6, weight="cost")
+
+
+def test_exceptions():
+    G = nx.Graph()
+    pytest.raises(nx.NetworkXError, nx.stoer_wagner, G)
+    G.add_node(1)
+    pytest.raises(nx.NetworkXError, nx.stoer_wagner, G)
+    G.add_node(2)
+    pytest.raises(nx.NetworkXError, nx.stoer_wagner, G)
+    G.add_edge(1, 2, weight=-2)
+    pytest.raises(nx.NetworkXError, nx.stoer_wagner, G)
+    G = nx.DiGraph()
+    pytest.raises(nx.NetworkXNotImplemented, nx.stoer_wagner, G)
+    G = nx.MultiGraph()
+    pytest.raises(nx.NetworkXNotImplemented, nx.stoer_wagner, G)
+    G = nx.MultiDiGraph()
+    pytest.raises(nx.NetworkXNotImplemented, nx.stoer_wagner, G)