two version of R2R are hereHEADmaster

1 files changed, 421 insertions, 0 deletions

diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/connectivity/tests/test_connectivity.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/connectivity/tests/test_connectivity.py
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+import itertools
+
+import pytest
+
+import networkx as nx
+from networkx.algorithms import flow
+from networkx.algorithms.connectivity import (
+    local_edge_connectivity,
+    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 = {"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 = {"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)
+    # https://doi.org/10.1111/0081-1750.00098
+    # 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)
+    # https://doi.org/10.1111/0081-1750.00098
+    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()
+        )