Vehicle-cpp/hkpc/software/networkx/algorithms/connectivity/tests/test_connectivity.py

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()
        )