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

# 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 = [{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(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