Python networkx.node_connectivity() Examples

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:
        assert_equal(1, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__)) 

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:
        assert_equal(1, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__)) 

def test_example_1_detail_3_and_4():
    G = graph_example_1()
    result = k_components(G)
    # In this example graph there are 8 3-components, 4 with 15 nodes
    # and 4 with 5 nodes.
    assert_equal(len(result[3]), 8)
    assert_equal(len([c for c in result[3] if len(c) == 15]), 4)
    assert_equal(len([c for c in result[3] if len(c) == 5]), 4)
    # There are also 8 4-components all with 5 nodes.
    assert_equal(len(result[4]), 8)
    assert_true(all(len(c) == 5 for c in result[4]))
    # Finally check that the k-components detected have actually node
    # connectivity >= k.
    for k, components in result.items():
        if k < 3:
            continue
        for component in components:
            K = nx.node_connectivity(G.subgraph(component))
            assert_greater_equal(K, k) 

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:
        assert_equal(1, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__)) 

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)
        assert_equal(3, local_edge_connectivity(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, local_node_connectivity(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, nx.node_connectivity(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, nx.edge_connectivity(G, **kwargs), # node 5 has degree 2
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, nx.node_connectivity(G, **kwargs),
                     msg=msg.format(flow_func.__name__)) 

def test_torrents_and_ferraro_detail_3_and_4():
    G = torrents_and_ferraro_graph()
    result = nx.k_components(G)
    # In this example graph there are 8 3-components, 4 with 15 nodes
    # and 4 with 5 nodes.
    assert_equal(len(result[3]), 8)
    assert_equal(len([c for c in result[3] if len(c) == 15]), 4)
    assert_equal(len([c for c in result[3] if len(c) == 5]), 4)
    # There are also 8 4-components all with 5 nodes.
    assert_equal(len(result[4]), 8)
    assert_true(all(len(c) == 5 for c in result[4]))
    # Finally check that the k-components detected have actually node
    # connectivity >= k.
    for k, components in result.items():
        if k < 3:
            continue
        for component in components:
            K = nx.node_connectivity(G.subgraph(component))
            assert_greater_equal(K, k) 

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)
        # edge disjoint paths
        edge_paths = list(nx.edge_disjoint_paths(G, 'A', 'Z', **kwargs))
        assert_true(are_edge_disjoint_paths(G, edge_paths), msg=msg.format(flow_func.__name__))
        assert_equal(
            nx.edge_connectivity(G, 'A', 'Z'),
            len(edge_paths),
            msg=msg.format(flow_func.__name__),
        )
        # node disjoint paths
        node_paths = list(nx.node_disjoint_paths(G, 'A', 'Z', **kwargs))
        assert_true(are_node_disjoint_paths(G, node_paths), msg=msg.format(flow_func.__name__))
        assert_equal(
            nx.node_connectivity(G, 'A', 'Z'),
            len(node_paths),
            msg=msg.format(flow_func.__name__),
        ) 

def test_florentine_families():
    G = nx.florentine_families_graph()
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        # edge disjoint paths
        edge_dpaths = list(nx.edge_disjoint_paths(G, 'Medici', 'Strozzi', **kwargs))
        assert_true(are_edge_disjoint_paths(G, edge_dpaths), msg=msg.format(flow_func.__name__))
        assert_equal(
            nx.edge_connectivity(G, 'Medici', 'Strozzi'),
            len(edge_dpaths),
            msg=msg.format(flow_func.__name__),
        )
        # node disjoint paths
        node_dpaths = list(nx.node_disjoint_paths(G, 'Medici', 'Strozzi', **kwargs))
        assert_true(are_node_disjoint_paths(G, node_dpaths), msg=msg.format(flow_func.__name__))
        assert_equal(
            nx.node_connectivity(G, 'Medici', 'Strozzi'),
            len(node_dpaths),
            msg=msg.format(flow_func.__name__),
        ) 

def test_karate():
    G = nx.karate_club_graph()
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        # edge disjoint paths
        edge_dpaths = list(nx.edge_disjoint_paths(G, 0, 33, **kwargs))
        assert_true(are_edge_disjoint_paths(G, edge_dpaths), msg=msg.format(flow_func.__name__))
        assert_equal(
            nx.edge_connectivity(G, 0, 33),
            len(edge_dpaths),
            msg=msg.format(flow_func.__name__),
        )
        # node disjoint paths
        node_dpaths = list(nx.node_disjoint_paths(G, 0, 33, **kwargs))
        assert_true(are_node_disjoint_paths(G, node_dpaths), msg=msg.format(flow_func.__name__))
        assert_equal(
            nx.node_connectivity(G, 0, 33),
            len(node_dpaths),
            msg=msg.format(flow_func.__name__),
        ) 

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)
        assert_equal(3, local_edge_connectivity(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, local_node_connectivity(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, nx.node_connectivity(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, nx.edge_connectivity(G, **kwargs),  # node 5 has degree 2
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, nx.node_connectivity(G, **kwargs),
                     msg=msg.format(flow_func.__name__)) 

def test_octahedral():
    G=nx.octahedral_graph()
    for flow_func in flow_funcs:
        assert_equal(4, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(4, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__)) 

def test_dodecahedral():
    G = nx.dodecahedral_graph()
    for flow_func in flow_funcs:
        assert_equal(3, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__)) 

def test_tutte():
    G = nx.tutte_graph()
    for flow_func in flow_funcs:
        assert_equal(3, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__)) 

def test_icosahedral():
    G=nx.icosahedral_graph()
    for flow_func in flow_funcs:
        assert_equal(5, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(5, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__)) 

def test_empty_graphs():
    for k in range(5, 25, 5):
        G = nx.empty_graph(k)
        for flow_func in flow_funcs:
            assert_equal(0, nx.node_connectivity(G, flow_func=flow_func),
                         msg=msg.format(flow_func.__name__))
            assert_equal(0, nx.edge_connectivity(G, flow_func=flow_func),
                         msg=msg.format(flow_func.__name__)) 

def test_all_pairs_connectivity_nbunch(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_equal(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_equal(sorted((k, sorted(v)) for k, v in A.items()),
                     sorted((k, sorted(v)) for k, v in C.items())) 

def test_alternative_flow_functions():
    graph_funcs = [graph_example_1, nx.davis_southern_women_graph]
    for graph_func in graph_funcs:
        G = graph_func()
        node_conn = nx.node_connectivity(G)
        for flow_func in flow_funcs:
            for cut in nx.all_node_cuts(G, flow_func=flow_func):
                assert_equal(node_conn, len(cut))
                H = G.copy()
                H.remove_nodes_from(cut)
                assert_false(nx.is_connected(H)) 

def _check_separating_sets(G):
    for Gc in nx.connected_component_subgraphs(G):
        if len(Gc) < 3:
            continue
        node_conn = nx.node_connectivity(Gc)
        for cut in nx.all_node_cuts(Gc):
            assert_equal(node_conn, len(cut))
            H = Gc.copy()
            H.remove_nodes_from(cut)
            assert_false(nx.is_connected(H)) 

def _check_connectivity(G):
    result = k_components(G)
    for k, components in result.items():
        if k < 3:
            continue
        for component in components:
            C = G.subgraph(component)
            K = nx.node_connectivity(C)
            assert_greater_equal(K, k) 

def test_dodecahedral():
    G = nx.dodecahedral_graph()
    for flow_func in flow_funcs:
        assert_equal(3, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__)) 

def _check_connectivity(G):
    result = k_components(G)
    for k, components in result.items():
        if k < 3:
            continue
        for component in components:
            C = G.subgraph(component)
            K = nx.node_connectivity(C)
            assert_greater_equal(K, k) 

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_equal(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_equal(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_equal(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(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_equal(sorted((k, sorted(v)) for k, v in A.items()),
                     sorted((k, sorted(v)) for k, v in C.items())) 

def test_interface_only_source():
    G = nx.complete_graph(5)
    for interface_func in [nx.node_connectivity, nx.edge_connectivity]:
        assert_raises(nx.NetworkXError, interface_func, G, s=0) 

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:
        assert_equal(nx.node_connectivity(G), 0,
                     msg=msg.format(flow_func.__name__))
        assert_equal(nx.edge_connectivity(G), 0,
                     msg=msg.format(flow_func.__name__)) 

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:
        assert_equal(nx.node_connectivity(G), 0,
                     msg=msg.format(flow_func.__name__))
        assert_equal(nx.edge_connectivity(G), 0,
                     msg=msg.format(flow_func.__name__)) 

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:
        assert_equal(nx.node_connectivity(G), 0,
                     msg=msg.format(flow_func.__name__))
        assert_equal(nx.edge_connectivity(G), 0,
                     msg=msg.format(flow_func.__name__))