Python networkx.is_connected() Examples

def decode_graph(adj, prefix):
    adj = np.asmatrix(adj)
    G = nx.from_numpy_matrix(adj)
    # G.remove_nodes_from(nx.isolates(G))
    print('num of nodes: {}'.format(G.number_of_nodes()))
    print('num of edges: {}'.format(G.number_of_edges()))
    G_deg = nx.degree_histogram(G)
    G_deg_sum = [a * b for a, b in zip(G_deg, range(0, len(G_deg)))]
    print('average degree: {}'.format(sum(G_deg_sum) / G.number_of_nodes()))
    if nx.is_connected(G):
        print('average path length: {}'.format(nx.average_shortest_path_length(G)))
        print('average diameter: {}'.format(nx.diameter(G)))
    G_cluster = sorted(list(nx.clustering(G).values()))
    print('average clustering coefficient: {}'.format(sum(G_cluster) / len(G_cluster)))
    cycle_len = []
    cycle_all = nx.cycle_basis(G, 0)
    for item in cycle_all:
        cycle_len.append(len(item))
    print('cycles', cycle_len)
    print('cycle count', len(cycle_len))
    draw_graph(G, prefix=prefix) 

def validate_cuts(G, s, t, solnValue, partition, capacity, flow_func):
    assert_true(all(n in G for n in partition[0]),
                msg=msg.format(flow_func.__name__))
    assert_true(all(n in G for n in partition[1]),
                msg=msg.format(flow_func.__name__))
    cutset = compute_cutset(G, partition)
    assert_true(all(G.has_edge(u, v) for (u, v) in cutset),
                msg=msg.format(flow_func.__name__))
    assert_equal(solnValue, sum(G[u][v][capacity] for (u, v) in cutset),
                 msg=msg.format(flow_func.__name__))
    H = G.copy()
    H.remove_edges_from(cutset)
    if not G.is_directed():
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
    else:
        assert_false(nx.is_strongly_connected(H),
                     msg=msg.format(flow_func.__name__)) 

def decode_graph(adj, prefix):
    adj = np.asmatrix(adj)
    G = nx.from_numpy_matrix(adj)
    # G.remove_nodes_from(nx.isolates(G))
    print('num of nodes: {}'.format(G.number_of_nodes()))
    print('num of edges: {}'.format(G.number_of_edges()))
    G_deg = nx.degree_histogram(G)
    G_deg_sum = [a * b for a, b in zip(G_deg, range(0, len(G_deg)))]
    print('average degree: {}'.format(sum(G_deg_sum) / G.number_of_nodes()))
    if nx.is_connected(G):
        print('average path length: {}'.format(nx.average_shortest_path_length(G)))
        print('average diameter: {}'.format(nx.diameter(G)))
    G_cluster = sorted(list(nx.clustering(G).values()))
    print('average clustering coefficient: {}'.format(sum(G_cluster) / len(G_cluster)))
    cycle_len = []
    cycle_all = nx.cycle_basis(G, 0)
    for item in cycle_all:
        cycle_len.append(len(item))
    print('cycles', cycle_len)
    print('cycle count', len(cycle_len))
    draw_graph(G, prefix=prefix) 

def dendritic_graph(self):
        """
        Builds skeleton of the topological representation (used internally)
        """
        diam = networkx.diameter(self.gl)
        g3 = networkx.Graph()
        dicdend = {}
        for n in range(diam-1):
            nodedist = []
            for k in self.pl:
                dil = networkx.shortest_path_length(self.gl, self.root, k)
                if dil == n:
                    nodedist.append(str(k))
            g2 = self.gl.subgraph(nodedist)
            dicdend[n] = sorted(networkx.connected_components(g2))
            for n2, yu in enumerate(dicdend[n]):
                g3.add_node(str(n) + '_' + str(n2))
                if n > 0:
                    for n3, yu2 in enumerate(dicdend[n-1]):
                        if networkx.is_connected(self.gl.subgraph(list(yu)+list(yu2))):
                            g3.add_edge(str(n) + '_' + str(n2), str(n-1) + '_' + str(n3))
        return g3, dicdend 

def test_octahedral_cutset():
    G=nx.octahedral_graph()
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        # edge cuts
        edge_cut = nx.minimum_edge_cut(G, **kwargs)
        assert_equal(4, len(edge_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_edges_from(edge_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
        # node cuts
        node_cut = nx.minimum_node_cut(G, **kwargs)
        assert_equal(4, len(node_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_nodes_from(node_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__)) 

def test_petersen_cutset():
    G = nx.petersen_graph()
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        # edge cuts
        edge_cut = nx.minimum_edge_cut(G, **kwargs)
        assert_equal(3, len(edge_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_edges_from(edge_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
        # node cuts
        node_cut = nx.minimum_node_cut(G, **kwargs)
        assert_equal(3, len(node_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_nodes_from(node_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__)) 

def validate_cuts(G, s, t, solnValue, partition, capacity, flow_func):
    assert_true(all(n in G for n in partition[0]),
                msg=msg.format(flow_func.__name__))
    assert_true(all(n in G for n in partition[1]),
                msg=msg.format(flow_func.__name__))
    cutset = compute_cutset(G, partition)
    assert_true(all(G.has_edge(u, v) for (u, v) in cutset),
                msg=msg.format(flow_func.__name__))
    assert_equal(solnValue, sum(G[u][v][capacity] for (u, v) in cutset),
                msg=msg.format(flow_func.__name__))
    H = G.copy()
    H.remove_edges_from(cutset)
    if not G.is_directed():
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
    else:
        assert_false(nx.is_strongly_connected(H),
                     msg=msg.format(flow_func.__name__)) 

def test_petersen_cutset():
    G = nx.petersen_graph()
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        # edge cuts
        edge_cut = nx.minimum_edge_cut(G, **kwargs)
        assert_equal(3, len(edge_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_edges_from(edge_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
        # node cuts
        node_cut = nx.minimum_node_cut(G, **kwargs)
        assert_equal(3, len(node_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_nodes_from(node_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__)) 

def test_icosahedral_cutset():
    G=nx.icosahedral_graph()
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        # edge cuts
        edge_cut = nx.minimum_edge_cut(G, **kwargs)
        assert_equal(5, len(edge_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_edges_from(edge_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
        # node cuts
        node_cut = nx.minimum_node_cut(G, **kwargs)
        assert_equal(5, len(node_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_nodes_from(node_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__)) 

def test_icosahedral_cutset():
    G = nx.icosahedral_graph()
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        # edge cuts
        edge_cut = nx.minimum_edge_cut(G, **kwargs)
        assert_equal(5, len(edge_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_edges_from(edge_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
        # node cuts
        node_cut = nx.minimum_node_cut(G, **kwargs)
        assert_equal(5, len(node_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_nodes_from(node_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__)) 

def validate_cuts(G, s, t, solnValue, partition, capacity, flow_func):
    assert_true(all(n in G for n in partition[0]),
                msg=msg.format(flow_func.__name__))
    assert_true(all(n in G for n in partition[1]),
                msg=msg.format(flow_func.__name__))
    cutset = compute_cutset(G, partition)
    assert_true(all(G.has_edge(u, v) for (u, v) in cutset),
                msg=msg.format(flow_func.__name__))
    assert_equal(solnValue, sum(G[u][v][capacity] for (u, v) in cutset),
                msg=msg.format(flow_func.__name__))
    H = G.copy()
    H.remove_edges_from(cutset)
    if not G.is_directed():
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
    else:
        assert_false(nx.is_strongly_connected(H),
                     msg=msg.format(flow_func.__name__)) 

def test_petersen_cutset():
    G = nx.petersen_graph()
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        # edge cuts
        edge_cut = nx.minimum_edge_cut(G, **kwargs)
        assert_equal(3, len(edge_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_edges_from(edge_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
        # node cuts
        node_cut = nx.minimum_node_cut(G, **kwargs)
        assert_equal(3, len(node_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_nodes_from(node_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__)) 

def generate_scalefree_graph(variables_count, m_edge, allow_subgraph):
    if not allow_subgraph:
        graph = nx.barabasi_albert_graph(variables_count, m_edge)
        is_connected = nx.is_connected(graph)
        while not is_connected:
            graph = nx.barabasi_albert_graph(variables_count, m_edge)
            is_connected = nx.is_connected(graph)
    else:
        graph = nx.barabasi_albert_graph(variables_count, m_edge)

    # In the obtained graph, low rank nodes will have a much higher edge count
    # than high rank nodes. We shuffle the nodes names to avoid this effect:
    new_nodes = list(range(variables_count))
    random.shuffle(new_nodes)
    node_mapping = {n: nn for n, nn in zip(graph.nodes, new_nodes)}

    new_graph = nx.Graph((node_mapping[e1], node_mapping[e2]) for e1, e2 in graph.edges)
    return new_graph 

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)
        # edge cutsets
        assert_equal(3, len(nx.minimum_edge_cut(G, 1, 11, **kwargs)),
                     msg=msg.format(flow_func.__name__))
        edge_cut = nx.minimum_edge_cut(G, **kwargs)
        # Node 5 has only two edges
        assert_equal(2, len(edge_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_edges_from(edge_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
        # node cuts
        assert_equal(set([6, 7]), minimum_st_node_cut(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(set([6, 7]), nx.minimum_node_cut(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        node_cut = nx.minimum_node_cut(G, **kwargs)
        assert_equal(2, len(node_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_nodes_from(node_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__)) 

def _generate_no_biconnected(max_attempts=50):
    attempts = 0
    while True:
        G = nx.fast_gnp_random_graph(100,0.0575)
        if nx.is_connected(G) and not nx.is_biconnected(G):
            attempts = 0
            yield G
        else:
            if attempts >= max_attempts:
                msg = "Tried %d times: no suitable Graph."%attempts
                raise Exception(msg % max_attempts)
            else:
                attempts += 1 

def test_is_connected(self):
        assert_true(nx.is_connected(self.grid))
        G = nx.Graph()
        G.add_nodes_from([1, 2])
        assert_false(nx.is_connected(G)) 

def is_connected(G):
    """Return True if the graph is connected, false otherwise.

    Parameters
    ----------
    G : NetworkX Graph
       An undirected graph.

    Returns
    -------
    connected : bool
      True if the graph is connected, false otherwise.

    Raises
    ------
    NetworkXNotImplemented:
        If G is undirected.

    Examples
    --------
    >>> G = nx.path_graph(4)
    >>> print(nx.is_connected(G))
    True

    See Also
    --------
    is_strongly_connected
    is_weakly_connected
    is_semiconnected
    is_biconnected
    connected_components

    Notes
    -----
    For undirected graphs only.

    """
    if len(G) == 0:
        raise nx.NetworkXPointlessConcept('Connectivity is undefined ',
                                          'for the null graph.')
    return len(set(_plain_bfs(G, arbitrary_element(G)))) == len(G) 

def connected_watts_strogatz_graph(n, k, p, tries=100, seed=None):
    """Returns a connected Watts–Strogatz small-world graph.

    Attempts to generate a connected graph by repeated generation of
    Watts–Strogatz small-world graphs.  An exception is raised if the maximum
    number of tries is exceeded.

    Parameters
    ----------
    n : int
        The number of nodes
    k : int
        Each node is joined with its `k` nearest neighbors in a ring
        topology.
    p : float
        The probability of rewiring each edge
    tries : int
        Number of attempts to generate a connected graph.
    seed : int, optional
         The seed for random number generator.

    See Also
    --------
    newman_watts_strogatz_graph()
    watts_strogatz_graph()

    """
    for i in range(tries):
        G = watts_strogatz_graph(n, k, p, seed)
        if nx.is_connected(G):
            return G
    raise nx.NetworkXError('Maximum number of tries exceeded') 

def is_tree_decomp(graph, decomp):
    """Check if the given tree decomposition is valid."""
    for x in graph.nodes():
        appear_once = False
        for bag in decomp.nodes():
            if x in bag:
                appear_once = True
                break
        ok_(appear_once)

    # Check if each connected pair of nodes are at least once together in a bag
    for (x, y) in graph.edges():
        appear_together = False
        for bag in decomp.nodes():
            if x in bag and y in bag:
                appear_together = True
                break
        ok_(appear_together)

    # Check if the nodes associated with vertex v form a connected subset of T
    for v in graph.nodes():
        subset = []
        for bag in decomp.nodes():
            if v in bag:
                subset.append(bag)
        sub_graph = decomp.subgraph(subset)
        ok_(nx.is_connected(sub_graph)) 

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 = "Tried %d times: no suitable Graph."
                raise Exception(msg % max_attempts)
            else:
                attempts += 1 

def test_edge_cutset_random_graphs():
    for flow_func in flow_funcs:
        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_equal(nx.edge_connectivity(G), len(cutset),
                         msg=msg.format(flow_func.__name__))
            G.remove_edges_from(cutset)
            assert_false(nx.is_connected(G), msg=msg.format(flow_func.__name__)) 

def test_node_cutset_random_graphs():
    for flow_func in flow_funcs:
        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_equal(nx.node_connectivity(G), len(cutset),
                         msg=msg.format(flow_func.__name__))
            G.remove_nodes_from(cutset)
            assert_false(nx.is_connected(G), msg=msg.format(flow_func.__name__)) 

def generate_random_graph(variables_count, p_edge, allow_subgraph):
    if not allow_subgraph:
        graph = nx.gnp_random_graph(variables_count, p_edge)
        is_connected = nx.is_connected(graph)
        while not is_connected:
            graph = nx.gnp_random_graph(variables_count, p_edge)
            is_connected = nx.is_connected(graph)
    else:
        graph = nx.gnp_random_graph(variables_count, p_edge)
    return graph 

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)
        # edge cuts
        edge_cut = nx.minimum_edge_cut(G, **kwargs)
        assert_equal(3, len(edge_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_edges_from(edge_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
        # node cuts
        node_cut = nx.minimum_node_cut(G, **kwargs)
        assert_equal(set([0]), node_cut, msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_nodes_from(node_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__)) 

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)
        # edge cutsets
        assert_equal(3, len(nx.minimum_edge_cut(G, 1, 11, **kwargs)),
                     msg=msg.format(flow_func.__name__))
        edge_cut = nx.minimum_edge_cut(G, **kwargs)
        # Node 5 has only two edges
        assert_equal(2, len(edge_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_edges_from(edge_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__))
        # node cuts
        assert_equal(set([6, 7]), minimum_st_node_cut(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(set([6, 7]), nx.minimum_node_cut(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        node_cut = nx.minimum_node_cut(G, **kwargs)
        assert_equal(2, len(node_cut), msg=msg.format(flow_func.__name__))
        H = G.copy()
        H.remove_nodes_from(node_cut)
        assert_false(nx.is_connected(H), msg=msg.format(flow_func.__name__)) 

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 = "Tried %d times: no suitable Graph." % attempts
                raise Exception(msg % max_attempts)
            else:
                attempts += 1 

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_equal(node_conn, len(cut))
                assert_false(nx.is_connected(nx.restricted_view(G, cut, []))) 

def enumerate_graphs(self):
        """
        Enumerating connected benchmark graphlets.
        """
        graphs = graph_atlas_g()
        self.interesting_graphs = {i: [] for i in range(2, self.args.graphlet_size+1)}
        for graph in graphs:
            if graph.number_of_nodes() > 1 and  graph.number_of_nodes() < self.args.graphlet_size+1:
                if nx.is_connected(graph):
                    self.interesting_graphs[graph.number_of_nodes()].append(graph) 

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_equal(node_conn, len(cut))
            assert_false(nx.is_connected(nx.restricted_view(G, cut, []))) 

def test_connected_raise(self):
        assert_raises(NetworkXNotImplemented, nx.connected_components, self.DG)
        assert_raises(NetworkXNotImplemented, nx.number_connected_components, self.DG)
        assert_raises(NetworkXNotImplemented, nx.node_connected_component, self.DG, 1)
        assert_raises(NetworkXNotImplemented, nx.is_connected, self.DG)
        assert_raises(nx.NetworkXPointlessConcept, nx.is_connected, nx.Graph())
        # deprecated
        assert_raises(NetworkXNotImplemented, nx.connected_component_subgraphs, self.DG)