Python networkx.strongly_connected_components() Examples

def test_condensation_as_quotient(self):
        """This tests that the condensation of a graph can be viewed as the
        quotient graph under the "in the same connected component" equivalence
        relation.

        """
        # This example graph comes from the file `test_strongly_connected.py`.
        G = nx.DiGraph()
        G.add_edges_from([(1, 2), (2, 3), (2, 11), (2, 12), (3, 4), (4, 3),
                          (4, 5), (5, 6), (6, 5), (6, 7), (7, 8), (7, 9),
                          (7, 10), (8, 9), (9, 7), (10, 6), (11, 2), (11, 4),
                          (11, 6), (12, 6), (12, 11)])
        scc = list(nx.strongly_connected_components(G))
        C = nx.condensation(G, scc)
        component_of = C.graph['mapping']
        # Two nodes are equivalent if they are in the same connected component.

        def same_component(u, v):
            return component_of[u] == component_of[v]

        Q = nx.quotient_graph(G, same_component)
        assert_true(nx.is_isomorphic(C, Q)) 

def _high_degree_components(G, k):
    """Helper for filtering components that cant be k-edge-connected.

    Removes and generates each node with degree less than k.  Then generates
    remaining components where all nodes have degree at least k.
    """
    # Iteravely remove parts of the graph that are not k-edge-connected
    H = G.copy()
    singletons = set(_low_degree_nodes(H, k))
    while singletons:
        # Only search neighbors of removed nodes
        nbunch = set(it.chain.from_iterable(map(H.neighbors, singletons)))
        nbunch.difference_update(singletons)
        H.remove_nodes_from(singletons)
        for node in singletons:
            yield {node}
        singletons = set(_low_degree_nodes(H, k, nbunch))

    # Note: remaining connected components may not be k-edge-connected
    if G.is_directed():
        for cc in nx.strongly_connected_components(H):
            yield cc
    else:
        for cc in nx.connected_components(H):
            yield cc 

def test_condensation_as_quotient(self):
        """This tests that the condensation of a graph can be viewed as the
        quotient graph under the "in the same connected component" equivalence
        relation.

        """
        # This example graph comes from the file `test_strongly_connected.py`.
        G = nx.DiGraph()
        G.add_edges_from([(1, 2), (2, 3), (2, 11), (2, 12), (3, 4), (4, 3),
                          (4, 5), (5, 6), (6, 5), (6, 7), (7, 8), (7, 9),
                          (7, 10), (8, 9), (9, 7), (10, 6), (11, 2), (11, 4),
                          (11, 6), (12, 6), (12, 11)])
        scc = list(nx.strongly_connected_components(G))
        C = nx.condensation(G, scc)
        component_of = C.graph['mapping']
        # Two nodes are equivalent if they are in the same connected component.

        def same_component(u, v):
            return component_of[u] == component_of[v]

        Q = nx.quotient_graph(G, same_component)
        assert_true(nx.is_isomorphic(C, Q)) 

def test_contract_scc1(self):
        G = nx.DiGraph()
        G.add_edges_from([
            (1, 2), (2, 3), (2, 11), (2, 12), (3, 4), (4, 3), (4, 5), (5, 6),
            (6, 5), (6, 7), (7, 8), (7, 9), (7, 10), (8, 9), (9, 7), (10, 6),
            (11, 2), (11, 4), (11, 6), (12, 6), (12, 11),
        ])
        scc = list(nx.strongly_connected_components(G))
        cG = nx.condensation(G, scc)
        # DAG
        assert_true(nx.is_directed_acyclic_graph(cG))
        # nodes
        assert_equal(sorted(cG.nodes()), [0, 1, 2, 3])
        # edges
        mapping={}
        for i, component in enumerate(scc):
            for n in component:
                mapping[n] = i
        edge = (mapping[2], mapping[3])
        assert_true(cG.has_edge(*edge))
        edge = (mapping[2], mapping[5])
        assert_true(cG.has_edge(*edge))
        edge = (mapping[3], mapping[5])
        assert_true(cG.has_edge(*edge)) 

def _high_degree_components(G, k):
    """Helper for filtering components that can't be k-edge-connected.

    Removes and generates each node with degree less than k.  Then generates
    remaining components where all nodes have degree at least k.
    """
    # Iteravely remove parts of the graph that are not k-edge-connected
    H = G.copy()
    singletons = set(_low_degree_nodes(H, k))
    while singletons:
        # Only search neighbors of removed nodes
        nbunch = set(it.chain.from_iterable(map(H.neighbors, singletons)))
        nbunch.difference_update(singletons)
        H.remove_nodes_from(singletons)
        for node in singletons:
            yield {node}
        singletons = set(_low_degree_nodes(H, k, nbunch))

    # Note: remaining connected components may not be k-edge-connected
    if G.is_directed():
        for cc in nx.strongly_connected_components(H):
            yield cc
    else:
        for cc in nx.connected_components(H):
            yield cc 

def number_strongly_connected_components(G):
    """Return number of strongly connected components in graph.

    Parameters
    ----------
    G : NetworkX graph
       A directed graph.

    Returns
    -------
    n : integer
       Number of strongly connected components

    See Also
    --------
    connected_components

    Notes
    -----
    For directed graphs only.
    """
    return len(list(strongly_connected_components(G))) 

def test_condensation_as_quotient(self):
        """This tests that the condensation of a graph can be viewed as the
        quotient graph under the "in the same connected component" equivalence
        relation.

        """
        # This example graph comes from the file `test_strongly_connected.py`.
        G = nx.DiGraph()
        G.add_edges_from([(1, 2), (2, 3), (2, 11), (2, 12), (3, 4), (4, 3),
                          (4, 5), (5, 6), (6, 5), (6, 7), (7, 8), (7, 9),
                          (7, 10), (8, 9), (9, 7), (10, 6), (11, 2), (11, 4),
                          (11, 6), (12, 6), (12, 11)])
        scc = list(nx.strongly_connected_components(G))
        C = nx.condensation(G, scc)
        component_of = C.graph['mapping']
        # Two nodes are equivalent if they are in the same connected component.
        same_component = lambda u, v: component_of[u] == component_of[v]
        Q = nx.quotient_graph(G, same_component)
        assert_true(nx.is_isomorphic(C, Q)) 

def test_strong_connected_components(random_network):
    from pathpy.classes.network import network_to_networkx
    from networkx import strongly_connected_components
    from pathpy.algorithms.components import connected_components

    wrong_gcc = 0
    for i in range(200):
        hn = random_network(n=10, m=30, directed=True, seed=i)

        hn_nx = network_to_networkx(hn)
        size_largest_nx = len(max(strongly_connected_components(hn_nx), key=len))

        components = connected_components(hn)
        size_largest = max(len(c) for c in components)

        if size_largest_nx != size_largest:
            # print(f'seed {i} | nx: {size_largest_nx}, pp: {size_largest}')
            wrong_gcc += 1

    assert wrong_gcc < 1, 'wrong results {wrong_gcc/i:0.1%}' 

def detect_deadlock(self):
        """
        Detects whether the system is in a deadlocked state,
        that is, is there a knot. Note that this code is taken
        and adapted from the NetworkX Developer Zone Ticket
        #663 knot.py (09/06/2015).
        """
        knots = []
        for c in nx.strongly_connected_components(self.statedigraph):
            subgraph = self.statedigraph.subgraph(c)
            nodes = set(subgraph.nodes())
            if len(nodes) == 1:
                n = nodes.pop()
                nodes.add(n)
                if set(self.statedigraph.successors(n)) == nodes:
                    knots.append(subgraph)
            else:
                for n in nodes:
                    successors = nx.descendants(self.statedigraph, n)
                    if successors <= nodes:
                        knots.append(subgraph)
                        break
        if len(knots) > 0:
            return True
        return False 

def _parse_loops_from_graph(self, graph):
        """
        Return all Loop instances that can be extracted from a graph.

        :param graph:   The graph to analyze.

        :return:        A list of all the Loop instances that were found in the graph.
        """
        outtop = []
        outall = []
        for subg in ( networkx.induced_subgraph(graph, nodes).copy() for nodes in networkx.strongly_connected_components(graph)):
            if len(subg.nodes()) == 1:
                if len(list(subg.successors(list(subg.nodes())[0]))) == 0:
                    continue
            thisloop, allloops = self._parse_loop_graph(subg, graph)
            if thisloop is not None:
                outall += allloops
                outtop.append(thisloop)
        return outtop, outall 

def _high_degree_components(G, k):
    """Helper for filtering components that cant be k-edge-connected.

    Removes and generates each node with degree less than k.  Then generates
    remaining components where all nodes have degree at least k.
    """
    # Iteravely remove parts of the graph that are not k-edge-connected
    H = G.copy()
    singletons = set(_low_degree_nodes(H, k))
    while singletons:
        # Only search neighbors of removed nodes
        nbunch = set(it.chain.from_iterable(map(H.neighbors, singletons)))
        nbunch.difference_update(singletons)
        H.remove_nodes_from(singletons)
        for node in singletons:
            yield {node}
        singletons = set(_low_degree_nodes(H, k, nbunch))

    # Note: remaining connected components may not be k-edge-connected
    if G.is_directed():
        for cc in nx.strongly_connected_components(H):
            yield cc
    else:
        for cc in nx.connected_components(H):
            yield cc 

def test_tarjan(self):
        scc = nx.strongly_connected_components
        for G, C in self.gc:
            assert_equal({frozenset(g) for g in scc(G)}, C) 

def test_connected_raise(self):
        G = nx.Graph()
        assert_raises(NetworkXNotImplemented, nx.strongly_connected_components, G)
        assert_raises(NetworkXNotImplemented, nx.kosaraju_strongly_connected_components, G)
        assert_raises(NetworkXNotImplemented, nx.strongly_connected_components_recursive, G)
        assert_raises(NetworkXNotImplemented, nx.is_strongly_connected, G)
        assert_raises(nx.NetworkXPointlessConcept, nx.is_strongly_connected, nx.DiGraph())
        assert_raises(NetworkXNotImplemented, nx.condensation, G)
        # deprecated
        assert_raises(NetworkXNotImplemented, nx.strongly_connected_component_subgraphs, G)

#    Commented out due to variability on Travis-CI hardware/operating systems
#    def test_linear_time(self):
#        # See Issue #2831
#        count = 100  # base case
#        dg = nx.DiGraph()
#        dg.add_nodes_from([0, 1])
#        for i in range(2, count):
#            dg.add_node(i)
#            dg.add_edge(i, 1)
#            dg.add_edge(0, i)
#        t = time.time()
#        ret = tuple(nx.strongly_connected_components(dg))
#        dt = time.time() - t
#
#        count = 200
#        dg = nx.DiGraph()
#        dg.add_nodes_from([0, 1])
#        for i in range(2, count):
#            dg.add_node(i)
#            dg.add_edge(i, 1)
#            dg.add_edge(0, i)
#        t = time.time()
#        ret = tuple(nx.strongly_connected_components(dg))
#        dt2 = time.time() - t
#        assert_less(dt2, dt * 2.3)  # should be 2 times longer for this graph 

def test_null_graph(self):
        G = nx.DiGraph()
        assert_equal(list(nx.strongly_connected_components(G)), [])
        assert_equal(list(nx.kosaraju_strongly_connected_components(G)), [])
        assert_equal(list(nx.strongly_connected_components_recursive(G)), [])
        assert_equal(len(nx.condensation(G)), 0)
        assert_raises(nx.NetworkXPointlessConcept, nx.is_strongly_connected, nx.DiGraph()) 

def attracting_components(G):
    """Generates the attracting components in `G`.

    An attracting component in a directed graph `G` is a strongly connected
    component with the property that a random walker on the graph will never
    leave the component, once it enters the component.

    The nodes in attracting components can also be thought of as recurrent
    nodes.  If a random walker enters the attractor containing the node, then
    the node will be visited infinitely often.

    Parameters
    ----------
    G : DiGraph, MultiDiGraph
        The graph to be analyzed.

    Returns
    -------
    attractors : generator of sets
        A generator of sets of nodes, one for each attracting component of G.

    Raises
    ------
    NetworkXNotImplemented :
        If the input graph is undirected.

    See Also
    --------
    number_attracting_components
    is_attracting_component

    """
    scc = list(nx.strongly_connected_components(G))
    cG = nx.condensation(G, scc)
    for n in cG:
        if cG.out_degree(n) == 0:
            yield scc[n] 

def test_contract_scc_edge(self):
        G = nx.DiGraph()
        G.add_edge(1, 2)
        G.add_edge(2, 1)
        G.add_edge(2, 3)
        G.add_edge(3, 4)
        G.add_edge(4, 3)
        scc = list(nx.strongly_connected_components(G))
        cG = nx.condensation(G, scc)
        assert_equal(sorted(cG.nodes()), [0, 1])
        if 1 in scc[0]:
            edge = (0, 1)
        else:
            edge = (1, 0)
        assert_equal(list(cG.edges()), [edge]) 

def test_contract_scc_isolate(self):
        # Bug found and fixed in [1687].
        G = nx.DiGraph()
        G.add_edge(1, 2)
        G.add_edge(2, 1)
        scc = list(nx.strongly_connected_components(G))
        cG = nx.condensation(G, scc)
        assert_equal(list(cG.nodes()), [0])
        assert_equal(list(cG.edges()), []) 

def flow_hierarchy(G, weight=None):
    """Returns the flow hierarchy of a directed network.

    Flow hierarchy is defined as the fraction of edges not participating
    in cycles in a directed graph [1]_.

    Parameters
    ----------
    G : DiGraph or MultiDiGraph
       A directed graph

    weight : key,optional (default=None)
       Attribute to use for node weights. If None the weight defaults to 1.

    Returns
    -------
    h : float
       Flow heirarchy value

    Notes
    -----
    The algorithm described in [1]_ computes the flow hierarchy through
    exponentiation of the adjacency matrix.  This function implements an
    alternative approach that finds strongly connected components.
    An edge is in a cycle if and only if it is in a strongly connected
    component, which can be found in $O(m)$ time using Tarjan's algorithm.

    References
    ----------
    .. [1] Luo, J.; Magee, C.L. (2011),
       Detecting evolving patterns of self-organizing networks by flow
       hierarchy measurement, Complexity, Volume 16 Issue 6 53-61.
       DOI: 10.1002/cplx.20368
       http://web.mit.edu/~cmagee/www/documents/28-DetectingEvolvingPatterns_FlowHierarchy.pdf
    """
    if not G.is_directed():
        raise nx.NetworkXError("G must be a digraph in flow_heirarchy")
    scc = nx.strongly_connected_components(G)
    return 1. - sum(G.subgraph(c).size(weight) for c in scc) / float(G.size(weight)) 

def get_cc(self, maha, maha_thresh):
        row, column = np.where(maha<maha_thresh)
        G = nx.DiGraph()
        for i in range(maha.shape[0]):
            G.add_node(i)
        for i, j in zip(row,column):
            G.add_edge(i, j)
        cc = [list(units) for units in nx.strongly_connected_components(G)]
        return cc 

def test_directed_aux_graph():
    # Graph similar to the one in
    # http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0136264
    a, b, c, d, e, f, g, h, i = 'abcdefghi'
    dipaths = [
        (a, d, b, f, c),
        (a, e, b),
        (a, e, b, c, g, b, a),
        (c, b),
        (f, g, f),
        (h, i)
    ]
    G = nx.DiGraph(it.chain(*[pairwise(path) for path in dipaths]))
    aux_graph = EdgeComponentAuxGraph.construct(G)

    components_1 = fset(aux_graph.k_edge_subgraphs(k=1))
    target_1 = fset([{a, b, c, d, e, f, g}, {h}, {i}])
    assert_equal(target_1, components_1)

    # Check that the directed case for k=1 agrees with SCCs
    alt_1 = fset(nx.strongly_connected_components(G))
    assert_equal(alt_1, components_1)

    components_2 = fset(aux_graph.k_edge_subgraphs(k=2))
    target_2 = fset([{i}, {e}, {d}, {b, c, f, g}, {h}, {a}])
    assert_equal(target_2, components_2)

    components_3 = fset(aux_graph.k_edge_subgraphs(k=3))
    target_3 = fset([{a}, {b}, {c}, {d}, {e}, {f}, {g}, {h}, {i}])
    assert_equal(target_3, components_3) 

def number_strongly_connected_components(G):
    """Return number of strongly connected components in graph.

    Parameters
    ----------
    G : NetworkX graph
       A directed graph.

    Returns
    -------
    n : integer
       Number of strongly connected components

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

    See Also
    --------
    strongly_connected_components
    number_connected_components
    number_weakly_connected_components

    Notes
    -----
    For directed graphs only.
    """
    return len(list(strongly_connected_components(G))) 

def is_strongly_connected(G):
    """Test directed graph for strong connectivity.

    Parameters
    ----------
    G : NetworkX Graph
       A directed graph.

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

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

    See Also
    --------
    is_weakly_connected
    is_semiconnected
    is_connected
    is_biconnected
    strongly_connected_components

    Notes
    -----
    For directed graphs only.
    """
    if len(G) == 0:
        raise nx.NetworkXPointlessConcept(
            """Connectivity is undefined for the null graph.""")

    return len(list(strongly_connected_components(G))[0]) == len(G) 

def test_tarjan(self):
        scc = nx.strongly_connected_components
        for G, C in self.gc:
            assert_equal({frozenset(g) for g in scc(G)}, C) 

def test_contract_scc_isolate(self):
        # Bug found and fixed in [1687].
        G = nx.DiGraph()
        G.add_edge(1, 2)
        G.add_edge(2, 1)
        scc = list(nx.strongly_connected_components(G))
        cG = nx.condensation(G, scc)
        assert_equal(list(cG.nodes()), [0])
        assert_equal(list(cG.edges()), []) 

def test_contract_scc_edge(self):
        G = nx.DiGraph()
        G.add_edge(1, 2)
        G.add_edge(2, 1)
        G.add_edge(2, 3)
        G.add_edge(3, 4)
        G.add_edge(4, 3)
        scc = list(nx.strongly_connected_components(G))
        cG = nx.condensation(G, scc)
        assert_equal(sorted(cG.nodes()), [0, 1])
        if 1 in scc[0]:
            edge = (0, 1)
        else:
            edge = (1, 0)
        assert_equal(list(cG.edges()), [edge]) 

def test_connected_raise(self):
        G=nx.Graph()
        assert_raises(NetworkXNotImplemented, nx.strongly_connected_components, G)
        assert_raises(NetworkXNotImplemented, nx.kosaraju_strongly_connected_components, G)
        assert_raises(NetworkXNotImplemented, nx.strongly_connected_components_recursive, G)
        assert_raises(NetworkXNotImplemented, nx.strongly_connected_component_subgraphs, G)
        assert_raises(NetworkXNotImplemented, nx.is_strongly_connected, G)
        assert_raises(nx.NetworkXPointlessConcept, nx.is_strongly_connected, nx.DiGraph())
        assert_raises(NetworkXNotImplemented, nx.condensation, G) 

def attracting_components(G):
    """Generates a list of attracting components in `G`.

    An attracting component in a directed graph `G` is a strongly connected
    component with the property that a random walker on the graph will never
    leave the component, once it enters the component.

    The nodes in attracting components can also be thought of as recurrent
    nodes.  If a random walker enters the attractor containing the node, then
    the node will be visited infinitely often.

    Parameters
    ----------
    G : DiGraph, MultiDiGraph
        The graph to be analyzed.

    Returns
    -------
    attractors : generator of sets
        A generator of sets of nodes, one for each attracting component of G.

    Raises
    ------
    NetworkXNotImplemented :
        If the input graph is undirected.

    See Also
    --------
    number_attracting_components
    is_attracting_component
    attracting_component_subgraphs

    """
    scc = list(nx.strongly_connected_components(G))
    cG = nx.condensation(G, scc)
    for n in cG:
        if cG.out_degree(n) == 0:
            yield scc[n] 

def get_cc(self, maha, maha_thresh):
        row, column = np.where(maha<maha_thresh)
        G = nx.DiGraph()
        for i in range(maha.shape[0]):
            G.add_node(i)
        for i, j in zip(row,column):
            G.add_edge(i, j)
        cc = [list(units) for units in nx.strongly_connected_components(G)]
        return cc 

def get_cc(maha, maha_thresh):
    row, column = np.where(maha<maha_thresh)
    G = nx.DiGraph()
    for i in range(maha.shape[0]):
        G.add_node(i)
    for i, j in zip(row,column):
        G.add_edge(i, j)
    cc = [list(units) for units in nx.strongly_connected_components(G)]
    return cc 

def test_contract_scc_edge(self):
        G = nx.DiGraph()
        G.add_edge(1, 2)
        G.add_edge(2, 1)
        G.add_edge(2, 3)
        G.add_edge(3, 4)
        G.add_edge(4, 3)
        scc = list(nx.strongly_connected_components(G))
        cG = nx.condensation(G, scc)
        assert_equal(cG.nodes(), [0, 1])
        if 1 in scc[0]:
            edge = (0, 1)
        else:
            edge = (1, 0)
        assert_equal(list(cG.edges()), [edge])