Python networkx.is_weakly_connected() Examples

def test_is_weakly_connected(self):
        for G, C in self.gc:
            U = G.to_undirected()
            assert_equal(nx.is_weakly_connected(G), nx.is_connected(U)) 

def test_connected_raise(self):
        G=nx.Graph()
        assert_raises(NetworkXNotImplemented,nx.weakly_connected_components, G)
        assert_raises(NetworkXNotImplemented,nx.number_weakly_connected_components, G)
        assert_raises(NetworkXNotImplemented,nx.weakly_connected_component_subgraphs, G)
        assert_raises(NetworkXNotImplemented,nx.is_weakly_connected, G) 

def test_is_weakly_connected(self):
        for G, C in self.gc:
            U = G.to_undirected()
            assert_equal(nx.is_weakly_connected(G), nx.is_connected(U)) 

def is_tree(G):
    """
    Returns True if `G` is a tree.

    A tree is a connected graph with no undirected cycles.

    For directed graphs, `G` is a tree if the underlying graph is a tree. The
    underlying graph is obtained by treating each directed edge as a single
    undirected edge in a multigraph.

    Parameters
    ----------
    G : graph
        The graph to test.

    Returns
    -------
    b : bool
        A boolean that is True if `G` is a tree.

    Notes
    -----
    In another convention, a directed tree is known as a *polytree* and then
    *tree* corresponds to an *arborescence*.

    See Also
    --------
    is_arborescence

    """
    if len(G) == 0:
        raise nx.exception.NetworkXPointlessConcept('G has no nodes.')

    if G.is_directed():
        is_connected = nx.is_weakly_connected
    else:
        is_connected = nx.is_connected

    # A connected graph with no cycles has n-1 edges.
    return len(G) - 1 == G.number_of_edges() and is_connected(G) 

def test_connected_raise(self):
        G = nx.Graph()
        assert_raises(NetworkXNotImplemented, nx.weakly_connected_components, G)
        assert_raises(NetworkXNotImplemented, nx.number_weakly_connected_components, G)
        assert_raises(NetworkXNotImplemented, nx.is_weakly_connected, G)
        # deprecated
        assert_raises(NetworkXNotImplemented, nx.weakly_connected_component_subgraphs, G) 

def test_null_graph(self):
        G = nx.DiGraph()
        assert_equal(list(nx.weakly_connected_components(G)), [])
        assert_equal(nx.number_weakly_connected_components(G), 0)
        assert_raises(nx.NetworkXPointlessConcept, nx.is_weakly_connected, G) 

def test_is_weakly_connected(self):
        for G, C in self.gc:
            U = G.to_undirected()
            assert_equal(nx.is_weakly_connected(G), nx.is_connected(U)) 

def is_tree(G):
    """
    Returns True if `G` is a tree.

    A tree is a connected graph with no undirected cycles.

    For directed graphs, `G` is a tree if the underlying graph is a tree. The
    underlying graph is obtained by treating each directed edge as a single
    undirected edge in a multigraph.

    Parameters
    ----------
    G : graph
        The graph to test.

    Returns
    -------
    b : bool
        A boolean that is True if `G` is a tree.

    Notes
    -----
    In another convention, a directed tree is known as a *polytree* and then
    *tree* corresponds to an *arborescence*.

    See Also
    --------
    is_arborescence

    """
    if len(G) == 0:
        raise nx.exception.NetworkXPointlessConcept('G has no nodes.')

    if G.is_directed():
        is_connected = nx.is_weakly_connected
    else:
        is_connected = nx.is_connected

    # A connected graph with no cycles has n-1 edges.
    return len(G) - 1 == G.number_of_edges() and is_connected(G) 

def test_connected_raise(self):
        G=nx.Graph()
        assert_raises(NetworkXNotImplemented,nx.weakly_connected_components, G)
        assert_raises(NetworkXNotImplemented,nx.number_weakly_connected_components, G)
        assert_raises(NetworkXNotImplemented,nx.weakly_connected_component_subgraphs, G)
        assert_raises(NetworkXNotImplemented,nx.is_weakly_connected, G) 

def _get_subgraphs(self, graph, name, size=3):
        subgraphs = set()
        # print "\nSubgraphs START: " + name
        target = nx.complete_graph(size)
        for sub_nodes in itertools.combinations(graph.nodes(),len(target.nodes())):
            subg = graph.subgraph(sub_nodes)
            if nx.is_weakly_connected(subg):
                # print subg.edges()
                subgraphs.add(subg)
        # print "Subgraphs END \n"
        return subgraphs 

def is_connected(self):
        """
        Test if the graph is connected.

        Return True if connected, False otherwise
        """
        try:
            return nx.is_weakly_connected(self.graph)
        except nx.exception.NetworkXException:
            return False 

def is_semiconnected(G):
    """Return True if the graph is semiconnected, False otherwise.

    A graph is semiconnected if, and only if, for any pair of nodes, either one
    is reachable from the other, or they are mutually reachable.

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

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

    Raises
    ------
    NetworkXNotImplemented :
        If the input graph is not directed.

    NetworkXPointlessConcept :
        If the graph is empty.

    Examples
    --------
    >>> G=nx.path_graph(4,create_using=nx.DiGraph())
    >>> print(nx.is_semiconnected(G))
    True
    >>> G=nx.DiGraph([(1, 2), (3, 2)])
    >>> print(nx.is_semiconnected(G))
    False

    See Also
    --------
    is_strongly_connected,
    is_weakly_connected
    """
    if len(G) == 0:
        raise nx.NetworkXPointlessConcept(
            'Connectivity is undefined for the null graph.')

    if not nx.is_weakly_connected(G):
        return False

    G = nx.condensation(G)
    path = nx.topological_sort(G)
    return all(G.has_edge(u, v) for u, v in zip(path[:-1], path[1:])) 

def get_largest_component(G, strongly=False):
    """
    https://github.com/gboeing/osmnx/blob/master/osmnx/utils.py
    Return a subgraph of the largest weakly or strongly connected component
    from a directed graph.
    Parameters
    ----------
    G : networkx multidigraph
    strongly : bool
        if True, return the largest strongly instead of weakly connected
        component
    Returns
    -------
    G : networkx multidigraph
        the largest connected component subgraph from the original graph
    """

    start_time = time.time()
    original_len = len(list(G.nodes()))

    if strongly:
        # if the graph is not connected retain only the largest strongly connected component
        if not nx.is_strongly_connected(G):

            # get all the strongly connected components in graph then identify the largest
            sccs = nx.strongly_connected_components(G)
            largest_scc = max(sccs, key=len)
            G = induce_subgraph(G, largest_scc)

            msg = ('Graph was not connected, retained only the largest strongly '
                   'connected component ({:,} of {:,} total nodes) in {:.2f} seconds')
            print(msg.format(len(list(G.nodes())), original_len, time.time()-start_time))
    else:
        # if the graph is not connected retain only the largest weakly connected component
        if not nx.is_weakly_connected(G):

            # get all the weakly connected components in graph then identify the largest
            wccs = nx.weakly_connected_components(G)
            largest_wcc = max(wccs, key=len)
            G = induce_subgraph(G, largest_wcc)

            msg = ('Graph was not connected, retained only the largest weakly '
                   'connected component ({:,} of {:,} total nodes) in {:.2f} seconds')
            print(msg.format(len(list(G.nodes())), original_len, time.time()-start_time))

    return G 

def average_shortest_path_length(G, weight=None):
    r"""Return the average shortest path length.

    The average shortest path length is

    .. math::

       a =\sum_{s,t \in V} \frac{d(s, t)}{n(n-1)}

    where `V` is the set of nodes in `G`,
    `d(s, t)` is the shortest path from `s` to `t`,
    and `n` is the number of nodes in `G`.

    Parameters
    ----------
    G : NetworkX graph

    weight : None or string, optional (default = None)
       If None, every edge has weight/distance/cost 1.
       If a string, use this edge attribute as the edge weight.
       Any edge attribute not present defaults to 1.

    Raises
    ------
    NetworkXError:
       if the graph is not connected.

    Examples
    --------
    >>> G=nx.path_graph(5)
    >>> print(nx.average_shortest_path_length(G))
    2.0

    For disconnected graphs you can compute the average shortest path
    length for each component:
    >>> G=nx.Graph([(1,2),(3,4)])
    >>> for g in nx.connected_component_subgraphs(G):
    ...     print(nx.average_shortest_path_length(g))
    1.0
    1.0

    """
    if G.is_directed():
        if not nx.is_weakly_connected(G):
            raise nx.NetworkXError("Graph is not connected.")
    else:
        if not nx.is_connected(G):
            raise nx.NetworkXError("Graph is not connected.")
    avg=0.0
    if weight is None:
        for node in G:
            path_length=nx.single_source_shortest_path_length(G, node)
            avg += sum(path_length.values())
    else:
        for node in G:
            path_length=nx.single_source_dijkstra_path_length(G, node, weight=weight)
            avg += sum(path_length.values())
    n=len(G)
    return avg/(n*(n-1)) 

def is_tree(G):
    """
    Returns ``True`` if ``G`` is a tree.

    A tree is a connected graph with no undirected cycles.

    For directed graphs, ``G`` is a tree if the underlying graph is a tree. The
    underlying graph is obtained by treating each directed edge as a single
    undirected edge in a multigraph.

    Parameters
    ----------
    G : graph
        The graph to test.

    Returns
    -------
    b : bool
        A boolean that is ``True`` if ``G`` is a tree.

    Notes
    -----
    In another convention, a directed tree is known as a *polytree* and then
    *tree* corresponds to an *arborescence*.

    See Also
    --------
    is_arborescence

    """
    if len(G) == 0:
        raise nx.exception.NetworkXPointlessConcept('G has no nodes.')

    # A connected graph with no cycles has n-1 edges.
    if G.number_of_edges() != len(G) - 1:
        return False

    if G.is_directed():
        is_connected = nx.is_weakly_connected
    else:
        is_connected = nx.is_connected

    return is_connected(G) 

def is_semiconnected(G):
    """Returns True if the graph is semiconnected, False otherwise.

    A graph is semiconnected if, and only if, for any pair of nodes, either one
    is reachable from the other, or they are mutually reachable.

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

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

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

    NetworkXPointlessConcept :
        If the graph is empty.

    Examples
    --------
    >>> G=nx.path_graph(4,create_using=nx.DiGraph())
    >>> print(nx.is_semiconnected(G))
    True
    >>> G=nx.DiGraph([(1, 2), (3, 2)])
    >>> print(nx.is_semiconnected(G))
    False

    See Also
    --------
    is_strongly_connected
    is_weakly_connected
    is_connected
    is_biconnected
    """
    if len(G) == 0:
        raise nx.NetworkXPointlessConcept(
            'Connectivity is undefined for the null graph.')

    if not nx.is_weakly_connected(G):
        return False

    G = nx.condensation(G)
    path = nx.topological_sort(G)
    return all(G.has_edge(u, v) for u, v in pairwise(path)) 

def _validate_graph(self):
        """Raise an exception if the link-joint structure is invalid.

        Checks for the following:

        - The graph is connected in the undirected sense.
        - The graph is acyclic in the directed sense.
        - The graph has only one base link.

        Returns
        -------
        base_link : :class:`.Link`
            The base link of the URDF.
        end_links : list of :class:`.Link`
            The end links of the URDF.
        """

        # Check that the link graph is weakly connected
        if not nx.is_weakly_connected(self._G):
            link_clusters = []
            for cc in nx.weakly_connected_components(self._G):
                cluster = []
                for n in cc:
                    cluster.append(n.name)
                link_clusters.append(cluster)
            message = ('Links are not all connected. '
                       'Connected components are:')
            for lc in link_clusters:
                message += '\n\t'
                for n in lc:
                    message += ' {}'.format(n)
            raise ValueError(message)

        # Check that link graph is acyclic
        if not nx.is_directed_acyclic_graph(self._G):
            raise ValueError('There are cycles in the link graph')

        # Ensure that there is exactly one base link, which has no parent
        base_link = None
        end_links = []
        for n in self._G:
            if len(nx.descendants(self._G, n)) == 0:
                if base_link is None:
                    base_link = n
                else:
                    raise ValueError('Links {} and {} are both base links!'
                                     .format(n.name, base_link.name))
            if len(nx.ancestors(self._G, n)) == 0:
                end_links.append(n)
        return base_link, end_links 

def _validate_graph(self):
        """Raise an exception if the link-joint structure is invalid.

        Checks for the following:

        - The graph is connected in the undirected sense.
        - The graph is acyclic in the directed sense.
        - The graph has only one base link.

        Returns
        -------
        base_link : :class:`.Link`
            The base link of the URDF.
        end_links : list of :class:`.Link`
            The end links of the URDF.
        """

        # Check that the link graph is weakly connected
        if not nx.is_weakly_connected(self._G):
            link_clusters = []
            for cc in nx.weakly_connected_components(self._G):
                cluster = []
                for n in cc:
                    cluster.append(n.name)
                link_clusters.append(cluster)
            message = ('Links are not all connected. '
                       'Connected components are:')
            for lc in link_clusters:
                message += '\n\t'
                for n in lc:
                    message += ' {}'.format(n)
            raise ValueError(message)

        # Check that link graph is acyclic
        if not nx.is_directed_acyclic_graph(self._G):
            raise ValueError('There are cycles in the link graph')

        # Ensure that there is exactly one base link, which has no parent
        base_link = None
        end_links = []
        for n in self._G:
            if len(nx.descendants(self._G, n)) == 0:
                if base_link is None:
                    base_link = n
                else:
                    raise ValueError('Links {} and {} are both base links!'
                                     .format(n.name, base_link.name))
            if len(nx.ancestors(self._G, n)) == 0:
                end_links.append(n)
        return base_link, end_links 

def is_fully_connected(graph):
    r"""
    Checks whether the input graph is fully connected in the undirected case
    or weakly connected in the directed case.

    Connected means one can get from any vertex u to vertex v by traversing
    the graph. For a directed graph, weakly connected means that the graph
    is connected after it is converted to an unweighted graph (ignore the
    direction of each edge)

    Parameters
    ----------
    graph: nx.Graph, nx.DiGraph, nx.MultiDiGraph, nx.MultiGraph, np.ndarray
        Input graph in any of the above specified formats. If np.ndarray, 
        interpreted as an :math:`n \times n` adjacency matrix

    Returns
    -------
    boolean: True if the entire input graph is connected

    References
    ----------
    http://mathworld.wolfram.com/ConnectedGraph.html
    http://mathworld.wolfram.com/WeaklyConnectedDigraph.html

    Examples
    --------
    >>> a = np.array([
    ...    [0, 1, 0],
    ...    [1, 0, 0],
    ...    [0, 0, 0]])
    >>> is_fully_connected(a)
    False
    """
    if type(graph) is np.ndarray:
        if is_symmetric(graph):
            g_object = nx.Graph()
        else:
            g_object = nx.DiGraph()
        graph = nx.from_numpy_array(graph, create_using=g_object)
    if type(graph) in [nx.Graph, nx.MultiGraph]:
        return nx.is_connected(graph)
    elif type(graph) in [nx.DiGraph, nx.MultiDiGraph]:
        return nx.is_weakly_connected(graph) 

def get_largest_component(G, strongly=False):
    """
    Get subgraph of MultiDiGraph's largest weakly/strongly connected component.

    Parameters
    ----------
    G : networkx.MultiDiGraph
        input graph
    strongly : bool
        if True, return the largest strongly instead of weakly connected
        component

    Returns
    -------
    G : networkx.MultiDiGraph
        the largest connected component subgraph from the original graph
    """
    original_len = len(list(G.nodes()))

    if strongly:
        # if the graph is not connected retain only the largest strongly connected component
        if not nx.is_strongly_connected(G):

            # get all the strongly connected components in graph then identify the largest
            sccs = nx.strongly_connected_components(G)
            largest_scc = max(sccs, key=len)
            G = induce_subgraph(G, largest_scc)

            msg = (
                f"Graph was not connected, retained only the largest strongly "
                f"connected component ({len(G)} of {original_len} total nodes)"
            )
            utils.log(msg)
    else:
        # if the graph is not connected retain only the largest weakly connected component
        if not nx.is_weakly_connected(G):

            # get all the weakly connected components in graph then identify the largest
            wccs = nx.weakly_connected_components(G)
            largest_wcc = max(wccs, key=len)
            G = induce_subgraph(G, largest_wcc)

            msg = (
                f"Graph was not connected, retained only the largest weakly "
                f"connected component ({len(G)} of {original_len} total nodes)"
            )
            utils.log(msg)

    return G 

def is_semiconnected(G):
    """Return True if the graph is semiconnected, False otherwise.

    A graph is semiconnected if, and only if, for any pair of nodes, either one
    is reachable from the other, or they are mutually reachable.

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

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

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

    NetworkXPointlessConcept :
        If the graph is empty.

    Examples
    --------
    >>> G=nx.path_graph(4,create_using=nx.DiGraph())
    >>> print(nx.is_semiconnected(G))
    True
    >>> G=nx.DiGraph([(1, 2), (3, 2)])
    >>> print(nx.is_semiconnected(G))
    False

    See Also
    --------
    is_strongly_connected
    is_weakly_connected
    is_connected
    is_biconnected
    """
    if len(G) == 0:
        raise nx.NetworkXPointlessConcept(
            'Connectivity is undefined for the null graph.')

    if not nx.is_weakly_connected(G):
        return False

    G = nx.condensation(G)
    path = nx.topological_sort(G)
    return all(G.has_edge(u, v) for u, v in pairwise(path))