Python networkx.disjoint_union() Examples

def draw_match(GA, GB, pairings, size=10):
    G = nx.disjoint_union(GA, GB)
    for i, jj in enumerate(pairings):
        j = len(GA) + jj
        if G.node[i]['label'] == G.node[j]['label']:
            G.add_edge(i, j, label=i, nesting=True)
    draw_graph(
        G,
        size=size,
        vertex_border=False,
        vertex_size=400,
        edge_label=None,
        edge_alpha=.2,
        dark_edge_color='label',
        dark_edge_dotted=False,
        dark_edge_alpha=1,
        colormap='Set2',
        ignore_for_layout='nesting')


# ----------------------------------------------------------------------------- 

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_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 disjoint_union_all(graphs):
    """Return the disjoint union of all graphs.

    This operation forces distinct integer node labels starting with 0
    for the first graph in the list and numbering consecutively.

    Parameters
    ----------
    graphs : list
       List of NetworkX graphs

    Returns
    -------
    U : A graph with the same type as the first graph in list

    Notes
    -----
    It is recommended that the graphs be either all directed or all undirected.

    Graph, edge, and node attributes are propagated to the union graph.
    If a graph attribute is present in multiple graphs, then the value
    from the last graph in the list with that attribute is used.
    """
    graphs = iter(graphs)
    U = next(graphs)
    for H in graphs:
        U = nx.disjoint_union(U, H)
    return U 

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 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_white_harary_2():
    # Figure 8 white and harary (2001)
    # # http://eclectic.ss.uci.edu/~drwhite/sm-w23.PDF
    G = nx.disjoint_union(nx.complete_graph(4), nx.complete_graph(4))
    G.add_edge(0, 4)
    # kappa <= lambda <= delta
    assert_equal(3, min(nx.core_number(G).values()))
    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(1, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__)) 

def test_spanner_unweighted_disconnected_graph():
    """Test spanner construction on a disconnected graph."""
    G = nx.disjoint_union(nx.complete_graph(10), nx.complete_graph(10))

    spanner = nx.spanner(G, 4, seed=_seed)
    _test_spanner(G, spanner, 4)

    spanner = nx.spanner(G, 10, seed=_seed)
    _test_spanner(G, spanner, 10) 

def test_already_branching(self):
        """Tests that a directed acyclic graph that is already a
        branching produces an isomorphic branching as output.

        """
        T1 = nx.balanced_tree(2, 2, create_using=nx.DiGraph())
        T2 = nx.balanced_tree(2, 2, create_using=nx.DiGraph())
        G = nx.disjoint_union(T1, T2)
        B = nx.dag_to_branching(G)
        assert_true(nx.is_isomorphic(G, B)) 

def test_white_harary1():
    # Figure 1b white and harary (2001)
    # 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)
    assert_equal(1, approx.node_connectivity(G)) 

def test_mixed_type_disjoint_union():
    G = nx.Graph()
    H = nx.MultiGraph()
    U = nx.disjoint_union(G, H) 

def test_disjoint_union_multigraph():
    G=nx.MultiGraph()
    G.add_edge(0,1,key=0)
    G.add_edge(0,1,key=1)
    H=nx.MultiGraph()
    H.add_edge(2,3,key=0)
    H.add_edge(2,3,key=1)
    GH=nx.disjoint_union(G,H)
    assert_equal( set(GH) , set(G)|set(H))
    assert_equal( set(GH.edges(keys=True)) , 
                  set(G.edges(keys=True))|set(H.edges(keys=True))) 

def test_mixed_type_disjoint_union():
    G = nx.Graph()
    H = nx.MultiGraph()
    U = nx.disjoint_union(G,H) 

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 = dict((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)

    G.name = 'Example graph for connectivity'
    return G 

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_white_harary_2():
    # Figure 8 white and harary (2001)
    # # http://eclectic.ss.uci.edu/~drwhite/sm-w23.PDF
    G = nx.disjoint_union(nx.complete_graph(4), nx.complete_graph(4))
    G.add_edge(0, 4)
    # kappa <= lambda <= delta
    assert_equal(3, min(nx.core_number(G).values()))
    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(1, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__)) 

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 = dict((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)

    G.name = 'Example graph for connectivity'
    return G 

def test_white_harary1():
    # Figure 1b white and harary (2001)
    # 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)
    assert_equal(1, approx.node_connectivity(G)) 

def test_disjoint_union_multigraph():
    G = nx.MultiGraph()
    G.add_edge(0, 1, key=0)
    G.add_edge(0, 1, key=1)
    H = nx.MultiGraph()
    H.add_edge(2, 3, key=0)
    H.add_edge(2, 3, key=1)
    GH = nx.disjoint_union(G, H)
    assert_equal(set(GH), set(G) | set(H))
    assert_equal(set(GH.edges(keys=True)),
                 set(G.edges(keys=True)) | set(H.edges(keys=True))) 

def disjoint_union_all(graphs):
    """Returns the disjoint union of all graphs.

    This operation forces distinct integer node labels starting with 0
    for the first graph in the list and numbering consecutively.

    Parameters
    ----------
    graphs : list
       List of NetworkX graphs

    Returns
    -------
    U : A graph with the same type as the first graph in list

    Raises
    ------
    ValueError
       If `graphs` is an empty list.

    Notes
    -----
    It is recommended that the graphs be either all directed or all undirected.

    Graph, edge, and node attributes are propagated to the union graph.
    If a graph attribute is present in multiple graphs, then the value
    from the last graph in the list with that attribute is used.
    """
    if not graphs:
        raise ValueError('cannot apply disjoint_union_all to an empty list')
    graphs = iter(graphs)
    U = next(graphs)
    for H in graphs:
        U = nx.disjoint_union(U, H)
    return U 

def test_white_harary1():
    # Figure 1b white and harary (2001)
    # 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)
    assert_equal(1, approx.node_connectivity(G)) 

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 = dict((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)

    G.name = 'Example graph for connectivity'
    return G 

def test_white_harary_2():
    # Figure 8 white and harary (2001)
    # # http://eclectic.ss.uci.edu/~drwhite/sm-w23.PDF
    G = nx.disjoint_union(nx.complete_graph(4), nx.complete_graph(4))
    G.add_edge(0, 4)
    # kappa <= lambda <= delta
    assert_equal(3, min(nx.core_number(G).values()))
    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(1, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__)) 

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 = dict((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)

    G.name = 'Example graph for connectivity'
    return G 

def test_mixed_type_disjoint_union():
    G = nx.Graph()
    H = nx.MultiGraph()
    U = nx.disjoint_union(G,H) 

def test_disjoint_union_multigraph():
    G=nx.MultiGraph()
    G.add_edge(0,1,key=0)
    G.add_edge(0,1,key=1)
    H=nx.MultiGraph()
    H.add_edge(2,3,key=0)
    H.add_edge(2,3,key=1)
    GH=nx.disjoint_union(G,H)
    assert_equal( set(GH) , set(G)|set(H))
    assert_equal( set(GH.edges(keys=True)) , 
                  set(G.edges(keys=True))|set(H.edges(keys=True))) 

def test_degree_relative_to_subgraph(self, dim):
        """Test that function removes nodes of small degree relative to the subgraph,
        not relative to the entire graph. This is done by creating an unbalanced barbell graph,
        with one "bell" larger than the other. The input subgraph is the small bell (a clique) plus
        a node from the larger bell. The function should remove only the node from the larger
        bell, since this has a low degree within the subgraph, despite having high degree overall"""
        g = nx.disjoint_union(nx.complete_graph(dim), nx.complete_graph(dim + 1))
        g.add_edge(dim, dim - 1)
        subgraph = list(range(dim + 1))
        assert clique.shrink(subgraph, g) == list(range(dim)) 

def __iadd__(self, other):
        """Extend atoms object by appending atoms from *other*."""
        if isinstance(other, ase.Atom):
            other = self.__class__([other])

        n1 = len(self)
        n2 = len(other)

        for name, a1 in self.arrays.items():
            a = np.zeros((n1 + n2, ) + a1.shape[1:], a1.dtype)
            a[:n1] = a1
            if name == 'masses':
                a2 = other.get_masses()
            else:
                a2 = other.arrays.get(name)
            if a2 is not None:
                a[n1:] = a2
            self.arrays[name] = a

        for name, a2 in other.arrays.items():
            if name in self.arrays:
                continue
            a = np.empty((n1 + n2, ) + a2.shape[1:], a2.dtype)
            a[n1:] = a2
            if name == 'masses':
                a[:n1] = self.get_masses()[:n1]
            else:
                a[:n1] = 0

            self.set_array(name, a)

        if isinstance(other, Gratoms):
            if isinstance(self._graph, nx.MultiGraph) & \
               isinstance(other._graph, nx.Graph):
                other._graph = nx.MultiGraph(other._graph)

            self._graph = nx.disjoint_union(self._graph, other._graph)

        return self 

def disjoint_union_all(graphs):
    """Return the disjoint union of all graphs.

    This operation forces distinct integer node labels starting with 0
    for the first graph in the list and numbering consecutively.

    Parameters
    ----------
    graphs : list
       List of NetworkX graphs

    Returns
    -------
    U : A graph with the same type as the first graph in list

    Notes
    -----
    It is recommended that the graphs be either all directed or all undirected.

    Graph, edge, and node attributes are propagated to the union graph.
    If a graph attribute is present in multiple graphs, then the value
    from the last graph in the list with that attribute is used.
    """
    graphs = iter(graphs)
    U = next(graphs)
    for H in graphs:
        U = nx.disjoint_union(U, H)
    return U