Python networkx.non_edges() Examples

def test_non_edges(self):
        # All possible edges exist
        graph = nx.complete_graph(5)
        nedges = list(nx.non_edges(graph))
        assert_equal(len(nedges), 0)

        graph = nx.path_graph(4)
        expected = [(0, 2), (0, 3), (1, 3)]
        nedges = list(nx.non_edges(graph))
        for (u, v) in expected:
            assert_true( (u, v) in nedges or (v, u) in nedges )

        graph = nx.star_graph(4)
        expected = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
        nedges = list(nx.non_edges(graph))
        for (u, v) in expected:
            assert_true( (u, v) in nedges or (v, u) in nedges )

        # Directed graphs
        graph = nx.DiGraph()
        graph.add_edges_from([(0, 2), (2, 0), (2, 1)])
        expected = [(0, 1), (1, 0), (1, 2)]
        nedges = list(nx.non_edges(graph))
        for e in expected:
            assert_true(e in nedges) 

def test_non_edges(self):
        # All possible edges exist
        graph = nx.complete_graph(5)
        nedges = list(nx.non_edges(graph))
        assert_equal(len(nedges), 0)

        graph = nx.path_graph(4)
        expected = [(0, 2), (0, 3), (1, 3)]
        nedges = list(nx.non_edges(graph))
        for (u, v) in expected:
            assert_true((u, v) in nedges or (v, u) in nedges)

        graph = nx.star_graph(4)
        expected = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
        nedges = list(nx.non_edges(graph))
        for (u, v) in expected:
            assert_true((u, v) in nedges or (v, u) in nedges)

        # Directed graphs
        graph = nx.DiGraph()
        graph.add_edges_from([(0, 2), (2, 0), (2, 1)])
        expected = [(0, 1), (1, 0), (1, 2)]
        nedges = list(nx.non_edges(graph))
        for e in expected:
            assert_true(e in nedges) 

def _apply_prediction(G, func, ebunch=None):
    """Applies the given function to each edge in the specified iterable
    of edges.

    `G` is an instance of :class:`networkx.Graph`.

    `func` is a function on two inputs, each of which is a node in the
    graph. The function can return anything, but it should return a
    value representing a prediction of the likelihood of a "link"
    joining the two nodes.

    `ebunch` is an iterable of pairs of nodes. If not specified, all
    non-edges in the graph `G` will be used.

    """
    if ebunch is None:
        ebunch = nx.non_edges(G)
    return ((u, v, func(u, v)) for u, v in ebunch) 

def test_non_edges(self):
        # All possible edges exist
        graph = nx.complete_graph(5)
        nedges = list(nx.non_edges(graph))
        assert_equal(len(nedges), 0)

        graph = nx.path_graph(4)
        expected = [(0, 2), (0, 3), (1, 3)]
        nedges = list(nx.non_edges(graph))
        for (u, v) in expected:
            assert_true((u, v) in nedges or (v, u) in nedges)

        graph = nx.star_graph(4)
        expected = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
        nedges = list(nx.non_edges(graph))
        for (u, v) in expected:
            assert_true((u, v) in nedges or (v, u) in nedges)

        # Directed graphs
        graph = nx.DiGraph()
        graph.add_edges_from([(0, 2), (2, 0), (2, 1)])
        expected = [(0, 1), (1, 0), (1, 2)]
        nedges = list(nx.non_edges(graph))
        for e in expected:
            assert_true(e in nedges) 

def _apply_prediction(G, func, ebunch=None):
    """Applies the given function to each edge in the specified iterable
    of edges.

    `G` is an instance of :class:`networkx.Graph`.

    `func` is a function on two inputs, each of which is a node in the
    graph. The function can return anything, but it should return a
    value representing a prediction of the likelihood of a "link"
    joining the two nodes.

    `ebunch` is an iterable of pairs of nodes. If not specified, all
    non-edges in the graph `G` will be used.

    """
    if ebunch is None:
        ebunch = nx.non_edges(G)
    return ((u, v, func(u, v)) for u, v in ebunch) 

def make_train_test_set(graph, radius,
                        test_proportion=.3, ratio_neg_to_pos=10):
    """make_train_test_set."""
    pos = [(u, v) for u, v in graph.edges()]
    neg = [(u, v) for u, v in nx.non_edges(graph)]
    random.shuffle(pos)
    random.shuffle(neg)
    pos_dim = len(pos)
    neg_dim = len(neg)
    max_n_neg = min(pos_dim * ratio_neg_to_pos, neg_dim)
    neg = neg[:max_n_neg]
    neg_dim = len(neg)
    tr_pos = pos[:-int(pos_dim * test_proportion)]
    te_pos = pos[-int(pos_dim * test_proportion):]
    tr_neg = neg[:-int(neg_dim * test_proportion)]
    te_neg = neg[-int(neg_dim * test_proportion):]

    # remove edges
    tr_graph = graph.copy()
    tr_graph.remove_edges_from(te_pos)
    tr_pos_graphs = list(_make_subgraph_set(tr_graph, radius, tr_pos))
    tr_neg_graphs = list(_make_subgraph_set(tr_graph, radius, tr_neg))
    te_pos_graphs = list(_make_subgraph_set(tr_graph, radius, te_pos))
    te_neg_graphs = list(_make_subgraph_set(tr_graph, radius, te_neg))

    tr_graphs = tr_pos_graphs + tr_neg_graphs
    te_graphs = te_pos_graphs + te_neg_graphs
    tr_targets = [1] * len(tr_pos_graphs) + [0] * len(tr_neg_graphs)

    te_targets = [1] * len(te_pos_graphs) + [0] * len(te_neg_graphs)
    tr_graphs, tr_targets = paired_shuffle(tr_graphs, tr_targets)
    te_graphs, te_targets = paired_shuffle(te_graphs, te_targets)

    return (tr_graphs, np.array(tr_targets)), (te_graphs, np.array(te_targets)) 

def show_graph(g, vertex_color='typeof', size=15, vertex_label=None):
    """show_graph."""
    degrees = [len(g.neighbors(u)) for u in g.nodes()]

    print(('num nodes=%d' % len(g)))
    print(('num edges=%d' % len(g.edges())))
    print(('num non edges=%d' % len(list(nx.non_edges(g)))))
    print(('max degree=%d' % max(degrees)))
    print(('median degree=%d' % np.percentile(degrees, 50)))

    draw_graph(g, size=size,
               vertex_color=vertex_color, vertex_label=vertex_label,
               vertex_size=200, edge_label=None)

    # display degree distribution
    size = int((max(degrees) - min(degrees)) / 1.5)
    plt.figure(figsize=(size, 3))
    plt.title('Degree distribution')
    _bins = np.arange(min(degrees), max(degrees) + 2) - .5
    n, bins, patches = plt.hist(degrees, _bins,
                                alpha=0.3,
                                facecolor='navy', histtype='bar',
                                rwidth=0.8, edgecolor='k')
    labels = np.array([str(int(i)) for i in n])
    for xi, yi, label in zip(bins, n, labels):
        plt.text(xi + 0.5, yi, label, ha='center', va='bottom')

    plt.xticks(bins + 0.5)
    plt.xlim((min(degrees) - 1, max(degrees) + 1))
    plt.ylim((0, max(n) * 1.1))
    plt.xlabel('Node degree')
    plt.ylabel('Counts')
    plt.grid(linestyle=":")
    plt.show() 

def _getall_false_edges(G, fe_train_frac):
    print("Generating all non-edges and splitting them in train and test...")
    train_E_false = list()
    test_E_false = list()
    for e in nx.non_edges(G):
        r = random.uniform(0, 1)
        if r <= fe_train_frac:
            train_E_false.append(e)
        else:
            test_E_false.append(e)

    return train_E_false, test_E_false 

def inter_community_non_edges(G, partition):
    """Returns the number of inter-community non-edges according to the
    given partition of the nodes of `G`.

    `G` must be a NetworkX graph.

    `partition` must be a partition of the nodes of `G`.

    A *non-edge* is a pair of nodes (undirected if `G` is undirected)
    that are not adjacent in `G`. The *inter-community non-edges* are
    those non-edges on a pair of nodes in different blocks of the
    partition.

    Implementation note: this function creates two intermediate graphs,
    which may require up to twice the amount of memory as required to
    store `G`.

    """
    # Alternate implementation that does not require constructing two
    # new graph objects (but does require constructing an affiliation
    # dictionary):
    #
    #     aff = dict(chain.from_iterable(((v, block) for v in block)
    #                                    for block in partition))
    #     return sum(1 for u, v in nx.non_edges(G) if aff[u] != aff[v])
    #
    return inter_community_edges(nx.complement(G), partition) 

def inter_community_non_edges(G, partition):
    """Returns the number of inter-community non-edges according to the
    given partition of the nodes of `G`.

    `G` must be a NetworkX graph.

    `partition` must be a partition of the nodes of `G`.

    A *non-edge* is a pair of nodes (undirected if `G` is undirected)
    that are not adjacent in `G`. The *inter-community non-edges* are
    those non-edges on a pair of nodes in different blocks of the
    partition.

    Implementation note: this function creates two intermediate graphs,
    which may require up to twice the amount of memory as required to
    store `G`.

    """
    # Alternate implementation that does not require constructing two
    # new graph objects (but does require constructing an affiliation
    # dictionary):
    #
    #     aff = dict(chain.from_iterable(((v, block) for v in block)
    #                                    for block in partition))
    #     return sum(1 for u, v in nx.non_edges(G) if aff[u] != aff[v])
    #
    return inter_community_edges(nx.complement(G), partition) 

def resource_allocation_index(G, ebunch=None):
    r"""Compute the resource allocation index of all node pairs in ebunch.

    Resource allocation index of `u` and `v` is defined as

    .. math::

        \sum_{w \in \Gamma(u) \cap \Gamma(v)} \frac{1}{|\Gamma(w)|}

    where :math:`\Gamma(u)` denotes the set of neighbors of `u`.

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

    ebunch : iterable of node pairs, optional (default = None)
        Resource allocation index will be computed for each pair of
        nodes given in the iterable. The pairs must be given as
        2-tuples (u, v) where u and v are nodes in the graph. If ebunch
        is None then all non-existent edges in the graph will be used.
        Default value: None.

    Returns
    -------
    piter : iterator
        An iterator of 3-tuples in the form (u, v, p) where (u, v) is a
        pair of nodes and p is their resource allocation index.

    Examples
    --------
    >>> import networkx as nx
    >>> G = nx.complete_graph(5)
    >>> preds = nx.resource_allocation_index(G, [(0, 1), (2, 3)])
    >>> for u, v, p in preds:
    ...     '(%d, %d) -> %.8f' % (u, v, p)
    ...
    '(0, 1) -> 0.75000000'
    '(2, 3) -> 0.75000000'

    References
    ----------
    .. [1] T. Zhou, L. Lu, Y.-C. Zhang.
       Predicting missing links via local information.
       Eur. Phys. J. B 71 (2009) 623.
       http://arxiv.org/pdf/0901.0553.pdf
    """
    if ebunch is None:
        ebunch = nx.non_edges(G)

    def predict(u, v):
        return sum(1 / G.degree(w) for w in nx.common_neighbors(G, u, v))

    return ((u, v, predict(u, v)) for u, v in ebunch) 

def jaccard_coefficient(G, ebunch=None):
    r"""Compute the Jaccard coefficient of all node pairs in ebunch.

    Jaccard coefficient of nodes `u` and `v` is defined as

    .. math::

        \frac{|\Gamma(u) \cap \Gamma(v)|}{|\Gamma(u) \cup \Gamma(v)|}

    where :math:`\Gamma(u)` denotes the set of neighbors of `u`.

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

    ebunch : iterable of node pairs, optional (default = None)
        Jaccard coefficient will be computed for each pair of nodes
        given in the iterable. The pairs must be given as 2-tuples
        (u, v) where u and v are nodes in the graph. If ebunch is None
        then all non-existent edges in the graph will be used.
        Default value: None.

    Returns
    -------
    piter : iterator
        An iterator of 3-tuples in the form (u, v, p) where (u, v) is a
        pair of nodes and p is their Jaccard coefficient.

    Examples
    --------
    >>> import networkx as nx
    >>> G = nx.complete_graph(5)
    >>> preds = nx.jaccard_coefficient(G, [(0, 1), (2, 3)])
    >>> for u, v, p in preds:
    ...     '(%d, %d) -> %.8f' % (u, v, p)
    ...
    '(0, 1) -> 0.60000000'
    '(2, 3) -> 0.60000000'

    References
    ----------
    .. [1] D. Liben-Nowell, J. Kleinberg.
           The Link Prediction Problem for Social Networks (2004).
           http://www.cs.cornell.edu/home/kleinber/link-pred.pdf
    """
    if ebunch is None:
        ebunch = nx.non_edges(G)

    def predict(u, v):
        cnbors = list(nx.common_neighbors(G, u, v))
        union_size = len(set(G[u]) | set(G[v]))
        if union_size == 0:
            return 0
        else:
            return len(cnbors) / union_size

    return ((u, v, predict(u, v)) for u, v in ebunch) 

def adamic_adar_index(G, ebunch=None):
    r"""Compute the Adamic-Adar index of all node pairs in ebunch.

    Adamic-Adar index of `u` and `v` is defined as

    .. math::

        \sum_{w \in \Gamma(u) \cap \Gamma(v)} \frac{1}{\log |\Gamma(w)|}

    where :math:`\Gamma(u)` denotes the set of neighbors of `u`.

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

    ebunch : iterable of node pairs, optional (default = None)
        Adamic-Adar index will be computed for each pair of nodes given
        in the iterable. The pairs must be given as 2-tuples (u, v)
        where u and v are nodes in the graph. If ebunch is None then all
        non-existent edges in the graph will be used.
        Default value: None.

    Returns
    -------
    piter : iterator
        An iterator of 3-tuples in the form (u, v, p) where (u, v) is a
        pair of nodes and p is their Adamic-Adar index.

    Examples
    --------
    >>> import networkx as nx
    >>> G = nx.complete_graph(5)
    >>> preds = nx.adamic_adar_index(G, [(0, 1), (2, 3)])
    >>> for u, v, p in preds:
    ...     '(%d, %d) -> %.8f' % (u, v, p)
    ...
    '(0, 1) -> 2.16404256'
    '(2, 3) -> 2.16404256'

    References
    ----------
    .. [1] D. Liben-Nowell, J. Kleinberg.
           The Link Prediction Problem for Social Networks (2004).
           http://www.cs.cornell.edu/home/kleinber/link-pred.pdf
    """
    if ebunch is None:
        ebunch = nx.non_edges(G)

    def predict(u, v):
        return sum(1 / math.log(G.degree(w))
                   for w in nx.common_neighbors(G, u, v))

    return ((u, v, predict(u, v)) for u, v in ebunch) 

def preferential_attachment(G, ebunch=None):
    r"""Compute the preferential attachment score of all node pairs in ebunch.

    Preferential attachment score of `u` and `v` is defined as

    .. math::

        |\Gamma(u)| |\Gamma(v)|

    where :math:`\Gamma(u)` denotes the set of neighbors of `u`.

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

    ebunch : iterable of node pairs, optional (default = None)
        Preferential attachment score will be computed for each pair of
        nodes given in the iterable. The pairs must be given as
        2-tuples (u, v) where u and v are nodes in the graph. If ebunch
        is None then all non-existent edges in the graph will be used.
        Default value: None.

    Returns
    -------
    piter : iterator
        An iterator of 3-tuples in the form (u, v, p) where (u, v) is a
        pair of nodes and p is their preferential attachment score.

    Examples
    --------
    >>> import networkx as nx
    >>> G = nx.complete_graph(5)
    >>> preds = nx.preferential_attachment(G, [(0, 1), (2, 3)])
    >>> for u, v, p in preds:
    ...     '(%d, %d) -> %d' % (u, v, p)
    ...
    '(0, 1) -> 16'
    '(2, 3) -> 16'

    References
    ----------
    .. [1] D. Liben-Nowell, J. Kleinberg.
           The Link Prediction Problem for Social Networks (2004).
           http://www.cs.cornell.edu/home/kleinber/link-pred.pdf
    """
    if ebunch is None:
        ebunch = nx.non_edges(G)

    return ((u, v, G.degree(u) * G.degree(v)) for u, v in ebunch)