Complement graph class for small footprint when working on dense graphs.

This class allows you to add the edges that do not exist in the dense graph. However, when applying algorithms to this complement graph data structure, it behaves as if it were the dense version. So it can be used directly in several NetworkX algorithms.

This subclass has only been tested for k-core, connected_components, and biconnected_components algorithms but might also work for other algorithms.

# Author: Jordi Torrents <>

#    Copyright (C) 2015-2019 by
#    Jordi Torrents <>
#    All rights reserved.
#    BSD license.
import networkx as nx
from networkx.exception import NetworkXError
import matplotlib.pyplot as plt

__all__ = ['AntiGraph']

class AntiGraph(nx.Graph):
    Class for complement graphs.

    The main goal is to be able to work with big and dense graphs with
    a low memory footprint.

    In this class you add the edges that *do not exist* in the dense graph,
    the report methods of the class return the neighbors, the edges and
    the degree as if it was the dense graph. Thus it's possible to use
    an instance of this class with some of NetworkX functions.

    all_edge_dict = {'weight': 1}

    def single_edge_dict(self):
        return self.all_edge_dict
    edge_attr_dict_factory = single_edge_dict

    def __getitem__(self, n):
        """Return a dict of neighbors of node n in the dense graph.

        n : node
           A node in the graph.

        adj_dict : dictionary
           The adjacency dictionary for nodes connected to n.

        return dict((node, self.all_edge_dict) for node in
                    set(self.adj) - set(self.adj[n]) - set([n]))

    def neighbors(self, n):
        """Return an iterator over all neighbors of node n in the
           dense graph.

            return iter(set(self.adj) - set(self.adj[n]) - set([n]))
        except KeyError:
            raise NetworkXError("The node %s is not in the graph." % (n,))

    def degree(self, nbunch=None, weight=None):
        """Return an iterator for (node, degree) in the dense graph.

        The node degree is the number of edges adjacent to the node.

        nbunch : iterable container, optional (default=all nodes)
            A container of nodes.  The container will be iterated
            through once.

        weight : string or None, optional (default=None)
           The edge attribute that holds the numerical value used
           as a weight.  If None, then each edge has weight 1.
           The degree is the sum of the edge weights adjacent to the node.

        nd_iter : iterator
            The iterator returns two-tuples of (node, degree).

        See Also

        >>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
        >>> list(  # node 0 with degree 1
        [(0, 1)]
        >>> list([0, 1]))
        [(0, 1), (1, 2)]

        if nbunch is None:
            nodes_nbrs = ((n, {v: self.all_edge_dict for v in
                               set(self.adj) - set(self.adj[n]) - set([n])})
                          for n in self.nodes())
        elif nbunch in self:
            nbrs = set(self.nodes()) - set(self.adj[nbunch]) - {nbunch}
            return len(nbrs)
            nodes_nbrs = ((n, {v: self.all_edge_dict for v in
                               set(self.nodes()) - set(self.adj[n]) - set([n])})
                          for n in self.nbunch_iter(nbunch))

        if weight is None:
            return ((n, len(nbrs)) for n, nbrs in nodes_nbrs)
            # AntiGraph is a ThinGraph so all edges have weight 1
            return ((n, sum((nbrs[nbr].get(weight, 1)) for nbr in nbrs))
                    for n, nbrs in nodes_nbrs)

    def adjacency_iter(self):
        """Return an iterator of (node, adjacency set) tuples for all nodes
           in the dense graph.

        This is the fastest way to look at every edge.
        For directed graphs, only outgoing adjacencies are included.

        adj_iter : iterator
           An iterator of (node, adjacency set) for all nodes in
           the graph.

        for n in self.adj:
            yield (n, set(self.adj) - set(self.adj[n]) - set([n]))

if __name__ == '__main__':
    # Build several pairs of graphs, a regular graph
    # and the AntiGraph of it's complement, which behaves
    # as if it were the original graph.
    Gnp = nx.gnp_random_graph(20, 0.8, seed=42)
    Anp = AntiGraph(nx.complement(Gnp))
    Gd = nx.davis_southern_women_graph()
    Ad = AntiGraph(nx.complement(Gd))
    Gk = nx.karate_club_graph()
    Ak = AntiGraph(nx.complement(Gk))
    pairs = [(Gnp, Anp), (Gd, Ad), (Gk, Ak)]
    # test connected components
    for G, A in pairs:
        gc = [set(c) for c in nx.connected_components(G)]
        ac = [set(c) for c in nx.connected_components(A)]
        for comp in ac:
            assert comp in gc
    # test biconnected components
    for G, A in pairs:
        gc = [set(c) for c in nx.biconnected_components(G)]
        ac = [set(c) for c in nx.biconnected_components(A)]
        for comp in ac:
            assert comp in gc
    # test degree
    for G, A in pairs:
        node = list(G.nodes())[0]
        nodes = list(G.nodes())[1:4]
        assert ==
        assert sum(d for n, d in == sum(d for n, d in
        # AntiGraph is a ThinGraph, so all the weights are 1
        assert sum(d for n, d in == sum(d for n, d in'weight'))
        assert sum(d for n, d in == sum(d for n, d in


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