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Source code for networkx.algorithms.community.kclique

#-*- coding: utf-8 -*-
#    Copyright (C) 2011 by 
#    Conrad Lee <conradlee@gmail.com>
#    Aric Hagberg <hagberg@lanl.gov>
#    All rights reserved.
#    BSD license.
from collections import defaultdict
import networkx as nx
__author__ = """\n""".join(['Conrad Lee <conradlee@gmail.com>',
                            'Aric Hagberg <aric.hagberg@gmail.com>'])
__all__ = ['k_clique_communities']

[docs]def k_clique_communities(G, k, cliques=None): """Find k-clique communities in graph using the percolation method. A k-clique community is the union of all cliques of size k that can be reached through adjacent (sharing k-1 nodes) k-cliques. Parameters ---------- G : NetworkX graph k : int Size of smallest clique cliques: list or generator Precomputed cliques (use networkx.find_cliques(G)) Returns ------- Yields sets of nodes, one for each k-clique community. Examples -------- >>> G = nx.complete_graph(5) >>> K5 = nx.convert_node_labels_to_integers(G,first_label=2) >>> G.add_edges_from(K5.edges()) >>> c = list(nx.k_clique_communities(G, 4)) >>> list(c[0]) [0, 1, 2, 3, 4, 5, 6] >>> list(nx.k_clique_communities(G, 6)) [] References ---------- .. [1] Gergely Palla, Imre Derényi, Illés Farkas1, and Tamás Vicsek, Uncovering the overlapping community structure of complex networks in nature and society Nature 435, 814-818, 2005, doi:10.1038/nature03607 """ if k < 2: raise nx.NetworkXError("k=%d, k must be greater than 1."%k) if cliques is None: cliques = nx.find_cliques(G) cliques = [frozenset(c) for c in cliques if len(c) >= k] # First index which nodes are in which cliques membership_dict = defaultdict(list) for clique in cliques: for node in clique: membership_dict[node].append(clique) # For each clique, see which adjacent cliques percolate perc_graph = nx.Graph() perc_graph.add_nodes_from(cliques) for clique in cliques: for adj_clique in _get_adjacent_cliques(clique, membership_dict): if len(clique.intersection(adj_clique)) >= (k - 1): perc_graph.add_edge(clique, adj_clique) # Connected components of clique graph with perc edges # are the percolated cliques for component in nx.connected_components(perc_graph): yield(frozenset.union(*component))
def _get_adjacent_cliques(clique, membership_dict): adjacent_cliques = set() for n in clique: for adj_clique in membership_dict[n]: if clique != adj_clique: adjacent_cliques.add(adj_clique) return adjacent_cliques