# Source code for networkx.algorithms.community.kclique

from collections import defaultdict

import networkx as nx

__all__ = ["k_clique_communities"]

[docs] @nx._dispatchable 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.community.k_clique_communities(G, 4)) >>> sorted(list(c[0])) [0, 1, 2, 3, 4, 5, 6] >>> list(nx.community.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(f"k={k}, k must be greater than 1.") 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))