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| from collections import defaultdict | |
| import networkx as nx | |
| __all__ = ["k_clique_communities"] | |
| 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)) | |
| 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 | |