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networkx.algorithms.community.kclique.k_clique_communities

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

Return type

Yields sets of nodes, one for each k-clique community.

Examples

>>> from networkx.algorithms.community import k_clique_communities
>>> G = nx.complete_graph(5)
>>> K5 = nx.convert_node_labels_to_integers(G,first_label=2)
>>> G.add_edges_from(K5.edges())
>>> c = list(k_clique_communities(G, 4))
>>> sorted(list(c[0]))
[0, 1, 2, 3, 4, 5, 6]
>>> list(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