networkx.algorithms.approximation.clique.clique_removal¶

clique_removal(G)[source]¶

Repeatedly remove cliques from the graph.

Results in a \(O(|V|/(\log |V|)^2)\) approximation of maximum clique and independent set. Returns the largest independent set found, along with found maximal cliques.

Parameters: G (NetworkX graph) – Undirected graph
Returns: max_ind_cliques – 2-tuple of Maximal Independent Set and list of maximal cliques (sets).
Return type: (set, list) tuple

References

1: Boppana, R., & Halldórsson, M. M. (1992). Approximating maximum independent sets by excluding subgraphs. BIT Numerical Mathematics, 32(2), 180–196. Springer.