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Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

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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.