clique_removal

clique_removal(G)

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:

GNetworkX graph

Undirected graph

Returns:

max_ind_cliques(set, list) tuple

2-tuple of Maximal Independent Set and list of maximal cliques (sets).

Raises:

NetworkXNotImplemented

If the graph is directed or is a multigraph.

References

[1]

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

Examples

>>> G = nx.path_graph(10)
>>> nx.approximation.clique_removal(G)
({0, 2, 4, 6, 9}, [{0, 1}, {2, 3}, {4, 5}, {6, 7}, {8, 9}])