max_clique#

max_clique(G)[source]#

Find the Maximum Clique

Finds the \(O(|V|/(log|V|)^2)\) apx of maximum clique/independent set in the worst case.

Parameters:

GNetworkX graph: Undirected graph

Returns:

cliqueset: The apx-maximum clique of the graph

Raises:

NetworkXNotImplemented: If the graph is directed or is a multigraph.

Notes

A clique in an undirected graph G = (V, E) is a subset of the vertex set C subseteq V such that for every two vertices in C there exists an edge connecting the two. This is equivalent to saying that the subgraph induced by C is complete (in some cases, the term clique may also refer to the subgraph).

A maximum clique is a clique of the largest possible size in a given graph. The clique number omega(G) of a graph G is the number of vertices in a maximum clique in G. The intersection number of G is the smallest number of cliques that together cover all edges of G.

https://en.wikipedia.org/wiki/Maximum_clique

References

[1]

Boppana, R., & Halldórsson, M. M. (1992). Approximating maximum independent sets by excluding subgraphs. BIT Numerical Mathematics, 32(2), 180–196. Springer. doi:10.1007/BF01994876

Examples

>>> G = nx.path_graph(10)
>>> nx.approximation.max_clique(G)
{8, 9}