Find the Maximum Clique

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


G (NetworkX graph) – Undirected graph


clique – The apx-maximum clique of the graph

Return type



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.



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