networkx.algorithms.approximation.clique.max_clique¶

max_clique
(G)[source]¶ Find the Maximum Clique
Finds the \(O(V/(logV)^2)\) apx of maximum clique/independent set in the worst case.
Parameters: G (NetworkX graph) – Undirected graph Returns: clique – The apxmaximum clique of the graph Return type: set 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