A maximum clique of a graph G is a clique (i.e., complete subgraph) of maximum possible size for G. Note that some authors refer to maximum cliques simply as "cliques." The size of the maximum clique is known as a graph's clique number, and the problem of finding the size of a clique for a given graph is an NP-complete problem. A maximum clique in a given graph g can be found in the Wolfram Language using FindClique[g][[1]]. The command Sort[FindClique[g, Length /@ FindClique[g], All]] will find all maximum cliques.

caveman graph | clique | clique graph | clique number | complete graph | induced subgraph | maximal clique | party problem | perfect graph | Ramsey number | Turán's theorem