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In the mathematical area of graph theory, a clique ( or ) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete. A maximal clique is a clique that cannot be extended by including one more adjacent vertex, that is, a clique which does not exist exclusively within the vertex set of a larger clique. Some authors define cliques in a way that requires them to be maximal, and use other terminology for complete subgraphs that are not maximal. An independent set (sometimes also called stable set) is a subset of vertices such that no two vertices are adjacent. A maximal independent set is an independent set cannot be extended to a larger independent set. A strong clique in a graph is a clique that has non-empty intersection with every maximal indepedent set.

Properties
Every strong clique is maximal. The converse does not hold.

There are graphs in which every maximal clique is strong. Such graphs are called CIS graphs.