Clique (graph theory)

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Image:Complete graph K5.svg

In graph theory, a clique in an undirected graph G, is a set of vertices V such that for every two vertices in V, there exists an edge connecting the two. This is equivalent to saying that the subgraph induced by V is a complete graph. The size of a clique is the number of vertices it contains.

Unfortunately finding cliques within a graph can be a hard problem. Finding a clique of a given size in a graph (the clique problem), for example, is NP-complete.

The opposite of a clique is an independent set, in the sense that every clique corresponds to an independent set in the complement graph.

See also

he:גרף מלא de:Knotenüberdeckungen, Cliquen und stabile Mengen pl:Klika (teoria grafów)