clique

A maximal complete subgraph of a graph is a clique, and the clique number $\omega(G)$ of a graph $G$ is the maximal order of a clique in $G$ . Simply, $\omega(G)$ is the maximal order of a complete subgraph of $G$ . Some authors however define a clique as any complete subgraph of $G$ and refer to the other definition as maximum clique.

Adapted with permission of the author from Modern Graph Theory by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.