Cluster graph

Сluster graph (кластерный граф) is a graph formed from the disjoint union of complete graphs (or cliques). Equivalently, a graph is a cluster graph if and only if it has no three-vertex induced path (i.e. three-vertex path as an induced subgraph) P₃; for this reason, the cluster graphs are also called P₃-free graphs. The cluster graphs are the graphs for which adjacency is an equivalence relation, and their connected components are the equivalence classes for this relation.