Modular product of graphs

In graph theory, the modular product of graphs G and H is a graph such that

Cliques in the modular product graph correspond to isomorphisms of induced subgraphs of G and H. Therefore, the modular product graph can be used to reduce problems of induced subgraph isomorphism to problems of finding cliques in graphs. Specifically, the largest graph that is an induced subgraph of both G and H corresponds to the maximum clique in their modular product. Although the problems of finding largest common induced subgraphs and of finding maximum cliques are both NP-complete, this reduction allows clique-finding algorithms to be applied to the common subgraph problem.