Recognition of prime graphs from a prime subgraph

Given a graph G , a subset M of V ( G ) is a module of G if for each v ∈ V ( G ) ∖ M , v is adjacent to all the elements of M or to none of them. A graph G is prime if | V ( G ) | ≥ 4 and the only modules of G are V ( G ) , 0̸ , and singleton vertex sets. Given a prime induced subgraph G [ X ] , we introduce a digraph that yields a necessary and sufficient condition for G to be prime.