Quotient graph

In graph theory, a quotient graph Q of a graph G is a graph whose vertices are blocks of a partition of the vertices of G and where block B is adjacent to block C if any vertex in B is adjacent to any vertex in C with respect to the edge set of G. In other words, if G has edge set E and vertex set V and R is the equivalence relation induced by the partition, then the quotient graph has vertex set V / R and edge set {([u]_R, [v]_R | (u, v) ∈ E(G)}. For example, the condensation of a strongly connected graph is the quotient graph where the strongly connected components form the blocks of the partition.