The transitive reduction of a binary relation R on a set X is the minimum relation R' on X with the same transitive closure as R. Thus a R' b for any elements a and b of X, provided that a R b and there exists no element c of X such that a R c and c R b. The transitive reduction of a graph G is the smallest graph R(G) such that C(G) = C(R(G)), where C(G) is the transitive closure of G.

reflexive reduction | transitive closure