Definition:Transitive Reduction/Graph Theory

Definition

Let $G = \struct {V, E}$ be a loop-digraph.

Let $G$ be expressed formally as a relational structure $\GG$.

A transitive reduction of $G$ is denoted $G^-$, and is defined as a transitive reduction of the relation $\GG$.

Hence it is a minimal loop-digraph on $V$ which has the same transitive closure as $\GG$.

Also see

• Results about transitive reductions can be found here.