 The transitive reduction of a DAG G is the graph with the fewest edges that represents the same reachability relation as G. It is a subgraph of G , formed by discarding the edges u → v for which G also contains a longer path connecting the same two vertices . Like the transitive closure , the transitive reduction is uniquely defined for DAGs . In contrast , for a directed graph that is not acyclic , there can be more than one minimal subgraph with the same reachability relation . 
