 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 . 
 The transitive reduction of a DAG G <a href='drop_aux' title='1'><mark>is</mark></a>the graph with the fewest edges <a href='null_relcl' title='2'><mark>that</mark></a><a href='uninflect' title='3'><mark>represents</mark></a> the same reachability relation as G. It <a href='drop_aux' title='4'><mark>is</mark></a>a subgraph of G , formed by discarding the edges u → v for which G also <a href='uninflect' title='5'><mark>contains</mark></a> 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 <a href='null_relcl' title='6'><mark>that</mark></a><a href='negative_concord' title='7'><mark>is</mark></a> <a href='negative_concord' title='8'><mark>not</mark></a>acyclic , <a href='dey_it' title='9'><mark>there</mark></a> can be more than one minimal subgraph with the same reachability relation . 
Da transitive reduction of a DAG G the graph with the fewest edges represent tdasame reachability relation as G. It a subgraph of G , formed by discarding the edges u → v for which G also contain a longer path connecting the same 2 vertices . Like thdaransitive closure , the transitive reduction is uniquely defined fir DAGs . In contrast , for a directed graph ain't acyclic , it can b more den one minimal subgraph with thedame reachability relation .