 If a DAG G has a reachability relation described by the partial order ≤ , then the transitive reduction of G is a subgraph of G that has an edge u → v for every pair in the covering relation of ≤ . Transitive reductions are useful in visualizing the partial orders they represent , because they have fewer edges than other graphs representing the same orders and therefore lead to simpler graph drawings . A Hasse diagram of a partial order is a drawing of the transitive reduction in which the orientation of each edge is shown by placing the starting vertex of the edge in a lower position than its ending vertex . 
 If a DAG G <a href='got' title='1'><mark>has</mark></a> a reachability relation described by the partial order ≤ , then the transitive reduction of G <a href='drop_aux' title='2'><mark>is</mark></a>a subgraph of G <a href='null_relcl' title='3'><mark>that</mark></a><a href='got' title='4'><mark>has</mark></a> an edge u → v for every pair in the covering relation of ≤ . Transitive reductions <a href='drop_aux' title='5'><mark>are</mark></a>useful in visualizing the partial orders they represent , because they <a href='got' title='6'><mark>have</mark></a> fewer edges than other graphs representing the same orders and therefore lead to simpler graph drawings . A Hasse diagram of a partial order <a href='drop_aux' title='7'><mark>is</mark></a>a drawing of the transitive reduction in which the orientation of each edge is shown by placing the starting vertex of the edge in a lower position than its ending vertex . 
If a DAG G got a reachability relation described by the partial order ≤ , then the transitive reduction of G a subgraph of G got an edge u → v for every pair in da covering relation of ≤ . Transitive reductions useful in visualizing tdapartial orders they represent , b/c they got fewer edges than other graphs representing thdaame orders and therefore lead to simpler graph drawings . A Hasse diagram of a partial order a drawing of thedaansitive reduction in which the daentation of each edge is shown by placing the starting vertex of the eda in a lower position den its ending vertex .