 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 ≤ . <unk> reductions are useful in <unk> 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 <unk> 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 . 
