 If G is a DAG , its transitive closure is the graph with the most edges that represents the same reachability relation . It has an edge u → v whenever u can reach v. That is , it has an edge for every related pair u ≤ v of distinct elements in the reachability relation of G , and may therefore be thought of as a direct translation of the reachability relation ≤ into graph @-@ <unk> terms . The same method of translating partial orders into DAGs works more generally : for every finite partially ordered set ( S , ≤ ) , the graph that has a vertex for each member of S and an edge for each pair of elements related by u ≤ v is automatically a <unk> closed DAG , and has ( S , ≤ ) as its reachability relation . In this way , every finite partially ordered set can be represented as the reachability relation of a DAG . 
