 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 @-@ theoretic 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 transitively 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 . 
 If G <a href='drop_aux' title='1'><mark>is</mark></a>a DAG , its transitive closure <a href='drop_aux' title='2'><mark>is</mark></a>the graph with the most edges <a href='null_relcl' title='3'><mark>that</mark></a><a href='uninflect' title='4'><mark>represents</mark></a> the same reachability relation . It <a href='got' title='5'><mark>has</mark></a> an edge u → v whenever u can reach v. That is , it <a href='got' title='6'><mark>has</mark></a> 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 @-@ theoretic terms . The same method of translating partial orders into DAGs works more generally : for every finite partially ordered set ( S , ≤ ) , the graph <a href='null_relcl' title='7'><mark>that</mark></a><a href='got' title='8'><mark>has</mark></a> a vertex for each member of S and an edge for each pair of elements related by u ≤ v <a href='drop_aux' title='9'><mark>is</mark></a>automatically a transitively closed DAG , and <a href='got' title='10'><mark>has</mark></a> ( S , ≤ ) as its reachability relation . In this way , every finite partially ordered set can be represented as the reachability relation of a DAG . 
If G a DAG , its transitive closure the graph with da most edges represent the same reachability relation . It got an edge u → v whenever u can reach v. That is , it got an edge for every related pair u ≤ v of distinct elements in tdareachability relation of G , and may therefore be thought of as a direct translation of the reachability relation ≤ into graph @-@ theoretic terms . The same method of translating partial orders into DAGs works more generally : for every finite partially ordered set ( S , ≤ ) , the graph got a vertex for each member of S and an edge for each pair of elements related by u ≤ v automatically a transitively closed DAG , and got ( S , ≤ ) as its reachability relation . In dis way , every finite partially ordered set can be represented as thdaeachability relation of a DAG .