 The reachability relationship in any directed acyclic graph can be formalized as a partial order ≤ on the vertices of the DAG . In this partial order , two vertices u and v are ordered as u ≤ v exactly when there exists a directed path from u to v in the DAG ; that is , when v is reachable from u . However , different DAGs may give rise to the same reachability relation and the same partial order . For example , the DAG with two edges a → b and b → c has the same reachability relation as the graph with three edges a → b , b → c , and a → c . Both of these <unk> produce the same partial order , in which the vertices are ordered as a ≤ b ≤ c . 
