Reachability preorder ($u⪯v⟺\text{a directed path from }u\text{ to }v\text{ exists}$)

Reachability in a directed graph, allowing length-zero paths, is a preorder: zero steps give reflexivity and concatenation gives transitivity. Distinct mutually reachable vertices violate antisymmetry. Its equivalence classes under mutual reachability are the strongly connected components; the induced reachability relation on those classes is a partial order. Equivalently, contracting the classes gives the acyclic condensation graph.