The relation divides is a partial order: it is reflexive, antisymmetric, and transitive. These properties are expressed in the directed graphs generated here. Reflexivity: there is a path of (zero) arrows from each vertex to itself. Antisymmetry: if there is a path of arrows from to , there cannot be a path in the reverse direction. Transitivity: a path of arrows from to can be appended to a path of arrows from to to create a path from to .