asymmetric relation

An asymmetric relation is is a homogeneous relation that is irreflexive and antisymmetric.

Formally,
a binary relation $R$ over set $S$ is asymmetric if for all $a,b\in S$,

• $(a,a)\notin R$ (irreflexive)
• if $(a,b)\in R$, then $(b,a)\notin R$ (antisymmetric)