Reflexive Reduction

The reflexive reduction of a binary Relation $R$ on a Set $X$ is the minimum relation $R'$ on $X$ with the same Reflexive Closure as $R$. Thus $a R' b$ for any elements $a$ and $b$ of $X$, provided that $a$ and $b$ are distinct and $a R b$.

See also Reflexive Closure, Relation, Transitive Reduction