The property of a binary relation that opposite directed relationships between two elements can hold only when those elements are equal. It does not require every pair to be comparable and does not prohibit a longer directed cycle whose reverse edges are initially absent. Taking reflexive transitive closure can therefore destroy this property.
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Antisymmetry is a property often discussed in the context of relations in mathematics, particularly in set theory and order theory. A relation \( R \) on a set \( A \) is said to be antisymmetric if, for any \( a \) and \( b \) in \( A \), whenever both \( a R b \) and \( b R a \) hold, it must also be the case that \( a = b \).