rel_cyclic: Cyclic Binary Relations

In agop: Aggregation Operators and Preordered Sets

Cyclic Binary Relations

Description

A binary relation R is cyclic, iff its transitive closure is not antisymmetric. Note that R may be reflexive and still acyclic, i.e., loops in R are not taken into account.

Usage

rel_is_cyclic(R)

Arguments

R	an object coercible to a 0-1 (logical) square matrix, representing a binary relation on a finite set.

Details

rel_is_cyclic has O(n^3) time complexity, where n is the number of rows in R (the implemented algorithm currently verifies whether a depth-first search-based topological sorting is possible). Missing values in R always result in NA.

Value

rel_is_cyclic returns a single logical value.

See Also

Other binary_relations: check_comonotonicity(), pord_nd(), pord_spread(), pord_weakdom(), rel_graph(), rel_is_antisymmetric(), rel_is_asymmetric(), rel_is_irreflexive(), rel_is_reflexive(), rel_is_symmetric(), rel_is_total(), rel_is_transitive(), rel_reduction_hasse()

agop documentation built on May 29, 2024, 9:54 a.m.