agop (version 0.2-2)

rel_is_cyclic: 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.

Value

rel_is_cyclic returns a single logical value.

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.

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