rel_is_cyclic {agop}R Documentation

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


[Package agop version 0.2-3 Index]