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