| 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()