rel_is_cyclic {agop} | R Documentation |
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)
R |
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
.
rel_is_cyclic
returns
a single logical value.
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()