Is it true that the rank if the Transitive Closure of an set x is ( rank of x )-1?
22.
Informally, the " transitive closure " gives you the set of all places you can get to from any starting place.
23.
Some clustering algorithms use single-linkage clustering, constructing a transitive closure of sequences with a non-redundant set of representative sequences.
24.
The extended transition relation is essentially the reflexive transitive closure of the transition graph that has been augmented to take edge labels into account.
25.
Taking + to be the union, ?to be the composition and * to be the reflexive transitive closure, we obtain a Kleene algebra.
26.
If the binary relation itself is transitive, then the transitive closure is that same binary relation; otherwise, the transitive closure is a different relation.
27.
If the binary relation itself is transitive, then the transitive closure is that same binary relation; otherwise, the transitive closure is a different relation.
28.
To obtain a new equivalence relation or preorder one must take the transitive closure ( reflexivity and symmetry in the case of equivalence relations are automatic ).
29.
The quasi-cardinal of a quasi-set is not defined in the usual sense ( by means of transitive closure contains no m-atoms.
30.
However, the transitive closure of set membership for such hypergraphs does induce a partial order, and " flattens " the hypergraph into a partially ordered set.
