Go backward to Reachability Go up to Top Go forward to Composition of Relations |
Let R and S be binary relations on Nn for some n in N.
The composition of R and S is
R o S = {<a, c>: a in Nn /\ c in Nn /\ (exists b: <a, b> in R /\ <b, c> in S)}.
For the corresponding adjacency matrix, we thus have
forall i in Nn, j in Nn: adjacency(<Nn, R o S>)i, j = true <=> exists k in Nn: Ai, k = true /\ Bk, j = true where A = adjacency(<Nn, R>), B = adjacency(<Nn, S>).