Re: Transitive Closure

"x" <x-false_at_yahoo.com> wrote in message news:40a4f84f$1_at_post.usenet.com...
> > > Wikipedia says: "...the transitive closure of a binary relation R on a
> > > set X is the smallest transitive relation on X that contains R."
> >
> > I have better definition. Assume that graph adjacency matrix is A. Then,
> > transitive closure is
> >
> > (1-A)^(-1) = I + A + A^2 + A^3 + ...
> >
> > On the other hand
> >
> > exp(A) = I + A +A^2/2 + A^3/6 + ...
> >
> > Which one is correct TC definition?
>
> What type have the elements of A ?

Elements of A have values 0 and 1. (Although, the adjacency matrix definition easily extends to graphs with weighted edges). Elements of TC(A), on the other hand, should be allowed at least Real. TC(A) is interpreted back to graph the following way: if matrix component value is non 0 then nodes are adjacent. Received on Fri May 14 2004 - 19:17:20 CEST