There is a very interesting paper about efficiently listing/enumerating all paths and cycles in a graph, that I just discovered a few days ago.

Maybe this will help someone out: http://www.cis.uoguelph.ca/~sawada/papers/PathListing.pdf ]]>

Fair enough, I see your point. Only the diagonal entries exhibit this behavior though. And actually, wikipedia states “Some authors do not require that all vertices of a path be distinct and instead use the term simple path to refer to such a path.”

]]>“Another example: (A^2)_{22} = 3, because there are 3 paths that link B with itself: B-A-B, B-D-B and B-E-B”

These clearly aren’t paths, since they use the same edge twice… ]]>

Uhm, why do you think vertices could be repeated?

]]>By intuition i’d say it calculates the amount of WALKS, not PATHS ? ]]>

Hi Frank,

thanks for catching the mistake! I’ve changed the directional vector of the first line, so that numbers should be correct now ðŸ™‚

This impacts what follows. ]]>