To clarify my question, for a given vertex, i I want to know how many paths from Start to End exists which goes through vertex i.

I see that FindPath can list all of the paths for me but I don't know how to count the number of the paths which contain i.

Also, what I really want to know is which nodes have the highest count, ie I want to do this for all nodes, i, and then sort the count.

Thanks for your reply but ... for an acyclic graph

(1) there are typically many paths between two vertices, (See FindPath documentation of Mathematics) (2) Most of these paths will not be the shortest path