I would like to know if there is a equation for the maximum number of shortest paths that pass through *r* where *r* is a node contained in any path from node *s* (a fixed node, i mean, *s* is the only source of paths) to any node *t* in an unweighted undirected acyclic graph. I've searched and found [this work][1] that show this number for grid graphs, but I'm interested in this number for general topology graph.

I would be grateful for any reference for a work in this subject, or a suggestion how to start to solve this problem. Thanks in advance.

  [1]: http://www.cse.fau.edu/~jie/research/publications/Publication_files/msp.pdf