A note on k-shortest paths problem
It is well-known that in a directed graph, if deleting any edge will not affect the shortest distance between two specific vertices s and t, then there are two edge-disjoint paths from s to t and both of them are shortest paths. In this article, we generalize this to shortest k edge-disjoint s-t paths for any positive integer k.  2010 Wiley Periodicals, Inc. J Graph Theory 67: 34-37, 2011
shortest path edge-disjoint nash equilibrium k-paths flow