Which algorithm can I use to find the next to shortest path in a graph?

Question

I want to find the next shortest path between 2 vertices in a graph and the path has a positive cost.The next shortest path is allowed to share edges of the shortest path .W

Answer 1

Use the K-shortest path algorithm, where k=2 for you, some sample reference:

Finding the k shortest paths. D. Eppstein. 35th IEEE Symp. Foundations of Comp. Sci., Santa Fe, 1994, pp. 154-165. Tech. Rep. 94-26, ICS, UCI, 1994. SIAM J. Computing 28(2):652-673, 1998.

http://www.ics.uci.edu/~eppstein/pubs/Epp-TR-94-26.pdf