Find the paths between two given nodes?

Question

Say I have nodes connected in the below fashion, how do I arrive at the number of paths that exist between given points, and path details?

1,2 //node 1 and 2         


        

Answer 1

What you're trying to do is essentially to find a path between two vertices in a (directed?) graph check out Dijkstra's algorithm if you need shortest path or write a simple recursive function if you need whatever paths exist.