+3  A: 

Breadth-first search will find a shortest path: http://en.wikipedia.org/wiki/Breadth-first_search

Dave
+3  A: 

Since you said the edges are all of the same weight, Dijkstra's algorithm (my usual first choice for this sort of thing) will just degrade to breadth first search so I suggest using that for simplicity.

Neil Williams
+1  A: 

You can choose from a number of algorithms for determining the shortest path. QuickGraph is good at this sort of thing.

Tim Robinson