Distance returns the number of edges in the shortest path from s to t. If no such path exists, the output is infinity.  The strategy is to use a breadth-first search (BFS).

For weighted graphs, the weights of edges are ignored. Use the AllPairsDistance, DijkstrasAlgorithm or BellmanFordAlgorithm commands to compute weighted distances between vertices.

To find a path from s to t with minimum distance use the ShortestPath command.