Josh Adell's Blog: Path finding with Neo4j
The thing that makes graphing databases useful is the ability to find relationship paths from one node to another. There are many algorithms for finding paths efficiently, depending on the use case.
He includes some code showing the REST request (made via this client) to fetch these street-based relationships. He then creates a little sample script that provides driving directions from one intersection to another with a "findPathsTo" call. He modifies it a bit later on to use the Dijkstra algorithm.