I don't know how your database is implementing things under the hood, so I don't know. I'll just list the major advantages of a graph database:
1) Edges stored with nodes. You can almost certainly read an edge and all it's neighbors with a single disk seek. This is unlikely to be the case for a SQL system.
2) Compute time is always O( portion of graph traversed), not O(graph size), and is always under the control of the user. In SQL, this will vary quite a bit with implementation.
3) You can specify various heuristics for the traversal - depth first, breadth first, etc. This is important if the specific nature of your data will affect the speed of the query.