I don't believe using the Neo4j Traversal Framework via the REST DB binding is properly supported, nor is it advisable. If you traverse via REST, each node and each relationship will be retrieved over the network as the traversal proceeds, incurring a tremendous overhead for the traversal.
Edit: The above is not true, the REST traverser is smarter than I thought.
In general, it will be faster to use Cypher, and access the Neo4j Server using JDBC. Read more about JDBC here: https://github.com/neo4j-contrib/neo4j-jdbc
If you really want to use the Traversal Framework, you should use Server Extensions, which allow you to design a traversal to run on the server itself, and then only move the result of the traversal over the network. Read more about server extensions here: http://docs.neo4j.org/chunked/stable/server-unmanaged-extensions.html