I have a Neo4j graph with 12 inputs and 4 outputs, and am trying to write a query with the Java Traverser that will return the 14 unique paths from an input to an output node. All the queries I have tried return only a subset of the 14 paths. For example, the code below returns 4 paths, but the other 10 all stop 1 node short of the output.

RelationshipType relType = RelationshipTypes.EDGE;
TraversalDescription td = new TraversalDescriptionImpl()
      .depthFirst()
      .relationships(relType, Direction.OUTGOING);
for (Node node : inputs){
    Traverser tv = td.traverse(node);
    Iterator<Path> iter = tv.iterator();
    // ... print path
}

I've tried uniqueness and depth settings as well, with no effect.

The query below returns all 14 paths using the web interface, but when I use the ExecutionEngine class, I only get 13 paths back.

START s=node(*) 
MATCH (s)-[p:EDGE*]->(c)
WHERE s.type! = "INPUT" AND c.type! = "OUTPUT"
RETURN p

How do I get all the unique paths using the Java API?