Depth/Breadth First Search Traversal

Question

I am using gremlin with AWS Neptune, and for certain reasons, I want to traverse the graph in either depth-first or breadth-first manner (doesn't matter). This is what I am doing currently:

g.V('0').repeat(out('connected_to').dedup().where(without('z')).aggregate('z')).until(out('connected_to').dedup().where(without('z')).count().is(0)).select('z').limit(1).unfold()

I know that a path exists from vertex '0' to every other vertex in the graph, but there may be cycles in the graph and so, I use the Collection 'z' to keep track of visited nodes, making sure I do not revisit such a node.

If this were to work, I would have all 1000 vertices of the graph in 'z' at the end. But that isn't the case. I get 600 vertices and some vertices are missing even though they have clear incoming edges from other vertices that are in 'z'. What's wrong with my logic here?