Query to check if there is a cycle in a graph with edges visited only once

Question

How to write an query runs on my graph, that outputs 'false' if there is NO path traversing through each edge only once and return to the starting point.

Answer 1

I was using the following sample graph:

g = TinkerGraph.open().traversal()
g.addV().property(id, 'blue').as('b').
  addV().property(id, 'orange').as('o').
  addV().property(id, 'red').as('r').
  addV().property(id, 'white').as('w').
  addE('bridge').from('w').to('b').
  addE('bridge').from('w').to('o').
  addE('bridge').from('w').to('r').
  addE('bridge').from('w').to('r').
  addE('bridge').from('o').to('b').
  addE('bridge').from('o').to('b').
  addE('bridge').from('o').to('r').
  addE('bridge').from('o').to('r').iterate()

The following query returns the first possible path:

gremlin> g.V().sideEffect(outE("bridge").aggregate("bridges")).barrier().
......1>   repeat(bothE().or(__.not(select('e')),
......2>                     __.not(filter(__.as('x').select(all, 'e').unfold().where(eq('x'))))).as('e').otherV()).
......3>     until(select(all, 'e').count(local).as("c").select("bridges").count(local).where(eq("c"))).limit(1).
......4>   path().by(id).by(constant(" -> ")).map {String.join("", it.get().objects())}
==>orange -> blue -> white -> orange -> red -> white -> red -> orange -> blue

If all you need is a boolean value, then just append .hasNext():

g.V().sideEffect(outE("bridge").aggregate("bridges")).barrier().
  repeat(bothE().or(__.not(select('e')),
                    __.not(filter(__.as('x').select(all, 'e').unfold().where(eq('x'))))).as('e').otherV()).
    until(select(all, 'e').count(local).as("c").select("bridges").count(local).where(eq("c"))).hasNext()