Check if intersection of two edges exists in a graph

Given two edges, e1 and e2, I would like to know if there is a way in GSQL of getting its intersection and then check if it exists in the graph. For example:

e1 = (1, 2)
e2 = (2, 3)

Then the intersection would be the edge (1, 3), which is an edge I would like to know if it exists in the graph.

This code should fulfill your request. It would be much easier to do in GSQL Syntax v2, but I was running into cryptic error messages that I could not get around.

Thus, here it is in Syntax v1, which will actually run more efficiently than a Syntax v2 implementation:

  // Variables
  EDGE answer;
  SetAccum<VERTEX> @@starting;
  start = {ANY};

  // @@starting should have 2 possible start vertices
  hop1 = SELECT t FROM start:s - (:e) - :t 
                  WHERE e == e1 
                  POST-ACCUM @@starting += s;

  // Now @@starting contains the only actual starting vertex 
  // (Not the one shared by both e1 and e2)
  hop2 = SELECT t FROM hop1:s - (:e) - :t 
                  WHERE e == e2 
                  POST-ACCUM @@starting.remove(s);
  // Check if starting and ending vertices can be connected with 1 hop
  checkIntersection = SELECT t FROM hop2:s - (:e) - :t 
                               WHERE @@starting.contains(t) 
                               ACCUM answer = e;
  PRINT answer;
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