In the above picture we can see that , I can traverse to node 5 from both node 1 and 2 , but while traversing from 1 only one vertex in encountered which is 3 but for two it is 5 and 4 .
How can I write a gremlin query , that will return the number of vertex encountered .
When asking questions about Gremlin a picture can be helpful, but it is far more important to provide a Gremlin script that creates some sample data - like this:
g.addV().property(id,1).as('1').
addV().property(id,2).as('2').
addV().property(id,3).as('3').
addV().property(id,4).as('4').
addV().property(id,5).as('5').
addE('link').from('1').to('3').
addE('link').from('2').to('3').
addE('link').from('2').to('4').
addE('link').from('3').to('5').
addE('link').from('4').to('5').iterate()
In answer to your question, I think you just need to use path() step to show where Gremlin has traversed:
gremlin> g.V().repeat(out()).emit().path()
==>[v[1],v[3]]
==>[v[1],v[3],v[5]]
==>[v[2],v[3]]
==>[v[2],v[4]]
==>[v[2],v[3],v[5]]
==>[v[2],v[4],v[5]]
==>[v[3],v[5]]
==>[v[4],v[5]]
If you're just interested in paths between vertices 1/2 and 5 then you can add some restrictions:
gremlin> g.V(1,2).repeat(out()).emit(hasId(5)).path()
==>[v[1],v[3],v[5]]
==>[v[2],v[3],v[5]]
==>[v[2],v[4],v[5]]
Building on that further, if you want to count the vertices in the middle of the path, then you could unfold() the paths, filter away your start/end vertices and count():
gremlin> g.V(2).
......1> repeat(out()).
......2> emit(hasId(5)).
......3> path().
......4> unfold().
......5> not(hasId(2,5)).
......6> dedup().
......7> count()
==>2
Hopefully, that gives you some inspiration. There are a lot of nice examples of this in Gremlin Recipes.
