For the graph below
Is the relation stated below transitive?
{(u, v) | there is an even path that contains the vertices u, v}
I believe it is as I can not find any counterexamples but want to double check.
Also I am thinking of the path (1,{1,5},5,{5,2},2) covering all occurrences of the vertices (1,5,2)
and (5,{5,2},2,{2,6},6) for the rest.