hey when you have 9 vertex digraph
in order to have transitive relation do all the vertices of the graph need to be connected in a triagular way??
"Transitive" means "if A <--> B and B <--> C then A <--> C". I'm not sure what you mean by "all connected in a triangular way". The digraph doesn't have to be "connected" at all. With 9 vertices you could have three disconnected triangles, or (because of the "if" part) one triangle and 3 separate segments between two vertices or any combination. Or even 9 unconnected points as vertices.