Clarification on the definition of multigraph If I have a graph that has an edge that straight connects vertice $A$ to $B$ and another that connects vertice $A$ to $C$ then to $B$ is it considered a multigraph? Clarification will be much appreciated. Thanks.

If I understood correctly, the edges make a triangle. That is not (necessarily) a multigraph. In a regular graph there may be many paths between two vertices. It is only single edges that cannot be doubled. If you want to disallow any such multiple paths, however, your graph is called a _tree_ (as long as it's connected).