Forward edges in undirected graph using BFS Introduction to Algorithms books claims BFS only classifies an edge for an undirected graph to be either tree or cross edge. But how about this simple example below where forward edges are naturally appearing?

Given graph with just 2 vertices A and B and 3 edges from A to B!

 exploring A adjacent vertices

(1) A->B (tree edge, A is now marked as an ancestor for B and B is A's descendant)

(2) A->B (forward edge? B is not yet processed (gray) and we found an edge to it from its ancestor(A))

(3) A->B forward edge using the same reasoning as in (2)!

What am I missing here?
My example was a multigraph (multiple edges between a given pair of vertices is allowed). And in multigraph BFS does "produce" forward edges!