Graph Theory - Can two vertices have two distinct edges? My question is simple:
Can two vertices in a graph have two distinct edges connecting them? Why or why not?


I put this answer up only because OP asked for it in a comment, and also to present the other two terms I've heard of besides the widely used "simple graph".
In a graph, two or more edges connecting two distinct vertices are called parallel edges,
and an edge connecting only one vertex to itself is called a loop.
According to some sources: a graph allowing no loop or parallel edges is a "simple graph", a graph allowing parallel edges but no loops is a "multigraph", and if both parallel edges and loops are allowed the graph is a "pseudograph". [It's not clear to me whether a multigraph must have at least one case of a parallel edge, or whether a pseudograph which happens not to have loops would qualify as a multigraph.]
I also don't know whether there is general agreement about the definitions of multigraph and pseudograph. (Nor do I think it matters much provided a text/article makes the definitions used clear.)
