Definition:Multigraph/Multiple Edge

Definition
Let $G = \left({V, E}\right)$ be a multigraph.

A multiple edge is an edge of $G$ which has another edge with the same endvertices.

Otherwise it is a simple edge.

Multiplicity
The multiplicity of an edge is the number of edges having the same pair of endvertices.

For example, simple edges have multiplicity $1$.

Thus, an edge is a multiple edge iff its multiplicity exceeds $1$.

Also see

 * Parallel Edges, a closely related concept