Multigraph

Definition

A multigraph is a triple $G = (V, E, r)$ of a set $V$ of vertices, a set $E$ of edges, and a map $r$. The map $r$ assigns to each edge $e \in E$ a set $r(e) \subseteq V$ of one or two vertices, the ends of $e$. Two distinct edges may have the same ends. Such edges are parallel, or multiple, edges. An edge with only one end is a loop.

Remarks

Some authors do not allow loops in a multigraph, and they call a multigraph with loops a pseudograph. A graph is a multigraph without loops and without parallel edges. The Seven Bridges of Königsberg form a multigraph with $4$ vertices and $7$ edges.

Explanations

L1 human

A multigraph is like a graph, but two points can be joined by several lines. A road map with two different roads between the same two towns is a multigraph.