Definition:Loop (Graph Theory)

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

A loop is an edge $e$ of $G$ whose endvertices are the same vertex.

Thus if $e$ is a loop on the vertex $v$, it would be written $e = vv$.

Also known as
Some authors refer to such an edge $e = vv$ as a self-loop at vertex $v$.