# Definition:Loop (Graph Theory)

From ProofWiki

## 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 a **loop** $e$ on the vertex $v$ would be written:

- $e = vv$

## Also known as

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

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 1.6$: Networks as Mathematical Models