# Definition:Loop-Graph

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## Definition

A **loop-graph** is a graph which allows an edge to start and end at the same vertex:

Such an edge is called a loop.

### Formal Definition

A **loop-graph** $G$ is a non-empty set $V$ together with a symmetric relation $E$ on $G$.

Thus it can be seen that a loop-graph is a simple graph with the stipulation that the relation $E$ does not need to be antireflexive.

### Incidence

## Also known as

Some presentations of this subject omit the hyphen and call this a **loop graph**.

**Loop-graphs** and **loop-multigraphs** are also often known as **pseudographs**.

However, the precise definition of the latter term varies in the literature, and its precise meaning can be misunderstood. Its use is therefore not recommended.

## Also see

- Results about
**loop-graphs**can be found**here**.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.6$: Networks as Mathematical Models