# Definition:Circuit (Graph Theory)

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## Definition

A **circuit** is a **closed** **trail** with at least one **edge**.

### Subgraph

The set of vertices and edges which go to make up a **circuit** form a subgraph.

This subgraph itself is also referred to as a **circuit**.

## Also defined as

Some sources specifically state that a **circuit** must have at least $3$ edges.

However, as defined on $\mathsf{Pr} \infty \mathsf{fWiki}$, this criterion emerges as a consequence of the definition.

## Also known as

Some sources refer to a **circuit** as a **closed trail**.

## Also see

- Results about
**circuit**in the context of**graph theory**can be found**here**.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 2.3$: Connected Graphs - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**circuit** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**walk** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**circuit** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**walk** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**closed**(in graph theory)