# Definition:Cycle (Graph Theory)

## Definition

A cycle is a circuit in which no vertex except the first (which is also the last) appears more than once.

Alternatively, a cycle can be defined as a closed path.

An $n$-cycle is a cycle with $n$ vertices.

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

This subgraph itself is also referred to as a cycle.

### Odd Cycle

An odd cycle is a cycle with odd length, that is, with an odd number of edges.

### Even Cycle

An even cycle is a cycle with even length, that is, with an even number of edges.