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.

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.

Also known as
Some sources refer to a cycle as a closed path.

Some sources specify a cycle as having at least one edge.