\begin{definition}[Definition:Cycle (Graph Theory)]
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'''.
\end{definition}