\begin{definition}[Definition:Path (Graph Theory)]
A '''path''' is a trail in which all vertices (except perhaps the first and last ones) are distinct.
A path between two vertices $u$ and $v$ is called a '''$u$-$v$ path'''.
The set of vertices and edges which go to make up a '''path''' form a subgraph.
This subgraph itself is also referred to as a '''path'''.
\end{definition}