A walk on a graph is:
- an alternating series of vertices and edges
- beginning and ending with a vertex
- in which each edge is incident with the vertex immediately preceding it and the vertex immediately following it.
A walk between two vertices $u$ and $v$ is called a $u$-$v$ walk.
A closed walk is a walk whose first vertex is the same as the last.
That is, it is a walk which ends where it starts.
That is, it is a walk which ends on a different vertex from the one where it starts.
Also known as
Some sources refer to a walk as a path, and use the term simple path to define what we have here as a path.