Definition:Walk (Graph Theory)

Definition
Let $G = \struct {V, E}$ be a graph.

A walk $W$ on $G$ is:
 * an alternating sequence of vertices $v_1, v_2, \ldots$ and edges $e_1, e_2, \ldots$ of $G$
 * beginning and ending with a vertex
 * in which edge $e_j$ of $W$ is incident with the vertex $v_j$ and the vertex $v_{j + 1}$.

A walk between two vertices $u$ and $v$ is called a $u$-$v$ walk.

To describe a walk on a simple graph it is sufficient to list just the vertices in order, as the edges (being unique between vertices) are unambiguous.

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.

Also see

 * Definition:Trail: a walk in which all edges are distinct.


 * Definition:Path (Graph Theory): a walk in which all vertices are distinct.


 * Definition:Circuit (Graph Theory): a closed trail.


 * Definition:Cycle (Graph Theory): a closed path.