Definition:Walk (Graph Theory)/Length

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This page is about length of a walk in the context of Graph Theory. For other uses, see Length.


The length of a walk (or a path, or a trail) is the number of edges it has, counting repeated edges as many times as they appear.

A walk is said to be of infinite length if and only if it has infinitely many edges.

Zero Length Walk

A zero length walk is a walk which consists of one vertex.


Arbitrary Example 1

In the graph below:


the path $1, 3, 4$ has length $2$.

The vertex $5$ forms a zero length walk.

Arbitrary Example 2

In the rooted tree below:


the path from $1$ to $9$ has length $4$.