Distance in a graph

Definition

Let $G$ be a graph and let $u, v$ be vertices of $G$ . If $v$ is reachable from $u$ , the distance $d(u, v)$ is the smallest length of a walk from $u$ to $v$ . If $v$ is not reachable from $u$ , then $d(u, v) = \infty$ .

Remarks

A shortest walk is a path, so $d(u, v)$ is also the smallest length of a path. Such a path is a geodesic. On a connected graph, $d$ is a metric: $d(u, v) = 0$ only for $u = v$ , it is symmetric, and it satisfies the triangle inequality.

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Graph definition
Walk definition
Reachability definition
Distance in a graph definition

Tag	`0WPZ5YPAGR`
URI	`m2://0WPZ5YPAGR`
Kind	definition
Writing	W1 stated
MSC	05C12
Defines	Distance in a graph
Uses	Walk, Reachability

Distance in a graph

Definition

Remarks

Reading path

Further reading

What this page needs for W2

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