# Distance (graph theory)

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In the mathematical field of graph theory, the **distance** between two vertices in a graph is the number of edges in a shortest path connecting them. This is also known as the **geodesic distance**.

There are a number of other measurements defined in terms of distance:

The **eccentricity** of a vertex is the greatest distance between and any other vertex.

The **radius** of a graph is the minimum eccentricity of any vertex.

The **diameter** of a graph is the maximum eccentricity of any vertex in the graph. That is, it is the greatest distance between any two vertices. A **peripheral vertex** in a graph of diameter is one that is distance from some other vertex—that is, a vertex that achieves the diameter.

A **pseudo-peripheral vertex** has the property that for any vertex , if is as far away from as possible, then is as far away from as possible. Formally, if the distance from to equals the eccentricity of , then it equals the eccentricity of .

## Algorithm for finding pseudo-peripheral verticesEdit

Often peripheral sparse matrix algorithms need a starting vertex with a high eccentricity. A peripheral vertex would be perfect, but is often hard to calculate. In most circumstances a pseudo-peripheral vertex can be used. A pseudo-peripheral vertex can easily be found with the following algorithm:

- Choose a vertex .
- Among all the vertices that are as far from as possible, let be one with minimal degree.
- If then set
*u*=*v*and repeat with step 2, else*v*is a pseudo-peripheral vertex.

## See alsoEdit

- he:מרחק (תורת הגרפים)

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