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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.
- he:מרחק (תורת הגרפים)
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