Graph Eccentricity

The eccentricity  of a graph vertex  in a connected graph  is the maximum graph distance between  and any other vertex  of . For a disconnected graph, all vertices are defined to have infinite eccentricity (West 2000, p. 71).

The maximum eccentricity is the graph diameter. The minimum graph eccentricity is called the graph radius.

Eccentricities are implemented as Eccentricity[g] in the Wolfram Language package Combinatorica` . A nonstandard version of graph eccentricity for a given vertex  is implemented as VertexEccentricity[g, v], which gives the eccentricity for the connected component in which  is contained. Precomputed standard eccentricities (assuming infinite values for disconnected graphs) for a number of named graphs can be obtained using GraphData[graph, "Eccentricities"].

REFERENCES

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 35, 1994.

Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 107, 1990.

West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2000.