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Graph Eccentricity


GraphEccentricities

The eccentricity epsilon(v) of a graph vertex v in a connected graph G is the maximum graph distance between v and any other vertex u of G. 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 v is implemented as VertexEccentricity[g, v], which gives the eccentricity for the connected component in which v is contained. Precomputed standard eccentricities (assuming infinite values for disconnected graphs) for a number of named graphs can be obtained using GraphData[graph, "Eccentricities"].


See also

Central Point, Graph Center, Graph Diameter, Graph Periphery, Graph Radius, Peripheral Point

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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.

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Graph Eccentricity

Cite this as:

Weisstein, Eric W. "Graph Eccentricity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GraphEccentricity.html

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