gives the length of the longest shortest path from the source s to every other vertex in the graph g.


uses rules vw to specify the graph g.

Details and Options


open allclose all

Basic Examples  (1)

Find the vertex eccentricity of vertex 1 in a graph:

Scope  (7)

VertexEccentricity works with undirected graphs:

Directed graphs:

Weighted graphs:


Mixed graphs:

Use rules to specify the graph:

VertexEccentricity works with large graphs:

Applications  (5)

In an PetersenGraph, every vertex has the same eccentricity:

Some Petersen graphs have different eccentricities for the inner and outer subgraphs:

Compute and highlight the vertex eccentricity for special graphs, including GridGraph:

Package this up as a function:

Many special graphs have constant vertex eccentricity:

A few will have varying eccentricity, where some vertices are more centrally located:

Most random graphs have small eccentricities:

The Gilbert random graph:

The BarabasiAlbert random graph:

The de Solla Price random graph:

Low eccentricity indicates close relation to everybody at the family gathering. Compare Larry and Rudy:

Properties & Relations  (3)

In a connected graph, the vertex eccentricity is related to GraphDistance:


The vertex eccentricity in a connected graph is related to GraphDiameter:




Illustrate the eccentricity of two vertices in a Petersen graph:

For a CompleteGraph, every vertex has eccentricity 1:

The eccentricity path in a PathGraph switches halfway through:

The eccentricity path in a CycleGraph measures both the GraphDiameter and GraphRadius:

In a WheelGraph of size 5 or more, the eccentricity is 1 at the hub and 2 elsewhere:

In a GridGraph, the eccentricity path always ends in a corner of the grid:

In a CompleteKaryTree, the eccentricity path always ends in a leaf:

Wolfram Research (2010), VertexEccentricity, Wolfram Language function, (updated 2015).


Wolfram Research (2010), VertexEccentricity, Wolfram Language function, (updated 2015).


Wolfram Language. 2010. "VertexEccentricity." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015.


Wolfram Language. (2010). VertexEccentricity. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2022_vertexeccentricity, author="Wolfram Research", title="{VertexEccentricity}", year="2015", howpublished="\url{}", note=[Accessed: 06-July-2022 ]}


@online{reference.wolfram_2022_vertexeccentricity, organization={Wolfram Research}, title={VertexEccentricity}, year={2015}, url={}, note=[Accessed: 06-July-2022 ]}