gives the set of vertices with minimum eccentricity in the graph g.


uses rules vw to specify the graph g.

Details and Options


open allclose all

Basic Examples  (1)

Give the graph center for a graph:

Highlight the center:

Scope  (7)

GraphCenter works with undirected graphs:

Directed graphs:

Weighted graphs:


Mixed graphs:

Use rules to specify the graph:

Works with large graphs:

Applications  (1)

People at a family gathering:

Use Subsets to create edges between all members of the family:

The resulting social graph:

Find the people who are most closely related to everybody at the gathering:

Properties & Relations  (7)

In a connected graph, the center can be found using VertexEccentricity:

For a CompleteGraph, every vertex is at the center:

For a PathGraph with positive weights, there is either one center vertex or two center vertices:

For a CycleGraph, all vertices are in the center:

For a WheelGraph of size 5 or more, the hub is the graph center:

For a GridGraph, the center forms a grid with all dimensions being one or two:

For a CompleteKaryTree, the root vertex is the center:

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


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


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


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


@misc{reference.wolfram_2022_graphcenter, author="Wolfram Research", title="{GraphCenter}", year="2015", howpublished="\url{}", note=[Accessed: 06-July-2022 ]}


@online{reference.wolfram_2022_graphcenter, organization={Wolfram Research}, title={GraphCenter}, year={2015}, url={}, note=[Accessed: 06-July-2022 ]}