GraphCenter

GraphCenter[g]

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

GraphCenter[{vw,…}]

uses rules vw to specify the graph g.

Details and Options

Examples

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:

Multigraphs:

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, https://reference.wolfram.com/language/ref/GraphCenter.html (updated 2015).

Text

Wolfram Research (2010), GraphCenter, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphCenter.html (updated 2015).

CMS

Wolfram Language. 2010. "GraphCenter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/GraphCenter.html.

APA

Wolfram Language. (2010). GraphCenter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphCenter.html

BibTeX

@misc{reference.wolfram_2025_graphcenter, author="Wolfram Research", title="{GraphCenter}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphCenter.html}", note=[Accessed: 25-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_graphcenter, organization={Wolfram Research}, title={GraphCenter}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphCenter.html}, note=[Accessed: 25-July-2025 ]}