# 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

• The following options can be given:
•  EdgeWeight Automatic weight for each edge Method Automatic method to use
• Possible Method settings include "Dijkstra", "FloydWarshall", and "Johnson".

# 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_2022_graphcenter, author="Wolfram Research", title="{GraphCenter}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphCenter.html}", note=[Accessed: 28-March-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_graphcenter, organization={Wolfram Research}, title={GraphCenter}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphCenter.html}, note=[Accessed: 28-March-2023 ]}