# GraphPeriphery

gives vertices that are maximally distant to at least one vertex in the graph g.

GraphPeriphery[{vw,}]

uses rules vw to specify the graph g.

# Details and Options

• GraphPeriphery is also known as peripheral vertices.
• The following options can be given:
•  EdgeWeight Automatic weight for each edge Method Automatic method to use
• With the default setting , the edge weight of an edge is taken to be the EdgeWeight of the graph g if available; otherwise, it is 1.
• Possible Method settings include "Dijkstra", "FloydWarshall", "Johnson", and "PseudoDiameter".

# Examples

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## Basic Examples(1)

Give the graph periphery for a graph:

Highlight the graph periphery:

## Scope(7)

GraphPeriphery works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

GraphPeriphery works with large graphs:

## Applications(1)

Find the people who are least related to everybody at a family gathering network:

## Properties & Relations(8)

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

Undirected connected graphs have at least two vertices on the periphery:

For a CompleteGraph, the periphery includes all vertices:

For a PathGraph with positive weights, the periphery consists of the endpoints:

With non-negative weights, the periphery forms two paths ending at the respective endpoints:

For a CycleGraph, all vertices are at the periphery:

For a WheelGraph of size 5 or more, all vertices but the hub are at the periphery:

For a GridGraph, the periphery consists of the vertices at the corners:

For a CompleteKaryTree, the periphery consists of the leaves:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_graphperiphery, author="Wolfram Research", title="{GraphPeriphery}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphPeriphery.html}", note=[Accessed: 10-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_graphperiphery, organization={Wolfram Research}, title={GraphPeriphery}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphPeriphery.html}, note=[Accessed: 10-September-2024 ]}