GraphPeriphery

GraphPeriphery[g]

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

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: 21-December-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: 21-December-2024 ]}