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gives vertices that are maximally distant to at least one vertex in the graph g.
Examplesopen allclose all Basic Examples (1)Give the graph periphery for a graph:
Highlight the graph periphery:
Scope (7)GraphPeriphery works with undirected 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). TextWolfram Research (2010), GraphPeriphery, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphPeriphery.html (updated 2015).
CMSWolfram Language. 2010. "GraphPeriphery." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/GraphPeriphery.html.
APAWolfram Language. (2010). GraphPeriphery. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphPeriphery.html
BibTeX@misc{reference.wolfram_2025_graphperiphery, author="Wolfram Research", title="{GraphPeriphery}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphPeriphery.html}", note=[Accessed: 12-July-2025 ]}
BibLaTeX@online{reference.wolfram_2025_graphperiphery, organization={Wolfram Research}, title={GraphPeriphery}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphPeriphery.html}, note=[Accessed: 12-July-2025 ]}
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