gives vertices that are maximally distant to at least one vertex in the graph g.
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 EdgeWeight->Automatic, 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".
Examplesopen allclose all
GraphPeriphery works with undirected graphs:
Use rules to specify the graph:
GraphPeriphery works with large graphs:
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).
Wolfram Language. 2010. "GraphPeriphery." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/GraphPeriphery.html.
Wolfram Language. (2010). GraphPeriphery. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphPeriphery.html