This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# GraphPeriphery

 GraphPeriphery[g] gives the set of vertices with maximum eccentricity in the graph g.
Give the graph periphery for a graph:
Highlight the graph periphery:
Give the graph periphery for a graph:
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Highlight the graph periphery:
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 Scope   (4)
GraphPeriphery works with undirected graphs:
Directed graphs:
Weighted graphs:
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 least related to everybody at the gathering:
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:
New in 8