This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

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:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
Highlight the graph periphery:
In[3]:=
Click for copyable input
Out[3]=
GraphPeriphery works with undirected graphs:
Directed graphs:
Weighted graphs:
Large graphs:
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