GraphCenter

GraphCenter[g]

gives the set of vertices with minimum eccentricity in the graph g.

GraphCenter[{vw,}]

uses rules vw to specify the graph g.

Details

Examples

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Basic Examples  (1)

Give the graph center for a graph:

Highlight the center:

Scope  (7)

GraphCenter works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

Works with 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 most closely related to everybody at the gathering:

Properties & Relations  (7)

In a connected graph, the center can be found using VertexEccentricity:

For a CompleteGraph, every vertex is at the center:

For a PathGraph with positive weights, there is either one center vertex or two center vertices:

For a CycleGraph, all vertices are in the center:

For a WheelGraph of size 5 or more, the hub is the graph center:

For a GridGraph, the center forms a grid with all dimensions being one or two:

For a CompleteKaryTree, the root vertex is the center:

Introduced in 2010
 (8.0)
 |
Updated in 2015
 (10.3)