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based on an earlier version of the Wolfram Language.
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GraphCenter

GraphCenter[g]
gives the set of vertices with minimum eccentricity in the graph g.
Give the graph center for a graph:
Highlight the center:
Give the graph center for a graph:
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Highlight the center:
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GraphCenter works with undirected graphs:
Directed graphs:
Weighted graphs:
Works with 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 most closely related to everybody at the gathering:
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:
New in 8