GraphCenter

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: