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On the Connectivity and the Diameter of Betweenness-Uniform Graphs

Publication at Faculty of Mathematics and Physics |
2021

Abstract

Betweenness centrality is a centrality measure based on the overall amount of shortest paths passing through a given vertex. A graph is betweenness-uniform if all its vertices have the same betweenness centrality.

We study the properties of betweenness-uniform graphs. In particular, we show that every connected betweenness-uniform graph is either a cycle or a 3-connected graph.

Also, we show that betweenness uniform graphs of high maximal degree have small diameter.