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.