On the Connectivity and the Diameter of Betweenness-Uniform Graphs
Combinatorics
2023-09-11 v2 Discrete Mathematics
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 -connected graph. Also, we show that betweenness uniform graphs of high maximal degree have small diameter.
Keywords
Cite
@article{arxiv.2109.10594,
title = {On the Connectivity and the Diameter of Betweenness-Uniform Graphs},
author = {David Hartman and Aneta Pokorná and Pavel Valtr},
journal= {arXiv preprint arXiv:2109.10594},
year = {2023}
}
Comments
minor changes; to bepublished in Discrete Applied Mathematics