Emergent Mind
On the Connectivity and the Diameter of Betweenness-Uniform Graphs
(2109.10594)
Published Sep 22, 2021
in
math.CO
and
cs.DM
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.
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