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On the Connectivity and the Diameter of Betweenness-Uniform Graphs (2109.10594v2)
Published 22 Sep 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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