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On the Connectivity and the Diameter of Betweenness-Uniform Graphs

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12601)

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.

Keywords

  • Betweenness centrality
  • Betweenness-uniform
  • Connectivity
  • Distance

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Acknowledgments

David Hartman and Aneta Pokorná were partially supported by ERC Synergy grant DYNASNET grant agreement no. 810115. Pavel Valtr was partially supported by the H2020-MSCA-RISE project CoSP- GA No. 823748.

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Correspondence to Aneta Pokorná .

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Hartman, D., Pokorná, A., Valtr, P. (2021). On the Connectivity and the Diameter of Betweenness-Uniform Graphs. In: Mudgal, A., Subramanian, C.R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2021. Lecture Notes in Computer Science(), vol 12601. Springer, Cham. https://doi.org/10.1007/978-3-030-67899-9_26

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  • DOI: https://doi.org/10.1007/978-3-030-67899-9_26

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