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On the structure and values of betweenness centrality in dense betweenness-uniform graphs
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SYSNO ASEP 0573762 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title On the structure and values of betweenness centrality in dense betweenness-uniform graphs Author(s) Ghanbari, B. (CZ)
Hartman, David (UIVT-O) RID, SAI, ORCID
Jelínek, V. (CZ)
Pokorná, Aneta (UIVT-O)
Šámal, R. (CZ)
Valtr, P. (CZ)Source Title EUROCOMB’23. Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications. - Brno : MUNI Press, 2023 / Kráľ D. ; Nešetřil J. Pages s. 478-484 Number of pages 7 s. Publication form Online - E Action EUROCOMB 2023: European Conference on Combinatorics, Graph Theory and Applications /12./ Event date 28.08.2023 - 01.09.2023 VEvent location Prague Country CZ - Czech Republic Event type EUR Language eng - English Country CZ - Czech Republic Keywords betweenness ; graphs OECD category Pure mathematics R&D Projects GA23-07074S GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 DOI 10.5817/CZ.MUNI.EUROCOMB23-066 Annotation Betweenness centrality is a network centrality measure based on the amount of shortest paths passing through a given vertex. A graph is betweenness-uniform (BUG)if all vertices have an equal value of betweenness centrality. In this contribution, we focus on betweenness-uniform graphs with betweenness centrality below one. We disprove a conjecture about the existence of a BUG with betweenness value α for any rational numberαfrom the interval (3/4,∞) by showing that only very few betweenness centrality values below 6/7 are attained for at least one BUG. Furthermore, among graphs with diameter at least three, there are no betweenness-uniform graphs with a betweenness centrality smaller than one. In graphs of smaller diameter, the same can be shown under a uniformity condition on the components of the complement. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2024 Electronic address https://journals.muni.cz/eurocomb/article/view/35600/31477
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