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DOI: 10.4230/LIPIcs.ISAAC.2018.36
An Adaptive Version of Brandes' Algorithm for Betweenness Centrality

Authors: Matthias Bentert, Alexander Dittmann, Leon Kellerhals, André Nichterlein, and Rolf Niedermeier

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Betweenness centrality - measuring how many shortest paths pass through a vertex - is one of the most important network analysis concepts for assessing the relative importance of a vertex. The well-known algorithm of Brandes [2001] computes, on an n-vertex and m-edge graph, the betweenness centrality of all vertices in O(nm) worst-case time. In follow-up work, significant empirical speedups were achieved by preprocessing degree-one vertices and by graph partitioning based on cut vertices. We further contribute an algorithmic treatment of degree-two vertices, which turns out to be much richer in mathematical structure than the case of degree-one vertices. Based on these three algorithmic ingredients, we provide a strengthened worst-case running time analysis for betweenness centrality algorithms. More specifically, we prove an adaptive running time bound O(kn), where k < m is the size of a minimum feedback edge set of the input graph.
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Matthias Bentert, Alexander Dittmann, Leon Kellerhals, André Nichterlein, and Rolf Niedermeier. An Adaptive Version of Brandes' Algorithm for Betweenness Centrality. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bentert_et_al:LIPIcs.ISAAC.2018.36,
  author =	{Bentert, Matthias and Dittmann, Alexander and Kellerhals, Leon and Nichterlein, Andr\'{e} and Niedermeier, Rolf},
  title =	{{An Adaptive Version of Brandes' Algorithm for Betweenness Centrality}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{36:1--36:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.36},
  URN =		{urn:nbn:de:0030-drops-99846},
  doi =		{10.4230/LIPIcs.ISAAC.2018.36},
  annote =	{Keywords: network science, social network analysis, centrality measures, shortest paths, tree-like graphs, efficient pre- and postprocessing, FPT in P}
}
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