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DOI: 10.4230/LIPIcs.ESA.2018.42

Scalable Katz Ranking Computation in Large Static and Dynamic Graphs

Authors: Alexander van der Grinten, Elisabetta Bergamini, Oded Green, David A. Bader, and Henning Meyerhenke

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract

Network analysis defines a number of centrality measures to identify the most central nodes in a network. Fast computation of those measures is a major challenge in algorithmic network analysis. Aside from closeness and betweenness, Katz centrality is one of the established centrality measures. In this paper, we consider the problem of computing rankings for Katz centrality. In particular, we propose upper and lower bounds on the Katz score of a given node. While previous approaches relied on numerical approximation or heuristics to compute Katz centrality rankings, we construct an algorithm that iteratively improves those upper and lower bounds until a correct Katz ranking is obtained. We extend our algorithm to dynamic graphs while maintaining its correctness guarantees. Experiments demonstrate that our static graph algorithm outperforms both numerical approaches and heuristics with speedups between 1.5 x and 3.5 x, depending on the desired quality guarantees. Our dynamic graph algorithm improves upon the static algorithm for update batches of less than 10000 edges. We provide efficient parallel CPU and GPU implementations of our algorithms that enable near real-time Katz centrality computation for graphs with hundreds of millions of nodes in fractions of seconds.

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Alexander van der Grinten, Elisabetta Bergamini, Oded Green, David A. Bader, and Henning Meyerhenke. Scalable Katz Ranking Computation in Large Static and Dynamic Graphs. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 42:1-42:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{vandergrinten_et_al:LIPIcs.ESA.2018.42,
  author =	{van der Grinten, Alexander and Bergamini, Elisabetta and Green, Oded and Bader, David A. and Meyerhenke, Henning},
  title =	{{Scalable Katz Ranking Computation in Large Static and Dynamic Graphs}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{42:1--42:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.42},
  URN =		{urn:nbn:de:0030-drops-95055},
  doi =		{10.4230/LIPIcs.ESA.2018.42},
  annote =	{Keywords: network analysis, Katz centrality, top-k ranking, dynamic graphs, parallel algorithms}
}

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Scalable Katz Ranking Computation in Large Static and Dynamic Graphs

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