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Scalable Katz Ranking Computation in Large Static and Dynamic Graphs

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

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Author Details

Alexander van der Grinten
  • Department of Computer Science, Humboldt-Universität zu Berlin, Germany
Elisabetta Bergamini
  • Karlsruhe Institute of Technology (KIT), Germany
Oded Green
  • School of Computational Science and Engineering, Georgia Institute of Technology, USA
David A. Bader
  • School of Computational Science and Engineering, Georgia Institute of Technology, USA
Henning Meyerhenke
  • Department of Computer Science, Humboldt-Universität zu Berlin, Germany

Funding

Most of the work was done while AvdG was affiliated with University of Cologne, Germany, and HM with Karlsruhe Institute of Technology and University of Cologne. Additionally, EB, AvdG and HM were partially supported by grant ME 3619/3-2 within German Research Foundation (DFG) Priority Programme 1736. Funding was also provided by Karlsruhe House of Young Scientists via the International Collaboration Package. Funding for OG and DB was provided in part by the Defense Advanced Research Projects Agency (DARPA) under Contract Number FA8750-17-C-0086. The content of the information in this document does not necessarily reflect the position or the policy of the Government, and no official endorsement should be inferred. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.ESA.2018.42

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
  • Theory of computation → Parallel algorithms
Keywords
  • network analysis
  • Katz centrality
  • top-k ranking
  • dynamic graphs
  • parallel algorithms

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References

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