2026-07-23T19:42:34Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:9505 2024-03-06T10:43:55Z ddc:004 open_access

Scalable Katz Ranking Computation in Large Static and Dynamic Graphs van der Grinten, Alexander Bergamini, Elisabetta Green, Oded Bader, David A. Meyerhenke, Henning network analysis Katz centrality top-k ranking dynamic graphs parallel algorithms 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Alexander van der Grinten and Elisabetta Bergamini and Oded Green and David A. Bader and Henning Meyerhenke 2018 Is Part Of LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2018.42 urn:nbn:de:0030-drops-95055 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.42 eng https://creativecommons.org/licenses/by/3.0/legalcode