Scalable Katz Ranking Computation in Large Static and Dynamic Graphs

Document Type

Article

Publication Date

7-7-2022

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 article, 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. Previous approaches relied on numerical approximation or heuristics to compute Katz centrality rankings; however, 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 and , depending on the desired quality guarantees. Our dynamic graph algorithm improves upon the static algorithm for update batches of less than 10,000 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 edges in fractions of seconds.

Identifier

85149993229 (Scopus)

Publication Title

ACM Journal of Experimental Algorithmics

External Full Text Location

https://doi.org/10.1145/3524615

ISSN

10846654

Issue

1

Volume

27

Grant

FA8750-17-C-0086

Fund Ref

Defense Advanced Research Projects Agency

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