Scalable Katz Ranking Computation in Large Static and Dynamic Graphs

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× and 3.5×, 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.

Recent Advances in Fully Dynamic Graph Algorithms

“…A drawback of the algorithms by Nathan and Bader is that they are unable to reproduce the exact Katz ranking after dynamic updates. Van der Grinten et al [236] fixed this problem by presenting a dynamic algorithm that iteratively improves upper and lower bounds on the centrality scores. The computed scores are approximate, but the bounds guarantee the correct ranking.…”