SAKE: Estimating Katz Centrality Based on Sampling for Large-Scale Social Networks

Katz centrality is a fundamental concept to measure the influence of a vertex in a social network. However, existing approaches to calculating Katz centrality in a large-scale network are unpractical and computationally expensive. In this article, we propose a novel method to estimate Katz centrality based on graph sampling techniques, which object to achieve comparable estimation accuracy of the state-of-the-arts with much lower computational complexity. Specifically, we develop a Horvitz–Thompson estimate for Katz centrality by using a multi-round sampling approach and deriving an unbiased mean value estimator. We further propose SAKE, a Sampling-based Algorithm for fast Katz centrality Estimation. We prove that the estimator calculated by SAKE is probabilistically guaranteed to be within an additive error from the exact value. Extensive evaluation experiments based on four real-world networks show that the proposed algorithm can estimate Katz centralities for partial vertices with low sampling rate, low computation time, and it works well in identifying high influence vertices in social networks.