Sampling Based Katz Centrality Estimation 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 is unpractical and computationally expensive. In this paper, we propose a novel method to estimate Katz centrality based on graph sampling techniques. Specifically, we develop an unbiased estimator for Katz centrality using a multi-round sampling approach. 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. The computational complexity of SAKE is much lower than the state-of-the-arts. Extensive evaluation experiments based on four real world networks show that the proposed algorithm achieves low mean relative error with low sampling rate, and it works well in identifying high influence vertices in social networks.