Estimating Properties of Social Networks via Random Walk considering Private Nodes

Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a random walk have been studied. However, existing algorithms do not consider private nodes who hide their neighbors in real social networks, leading to some practical problems. Here we design random walk-based algorithms to accurately estimate properties without any problems caused by private nodes. First, we design a random walk-based sampling algorithm that comprises the neighbor selection to obtain samples having the Markov property and the calculation of weights for each sample to correct the sampling bias. Further, for two graph property estimators, we propose the weighting methods to reduce not only the sampling bias but also estimation errors due to private nodes. The proposed algorithms improve the estimation accuracy of the existing algorithms by up to 92.6% on real-world datasets.Comment: 26th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD 2020

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