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 S ampling-based A lgorithm for fast K atz centrality E stimation. 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.

中文翻译：

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清酒

Katz 中心性是衡量一个顶点在社交网络中的影响的基本概念。然而，在大规模网络中计算 Katz 中心性的现有方法是不切实际的并且计算成本很高。在本文中，我们提出了一种基于图采样技术来估计 Katz 中心性的新方法，该方法旨在以更低的计算复杂度实现与现有技术相当的估计精度。具体来说，我们通过使用多轮抽样方法并推导无偏均值估计量，开发了对 Katz 中心性的 Horvitz-Thompson 估计。我们进一步提出清酒， 一种 小号 基于放大 一种 快速算法 ķ 中心性 乙 估计。我们证明估计量由下式计算清酒被概率保证在与精确值的附加误差之内。基于四个现实世界网络的广泛评估实验表明，该算法可以在低采样率、低计算时间的情况下估计部分顶点的 Katz 中心性，并且在识别社交网络中的高影响力顶点方面效果很好。