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Discovering key users for defending network structural stability

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Abstract

The structural stability of a network reflects the ability of the network to maintain a sustainable service. As the leave of some users will significantly break network stability, it is critical to discover these key users for defending network stability. The model of k-core, a maximal subgraph where each vertex has at least k neighbors in the subgraph, is often used to measure the stability of a network. Besides, the coreness of a vertex, the largest k such that the k-core contains the vertex, is validated as the “best practice” for measuring the engagement of the vertex. In this paper, we propose and study the collapsed coreness problem: finding b vertices (users) s.t. the deletion of these vertices leads to the largest coreness loss (the total decrease of coreness from every vertex). We prove that the problem is NP-hard and hard to approximate. We show that the collapsed coreness is more effective and challenging than the existing models. An efficient greedy algorithm is proposed with powerful pruning rules. The algorithm is adapted to find the key users within a given time limit. Extensive experiments on 12 real-life graphs demonstrate the effectiveness of our model and the efficiency of the proposed method.

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All the source codes will be shared online after the manuscript is accepted.

Notes

  1. http://snap.stanford.edu

  2. http://networkrepository.com

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Acknowledgements

This work is supported by National Key Research and Development Plan (Grant No. 2018YFB1800701), National Natural Science Foundation of China (Grant No. 62002073), Guangzhou Basic and Applied Basic Research Foundation (Grant No. 202102020675), Guangdong Higher Education Innovation Group 2020KCXTD007, Guangdong Province Key Research and Development Plan (Grant No. 2019B010137004), and Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2019).

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The grants declared in Acknowledgements were received to assist with the preparation of this manuscript.

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Authors and Affiliations

  1. Guangzhou University, Guangzhou, China

    Fan Zhang, Shiyu Yang & Yu Jiang

  2. East China Normal University, Shanghai, China

    Jiadong Xie

  3. University of New South Wales, Sydney, Australia

    Kai Wang

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This article belongs to the Topical Collection: Special Issue on Large-Scale Graph Data Analytics

Guest Editors: Xuemin Lin, Lu Qin, Wenjie Zhang, and Ying Zhang

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Zhang, F., Xie, J., Wang, K. et al. Discovering key users for defending network structural stability. World Wide Web 25, 679–701 (2022). https://doi.org/10.1007/s11280-021-00905-3

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