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Discovering fortress-like cohesive subgraphs

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Abstract

Morris (Rev Econ Stud 67:57–78, 2000) defines the \(p\)-cohesion by a connected subgraph in which every vertex has at least a fraction p of its neighbors in the subgraph, i.e., at most a fraction (\(1-p\)) of its neighbors outside. We can find that a \(p\)-cohesion ensures not only inner-cohesiveness but also outer-sparseness. The textbook on networks by Easley and Kleinberg  (Networks, Crowds, and Markets - Reasoning About a Highly Connected World, Cambridge University Press, 2010) shows that \(p\)-cohesions are fortress-like cohesive subgraphs which can hamper the entry of the cascade, following the contagion model. Despite the elegant definition and promising properties, to our best knowledge, there is no existing study on \(p\)-cohesion regarding problem complexity and efficient computing algorithms. In this paper, we fill this gap by conducting a comprehensive theoretical analysis on the complexity of the problem and developing efficient computing algorithms. We focus on the minimal \(p\)-cohesion because they are elementary units of \(p\)-cohesions and the combination of multiple minimal \(p\)-cohesions is a larger \(p\)-cohesion. We demonstrate that the discovered minimal \(p\)-cohesions can be utilized to solve the MinSeed problem: finding a smallest set of initial adopters (seeds) such that all the network users are eventually influenced. Extensive experiments on 8 real-life social networks verify the effectiveness of this model and the efficiency of our algorithms.

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Acknowledgements

Fan Zhang is supported by National Natural Science Foundation of China under Grant 62002073 and Guangzhou Basic and Applied Basic Research Foundation under Grant 202102020675. Ying Zhang is supported by ARC DP180103096 and FT170100128. Lu Qin is supported by ARC DP160101513. Wenjie Zhang is supported by ARC DP180103096. Xuemin Lin is supported by NSFC61232006, ARC DP180103096, DP170101628 and the National Key R&D Program of China under grant 2018YFB1003504.

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Authors and Affiliations

  1. University of Technology Sydney, Sydney, Australia

    Conggai Li

  2. Guangzhou University, Guangzhou, China

    Fan Zhang

  3. AAII, University of Technology Sydney, Sydney, Australia

    Ying Zhang & Lu Qin

  4. University of New South Wales, Sydney, Australia

    Wenjie Zhang & Xuemin Lin

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  1. Conggai Li
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  2. Fan Zhang
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Correspondence to Fan Zhang.

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Li, C., Zhang, F., Zhang, Y. et al. Discovering fortress-like cohesive subgraphs. Knowl Inf Syst 63, 3217–3250 (2021). https://doi.org/10.1007/s10115-021-01624-x

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