Abstract
Although existing research has confirmed the importance of higher-order structures in identifying key nodes within networks, the challenge remains on how to effectively integrate different types of higher-order information to precisely locate nodes that may be inconspicuous in lower-order structures but play a crucial role in higher-order interactions. To address this challenge, this paper proposes a general Higher-order Graph Neural Network representation learning framework (HoGNN) that can flexibly adapt to various types of higher-order relationships. Based on a robust theoretical framework, we develop a network dismantling model, SPR(Structural and Processual Role-aware Network Dismantling), which integrates multi-dimensional higher-order relations from both macro and micro perspectives. Empirical analysis demonstrated that the proposed model exhibits superior dismantling efficiency on both real-world and synthetic networks, using the minimal number of target node removals to collapse the network. Moreover, we show that SPR is more resilient to interference and accurately identifies key nodes in networks with multi-dimensional complex structures.
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Data availability
All datasets supporting the findings of this study are available at the following GitHub repository: https://github.com/zhouwn/spr.
Code availability
The custom code that supports the findings of this study is available at the following GitHub repository: https://github.com/zhouwn/spr.
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Acknowledgements
The authors are grateful for the support from the National Key R&D Program of China (2022YFB3102600), National Natural Science Foundation of China (U25B2047, 62272469, 72474223, 62306322, 72025405, 72421002, 92467302, 72301285), Science and Technology Innovation Program of Hunan Province (2023RC1007, 2024RC3133, 2023JJ40685), the Innovation Research Foundation of National University of Defense Technology (JS24-04), the National Science and Technology Major Project for Brain Science and Brain-like Intelligence Technology (2025ZD0215700), the Major Program of Xiangjiang Laboratory (24XJJCYJ01001) and the Postgraduate Innovation Program of National University of Defense Technology (XJQY2024064). The authors thank Stefano Boccaletti for useful discussions.
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Idea and Supervise: Wennan Zhou, Suoyi Tan, Yang Fang, and Xiang Zhao. Data Analysis: Wennan Zhou, Suoyi Tan, Yang Fang, and Xiang Zhao. Writing Original Draft: Wennan Zhou, Suoyi Tan, and Yang Fang. Writing Discussions & Editing: Wennan Zhou, Suoyi Tan, Yang Fang, Xin Lü, Xiang Zhao.
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Zhou, W., Tan, S., Fang, Y. et al. Dismantling complex networks based on higher-order graph neural network. Commun Phys (2026). https://doi.org/10.1038/s42005-026-02601-y
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DOI: https://doi.org/10.1038/s42005-026-02601-y
