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Deep-learning-aided dismantling of interdependent networks

Nature Machine Intelligence volume 7, pages 1266–1277 (2025)Cite this article

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Abstract

Identifying the minimal set of nodes whose removal breaks a complex network apart, also referred as the network dismantling problem, is a highly non-trivial task with applications in multiple domains. Whereas network dismantling has been extensively studied over the past decade, research has primarily focused on the optimization problem for single-layer networks, neglecting that many, if not all, real networks display multiple layers of interdependent interactions. In such networks, the optimization problem is fundamentally different as the effect of removing nodes propagates within and across layers in a way that can not be predicted using a single-layer perspective. Here we propose a dismantling algorithm named MultiDismantler, which leverages multiplex network representation and deep reinforcement learning to optimally dismantle multilayer interdependent networks. MultiDismantler is trained on small synthetic graphs; when applied to large, either real or synthetic, networks, it displays exceptional dismantling performance, clearly outperforming all existing benchmark algorithms. We show that MultiDismantler is effective in guiding strategies for the containment of diseases in social networks characterized by multiple layers of social interactions. Also, we show that MultiDismantler is useful in the design of protocols aimed at delaying the onset of cascading failures in interdependent critical infrastructures.

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Fig. 1: The training process of MultiDismantler.
Fig. 2: Dismantling performance of synthetic and real-world interdependent networks under the metrics AUDC and C*.
Fig. 3: The dismantling process of two real-world multiplex networks by different dismantling algorithms.
Fig. 4: Preventing disease spreading and maintaining network robustness with MultiDismantler.

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Data availability

All data used in this Article are publicly available. To facilitate the reproducibility of our results, all necessary data are available at https://doi.org/10.24433/CO.0638082.v1 (ref. 51).

Code availability

The code developed for this research is available at https://doi.org/10.24433/CO.0638082.v1 (ref. 51).

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Acknowledgements

This work was supported by grants from National Natural Science Foundation of China (grant numbers 42450183 and 72371014) and support from the Beijing University of Chemical Technology, grant number 11170044127, PY2514; partial support was also received from the Air Force Office of Scientific Research (grant numbers FA9550-21-1-0446 and FA9550-24-1-0039). The funders had no role in the study design, data collection, and analysis, the decision to publish or any opinions, findings, conclusions or recommendations expressed in the Article.

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Authors and Affiliations

  1. College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, People’s Republic of China

    Weiwei Gu, Chen Yang & Jinqiang Hou

  2. School of Software Enginering, University of Science and Technology of China, Hefei, People’s Republic of China

    Lei Li

  3. Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA

    Filippo Radicchi

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  1. Weiwei Gu
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  5. Filippo Radicchi
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Contributions

W.W. and F.R. wrote the paper. W.W., C.Y. and F.R. designed the model and experiments. W.W., C.Y. and L.L. performed the experiments. C.Y., L.L. and J.H. plotted the figures.

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Correspondence to Chen Yang or Filippo Radicchi.

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Nature Machine Intelligence thanks Roger Guimerà and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–5, Tables 1–12 and References.

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Gu, W., Yang, C., Li, L. et al. Deep-learning-aided dismantling of interdependent networks. Nat Mach Intell 7, 1266–1277 (2025). https://doi.org/10.1038/s42256-025-01070-2

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