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Inference of hyperedges and overlapping communities in hypergraphs

Author

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  • Martina Contisciani

    (Max Planck Institute for Intelligent Systems, Cyber Valley)

  • Federico Battiston

    (Central European University)

  • Caterina De Bacco

    (Max Planck Institute for Intelligent Systems, Cyber Valley)

Abstract

Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to characterize the structural organization of hypergraphs. The method allows to infer missing hyperedges of any size in a principled way, and to jointly detect overlapping communities in presence of higher-order interactions. Furthermore, our model has an efficient numerical implementation, and it runs faster than dyadic algorithms on pairwise records projected from higher-order data. We apply our method to a variety of real-world systems, showing strong performance in hyperedge prediction tasks, detecting communities well aligned with the information carried by interactions, and robustness against addition of noisy hyperedges. Our approach illustrates the fundamental advantages of a hypergraph probabilistic model when modeling relational systems with higher-order interactions.

Suggested Citation

  • Martina Contisciani & Federico Battiston & Caterina De Bacco, 2022. "Inference of hyperedges and overlapping communities in hypergraphs," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
  • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-34714-7
    DOI: 10.1038/s41467-022-34714-7
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    References listed on IDEAS

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    Cited by:

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    2. Li, Tianyu & Wu, Yong & Ding, Qianming & Xie, Ying & Yu, Dong & Yang, Lijian & Jia, Ya, 2024. "Social contagion in high-order network with mutation," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Contreras-Aso, Gonzalo & Criado, Regino & Vera de Salas, Guillermo & Yang, Jinling, 2023. "Detecting communities in higher-order networks by using their derivative graphs," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    4. Luca Gallo & Lucas Lacasa & Vito Latora & Federico Battiston, 2024. "Higher-order correlations reveal complex memory in temporal hypergraphs," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    5. Liu, Run-Ran & Chu, Changchang & Meng, Fanyuan, 2023. "Higher-order interdependent percolation on hypergraphs," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    6. Anna Badalyan & Nicolò Ruggeri & Caterina De Bacco, 2024. "Structure and inference in hypergraphs with node attributes," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    7. Yuanzhao Zhang & Maxime Lucas & Federico Battiston, 2023. "Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes," Nature Communications, Nature, vol. 14(1), pages 1-8, December.

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