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Full reconstruction of simplicial complexes from binary contagion and Ising data

Author

Listed:
  • Huan Wang

    (Anhui University)

  • Chuang Ma

    (Anhui University)

  • Han-Shuang Chen

    (Anhui University)

  • Ying-Cheng Lai

    (Arizona State University)

  • Hai-Feng Zhang

    (Anhui University)

Abstract

Previous efforts on data-based reconstruction focused on complex networks with pairwise or two-body interactions. There is a growing interest in networks with higher-order or many-body interactions, raising the need to reconstruct such networks based on observational data. We develop a general framework combining statistical inference and expectation maximization to fully reconstruct 2-simplicial complexes with two- and three-body interactions based on binary time-series data from two types of discrete-state dynamics. We further articulate a two-step scheme to improve the reconstruction accuracy while significantly reducing the computational load. Through synthetic and real-world 2-simplicial complexes, we validate the framework by showing that all the connections can be faithfully identified and the full topology of the 2-simplicial complexes can be inferred. The effects of noisy data or stochastic disturbance are studied, demonstrating the robustness of the proposed framework.

Suggested Citation

  • Huan Wang & Chuang Ma & Han-Shuang Chen & Ying-Cheng Lai & Hai-Feng Zhang, 2022. "Full reconstruction of simplicial complexes from binary contagion and Ising data," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-30706-9
    DOI: 10.1038/s41467-022-30706-9
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    References listed on IDEAS

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    1. Zhesi Shen & Wen-Xu Wang & Ying Fan & Zengru Di & Ying-Cheng Lai, 2014. "Reconstructing propagation networks with natural diversity and identifying hidden sources," Nature Communications, Nature, vol. 5(1), pages 1-10, September.
    2. Iacopo Iacopini & Giovanni Petri & Alain Barrat & Vito Latora, 2019. "Simplicial models of social contagion," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
    3. Jose Casadiego & Mor Nitzan & Sarah Hallerberg & Marc Timme, 2017. "Model-free inference of direct network interactions from nonlinear collective dynamics," Nature Communications, Nature, vol. 8(1), pages 1-10, December.
    4. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    5. Long Ma & Xiao Han & Zhesi Shen & Wen-Xu Wang & Zengru Di, 2015. "Efficient Reconstruction of Heterogeneous Networks from Time Series via Compressed Sensing," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-12, November.
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    Cited by:

    1. Guo, Shiqiang & Wang, Juan & Zhao, Dawei & Xia, Chengyi, 2023. "Role of second-order reputation evaluation in the multi-player snowdrift game on scale-free simplicial complexes," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Zhao, Dandan & Li, Runchao & Peng, Hao & Zhong, Ming & Wang, Wei, 2022. "Percolation on simplicial complexes," Applied Mathematics and Computation, Elsevier, vol. 431(C).

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