Full reconstruction of simplicial complexes from binary contagion and Ising data

Huan Wang, Chuang Ma, Han Shuang Chen, Ying Cheng Lai, Hai Feng Zhang

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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.

Original languageEnglish (US)
Article number3043
JournalNature communications
Issue number1
StatePublished - Dec 2022

ASJC Scopus subject areas

  • General Physics and Astronomy
  • General Chemistry
  • General Biochemistry, Genetics and Molecular Biology


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