Reconstruction of higher-order complex networks under non-Markovian dynamics
Ziqi Yang1, Yi Zhao1, Michael Small2
1School of Science, Harbin Institute of Technology, Shenzhen 518055, China.
Chaos (Woodbury, N.Y.)
|July 20, 2026
Summary
This study introduces a new framework to reconstruct complex network structures from time series data, even with memory effects. It accurately untangles temporal-dynamical and higher-order structural information.
Area of Science:
- Complex Systems Science
- Network Science
- Data Analysis
Background:
- Understanding complex systems requires uncovering topological structures.
- Spreading processes with memory-dependent characteristics complicate structural analysis.
- Reconstructing higher-order structures from time series data is challenging.
Purpose of the Study:
- To develop a framework for full-order reconstruction of simplicial complexes from non-Markovian binary time series.
- To simultaneously address structural and dynamical complexities in complex systems.
- To model nonlinear aging effects in higher-order contagion.
Main Methods:
- Proposed a likelihood inference framework for simplicial complex reconstruction.
- Introduced a target-specific exposure clock and Weibull memory kernel.
- Employed a relaxation strategy for non-convex optimization and sparse optimization via fast iterative shrinkage-thresholding algorithm.
Main Results:
- Achieved robust reconstruction of simplicial complexes from non-Markovian time series.
- Successfully modeled nonlinear aging effects and memory-dependent contagion.
- Demonstrated framework adaptability to different memory effects and aging regimes.
- Untangled complex temporal-topological coupling by separating true simplices from spurious candidates.
Conclusions:
- The proposed framework enables accurate reconstruction of complex network structures beyond conventional Markovian models.
- The method is applicable even when true structural orders are unknown.
- This approach advances the understanding of complex systems with non-Markovian dynamics.
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