Higher-order networks provide a powerful framework for modeling complex interaction dynamics that go beyond simple pairwise relationships. However, on the other hand, in many real-world scenarios, the underlying network topology is not directly observable, but only time-series data of node dynamics are available. The structure of higher-order networks is inherently more intricate than that of traditional pairwise networks. These make the accurate reconstruction of higher-order networks a critical challenge. Existing methods are typically limited by insufficient accuracy, and they overlook the inherent symmetry priors in undirected higher-order networks. To address this issue, we incorporate symmetry priors into the reconstruction process by embedding symmetric constraints into the iterative equation and the solving procedure by employing the block coordinate descent method. The proposed approach ensures reconstruction accuracy while reducing computational complexity. Theoretical analysis and numerical experiments show that our method achieves accuracy comparable to the conventional global method with efficiency close to the point-by-point method, providing a practical and scalable methodology for higher-order network reconstruction.
Yan et al. (Sun,) studied this question.