2-simplex reconstruction driven by ternary-dynamics data

For the reconstruction of higher-order structures in complex networks, most research has mainly relied on binary time series data. Nevertheless, there are two limitations. On one hand, the binary state data are inadequate to capture the complexity and diversity of real-world systems. On the other hand, these results typically require long time series for accurate reconstruction and high data costs. Therefore, in this paper, we investigate how to obtain ternary-dynamics data, and then how to reconstruct 2-simplexes in high-order networks. First, a novel model is proposed on higher-order networks characterized by simplicial complexes, and its corresponding ternary dynamic propagation equations were derived to generate ternary-dynamics data. Further, based on Bayesian inference and maximum likelihood estimation, a new algorithm for reconstructing 2-simplexes driven by ternary-dynamics data is put forward. Finally, taking the reconstruction algorithm with binary-dynamic data as a comparison algorithm, abundant experiments are conducted for 2-simplex reconstruction on four real networks and three artificial higher-order networks. Then, we come to some conclusions. The proposed reconstruction algorithm in this paper achieves high reconstruction accuracy with short time-series data and saves data costs. Additionally, our findings reveal that the 1-order average degree of the network has little impact on the reconstruction of 2-simplexes, whereas a smaller 2-order average degree leads to better reconstruction performance.