Network reconstruction based on node centrality sorting and alternating direction method of multipliers

Reconstructing complex network structures from observational time series is a prominent and challenging issue in network science. Recent advancements have seen extensive application of statistical inference and compressed sensing methods for network reconstruction. However, there remains significant room for improvement in terms of the accuracy, speed, and noise robustness of existing representative reconstruction methods. Building on classical compressed sensing algorithms, this paper introduces a network reconstruction algorithm that leverages node centrality ranking and the alternating direction method of multipliers (ADMM). The algorithm first reorders the node state feature matrix based on node centrality assessments, then applies compressed sensing to the reordered matrix, and finally employs ADMM to optimize the matrix for network topology reconstruction. Theoretical analysis demonstrates that the proposed algorithm has lower complexity compared to representative compressed sensing reconstruction methods. Experimental results show that the proposed algorithm enhances reconstruction accuracy, reduces reconstruction time, and offers greater noise robustness compared to existing methods. This research advances the accuracy, applicability, and reliability of network reconstruction algorithms for large-scale networks and has the potential for extension to weighted network reconstruction with various constraints in the future.