Restricted Network Reconstruction from Time Series via Dempster-Shafer Evidence Theory

As a fundamental mathematical model for complex systems, complex networks describe interactions among social, infrastructural, and biological systems. However, the complete connection structure is often unobservable, making topology reconstruction from limited data-such as time series of unit states-a crucial challenge. To address network reconstruction under sparse local observations, this paper proposes a novel framework that integrates epidemic dynamics with Dempster-Shafer (DS) evidence theory. The core of our method lies in a two-level belief fusion process: (1) Intra-node fusion, which aggregates multiple independent SIR simulation results from a single seed node to generate robust local evidence represented as Basic Probability Assignments (BPAs), effectively quantifying uncertainty; (2) Inter-node fusion, which orthogonally combines BPAs from multiple seed nodes using DS theory to synthesize a globally consistent network topology. This dual-fusion design enables the framework to handle uncertainty and conflict inherent in sparse, stochastic observations. Extensive experiments demonstrate the effectiveness and robustness of the proposed approach. It achieves stable and high reconstruction accuracy on both a synthetic 16-node benchmark network and the real-world Zachary's Karate Club network. Furthermore, the method scales successfully to four large-scale real-world networks, attaining an average accuracy of 0.85, thereby confirming its practical applicability across networks of different scales and densities.