# Restricted Network Reconstruction from Time Series via Dempster–Shafer Evidence Theory

## TL;DR

This paper introduces a new method for reconstructing complex networks from limited time series data using epidemic dynamics and Dempster–Shafer theory.

## Contribution

The novel framework combines epidemic simulations with Dempster–Shafer evidence theory for robust network reconstruction under sparse observations.

## Key findings

- The method achieves high reconstruction accuracy on both synthetic and real-world networks.
- It successfully scales to large-scale networks with an average accuracy of 0.85.
- The dual-fusion design effectively handles uncertainty and conflict in sparse data.

## Abstract

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.