Theoretical framework can predict how complex networks behave

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Figure S4. (A-C) Average energy y of the spin glass model and corresponding predictability obtained by nine local-topology-based link prediction methods. Results are evaluated on synthetic networks generated by the (A) Barabási-Albert model, (B) Watts-Strogatz model and (C) Erdős-Rényi model. (D-F) Individual average energy shifts derived from the cavity field analysis for the SDM method. Credit: Proceedings of the National Academy of Sciences (2026). DOI: 10.1073/pnas.2535161123

The University of Hong Kong (HKU) has spearheaded an international research collaboration to develop a pioneering theoretical framework that deciphers the predictability of complex networks. A research team including Professor Qingpeng Zhang's group at the HKU Musketeers Foundation Institute of Data Science (HKU IDS) and the HKU Li Ka Shing Faculty of Medicine, together with researchers from Zhejiang University and Sapienza University of Rome, has developed a new theoretical framework to understand the predictability of complex networks.

The study, led by Dr. Fei Jing, a Postdoctoral Fellow supervised by Prof Zhang at HKU IDS, has been published in the Proceedings of the National Academy of Sciences . The international collaboration includes Professor Zi-Ke Zhang of Zhejiang University and Professor Giorgio PARISI of Sapienza University of Rome, the 2021 Nobel Laureate in Physics, as corresponding authors.

Cracking the code of network predictability

Complex systems are the backbone of the modern world, ranging from large-scale Artificial Intelligence (AI) models to intricate biological and social networks. To address the long-standing question of how inherently predictable these systems are, the research team introduced a rigorous theoretical framework drawing on concepts from statistical physics. By mapping network predictability onto the classical "spin glass" model, the team established a new way to analyze connection patterns.

Efficiency through localization

A key breakthrough of the study is the demonstration that the global predictability of large networks can be decomposed into local contributions from individual connections. This insight significantly reduces computational complexity, providing a robust foundation for more efficient algorithms to analyze large-scale networks. Leveraging this theoretical advance, the team proposed a highly efficient local sampling algorithm that relies solely on neighborhood-level information. This approach substantially improves the scalability of network prediction methods, making it feasible to process vast datasets.

The findings hold transformative potential across multiple disciplines, offering new metrics in the field of AI to evaluate and design model architectures while enhancing overall efficiency and interpretability. Furthermore, in the realm of biomedicine, the methodology could significantly accelerate the prediction of molecular interactions, potentially shortening the timeline for drug discovery and development by providing a more precise computational lens.

Publication details

Fei Jing et al, Predictability of complex networks, Proceedings of the National Academy of Sciences (2026). DOI: 10.1073/pnas.2535161123

Journal information: Proceedings of the National Academy of Sciences

Provided by The University of Hong Kong