Fundamental Dynamics of Popularity-Similarity Trajectories in Real Networks

作     者：Evangelos S. Papaefthymiou Costas Iordanou Fragkiskos Papadopoulos 

作者机构：Department of Electrical Engineering Computer Engineering and Informatics Cyprus University of Technology 3036 Limassol Cyprus. 

出 版 物：《Physical Review Letters》 (Phys Rev Lett)

年 卷 期：2024年第132卷第25期

页      面：257401-257401页

核心收录：

学科分类：07[理学] 0702[理学-物理学] 

基　　金：European Regional Development Fund, ERDF Research and Innovation Foundation, RIF 

主　　题：Evolving networks Real world networks Evolving network models Self-similarity 

摘      要：Real networks are complex dynamical systems, evolving over time with the addition and deletion of nodes and links. Currently, there exists no principled mathematical theory for their dynamics—a grand-challenge open problem. Here, we show that the popularity and similarity trajectories of nodes in hyperbolic embeddings of different real networks manifest universal self-similar properties with typical Hurst exponents H≪0.5. This means that the trajectories are predictable, displaying antipersistent or “mean-reverting behavior, and they can be adequately captured by a fractional Brownian motion process. The observed behavior can be qualitatively reproduced in synthetic networks that possess a latent geometric space, but not in networks that lack such space, suggesting that the observed subdiffusive dynamics are inherently linked to the hidden geometry of real networks. These results set the foundations for rigorous mathematical machinery for describing and predicting real network dynamics.