Characterization and optimization of satellite complex networks based on hyperbolic space

In recent years, the rapid advancement of mega-constellations in Low Earth Orbit (LEO) has led to the emergence of satellite communication networks characterized by a complex interplay between high- and low-altitude orbits and by unprecedented scale. Traditional network-representation methodologies in Euclidean space are insufficient to capture the dynamics and evolution of high-dimensional complex networks. By contrast, hyperbolic space offers greater scalability and stronger representational capacity than Euclidean-space methods, thereby providing a more suitable framework for representing large-scale satellite communication networks. This paper aims to address the burgeoning demands of large-scale space–air–ground integrated satellite communication networks by providing a comprehensive review of representation-learning methods for large-scale complex networks and their application within hyperbolic space. First, we briefly introduce several equivalent models of hyperbolic space. Then, we summarize existing representation methods and applications for large-scale complex networks. Building on these advances, we propose representation methods for complex satellite communication networks in hyperbolic space and discuss potential application prospects. Finally, we highlight several pressing directions for future research.