Graph-Theoretic Performance Analysis for Constellation Link Geometry via Random Geometric Networks

Satellite constellations with inter-satellite links (ISLs) for information sharing and coordination represent complex networks, where robustness against node failures is a key design concern. These networks feature variable ISL range capabilities, allowing connections across varying distances. This paper investigates how robustness metrics evolve with changing ISL ranges under degree, field-of-view, and connection constraints. We analyze algebraic connectivity, effective resistance, and latency of these networks, demonstrating that robustness improves with ISL range until a clear saturation point. Additionally, we show that random geometric graphs (RGGs) exhibit strikingly similar behavior to constrained constellation networks, suggesting shared underlying structural properties and offering a computationally efficient approximate model for design and trade-off studies.