Minimum Hop Count Calculation in LEO Satellite Networks Considering Non-Zero Phasing Factor

Efficient routing strategies are essential for Low Earth Orbit (LEO) satellite networks with non-zero phasing factors to ensure optimal inter-satellite communication. This paper presents a minimum hop count model tailored for such constellations and introduces discriminant conditions for distinguishing different path types, including first-last bridging paths and in-grid paths. A simulation-based verification framework is established to compare the proposed model with Dijkstra’s algorithm and to analyze hop count distribution and path type selection. Results from hop count distribution analysis, using the satellite indexed as $(0,0)$ as the source, show that: hop counts follow an approximately symmetric distribution centered around the mean; and the frequencies of selecting first-last bridging and in-grid paths are nearly equal. These findings provide theoretical support for the design and optimization of routing protocols in satellite constellations with non-zero phasing factors.