Mega-constellation networks (MCNs) based on low earth orbit (LEO) satellites have become increasingly important with many projects in the design or implementation phase. For those MCN systems with inter-satellite links (ISLs), the large number of satellites increases the routing complexity and the required hop-count of ISL paths. This paper aims to provide insights into the topology and routing design in MCNs through the analysis of ISL paths. We propose a theoretical model to explicitly estimate the ISL hop-count between ground users in MCNs with inclined orbits. The spatial distribution properties of hop-count are derived based on the proposed method. Based on an exemplary constellation, that is Starlink, the global distribution patterns of hop-count and the path difference caused by different access satellites are illustrated for the first time. In Starlink, the difference of the paths from different starting satellites can be up to 45 hops. The numerical results show that optimizing the constellation phasing factor can effectively reduce the average hop-count, for both the whole network and specific regional users. [ABSTRACT FROM AUTHOR]
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