Abstract
A low Earth orbit (LEO) satellite constellationnetwork (SCN) has become a promising solution for nonterrestrial networks. In LEO-SCNs, the shortest distance path (SDP) and the minimum hop path (MHP) are two types of important paths. This letter focuses on the proposition that all the SDPs belong to the MHP set and studies the conditions when the proposition holds or not. Based on the topological regularity and link distance variation patterns, this letter proves several simplified equivalent propositions and derives a discriminant function to judge if the proposition holds in an arbitrary constellation. Simulations verify the judging method and find that all the SDPs belong to the MHP set in constellations with small inclinations (less than 68$^\circ$) or large phasing offsets. The propositions can help to simplify the calculation of the SDP.
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