Analysis of the connectivity and robustness of inter-satellite links in a constellation

In the design of new constellation configurations or research of existing constellation performance, the connectivity and robustness of inter-satellite links (ISL) are needed for analysis. In this paper, graph theory is used to analyze the connectivity and robustness of the ISL in constellations, which are measured under the requirements of a short average distance and a small range of ISL azimuth angles, elevation angles and distances. The method to determine ISL connectivity by using the adjacency matrix of graph theory is put forward for the first time, and the standards of the ISL performance are given using: the number of ways between any two satellites, cutting point, cutting edge, k-connectivity degree and k-edge connectivity degree of graph theory. Finally, in the simulation, the ISLs in the Walker 24/6/1 constellation and the ISLs in the Walker 24/3/1 constellation are established from the optimal perspective of the azimuth angle, elevation angle and distance, and the characteristics of ISL in the Walker 24/6/1 and Walker 24/3/1 constellations are compared. The conclusions of this paper can be used as a reference for the design of new constellation configurations and analysis of existing ISLs.