By investigation of the topological characteristics of the kinematic structure of Satellite Gear Mechanism (SGM) with graph theory, the graph model of SGM is analyzed, and a topological expression model between input and output of SGM is established based on systematic design point. Meanwhile, the mathematical expression for SGM is deduced by integrating matrix theory and graph theory; thus, the topological characteristics of the kinematic structure of SGM can be converted into a matrix model, and the topological design problem of SGM into a matrix operation problem. In addition, a brief discussion about the measures for identification of isomorphism of the graph mode is made.