Abstract Symbolic code matrix, constant matrix and count matrix are defined. The first two matrixes are used to describe the elemental expressions of augmentation matrix and the node admittance equation is thus obtained. The third matrix is used to obtain the incoming degree matrix, and all the 1-factor gains of the coates graph are given according to the matrix. Using the code data, the determinant is expanded and all the same items in the expansion are merged. Thus the symbolic network function in which no term concellation occurs is generated.