The algorithm and program scheme to find out all valid trees and valid tree-pairs

The tree-pair method is a new approach of tree enumeration for symbolic network analysis, which based on the theorem that the determinant of a closed network is equal to the sum of all valid trees´ values and all valid tree-pairs´ values of the circuit´s graph. Thus the key to calculate the determinant is to find the trees and tree-pairs in the graph. The algorithm and the program scheme to find out all valid trees and valid tree-pairs are presented in this paper. A simulator of symbolic analysis by the algorithm is implemented. Some examples are solved successfully and shown in the paper.