Topological degrees of freedom and mixed analysis of electrical networks

A new concept of topological degrees of freedom is introduced as a generalization of the concepts of rank and nullity. This number.corresponds to the minimum number of independent variables taken in mixed analysis of electrical networks, which is a generalization of well-known node-pair and loop analysis. An explicit formula giving topological degrees of freedom and a graph-theoretical algorithm for finding all the minimum sets of independent variables are presented. Another new concept of extremal tree is introduced and shown to play a central role in obtaining the results.