Sign Matrices and Realizability of Conductance Matrices

Given a conductance matrix G of order n, the problem of realizing it by a network with n + 1 nodes can be split in two parts: to find the tree of the ports corresponding to the given matrix G; and to determine the actual resistances of the branches of the network. A procedure to solve the first (topological) problem is proposed, which is simply concerned with the signs of the elements of the given matrix G. The successful development of the procedure can be considered as a necessary and sufficient condition for the existence of a tree corresponding to G.