Necessary Conditions for the Realizability of n-Port Resistive Networks with more than (n + 1) Nodes

A new set of necessary conditions are presented for an nth-order square symmetric matrix Y with real entries to be the -port admittance matrix of a network containing positive resistors and nodes. The so called "supremacy" conditions represent a symmetric set of inequalities among products of pairs of elements in a matrix S obtained in a simple manner as a linear combination of entries in Y. The conditions are derived by augmenting the given matrix Y with an additional port to form a connected port structure, transforming the port structure until it is linear, applying the "uniform tapering conditions" and then eliminating the augmenting port. Extensions are given to the case of nodes with