On the structure of well-conditioned positive resistance networks

The unique structural composition of a (N+1)-terminal positive resistance network, including the network center, is illustrated by the parallel connection of the original network and of its associated terminal weight number network. The network is said to be well-conditioned if and only if all its associated terminal weight numbers are non-positive. Based on research, the author concludes that KCL (Kirchhoff's current law) and network topology (graph, matroid), which recognize only element incidence but not element values, do not suffice for the complete structural characterization and evaluation of electrical networks. In addition one must use terminal weight numbers, TWN (terminal weight numbers), which contain element value information, and their constraints and these must be established for every network class. When TWN and KCL are combined, necessary and sufficient conditions exist to solve every structural network problem.<>