Generalization of the Normal Tree Method for Networks Without Graphic Structures

We consider a network as a single linear timeinvariant (n + k)-port terminated by n source elements (independent sources, possibly nullators and norators) and k memory elements (capacitances and inductances). We generalize the well-known, classical normal tree method for this non-graphic environment and give computationally efficient algorithms to determine the unique solvability and the degree of freedom of the network. If only the k memory elements or only the n source elements are assigned to the ports, we consider the resulting multiport, decide whether source, respectively memory elements can be assigned to the remaining ports to ensure full or terminal solvability and in the first case we determine the spectrum of this n-port. As a byproduct, we find that the assignment of the memory elements does not influence the spectrum. Throughout, our tool is matroid theory (weighted and unweighted versions of the 2-matroid intersection algorithm and the linear matroid parity algorithm).