Topological formulas for subnetwork extraction theorems and multiterminal feedback networks

Abstract

The concepts of modified graphs of a composite graph with respect to two vertexpairs and a hyperedge-decomposition are introduced, respectively. By applying them and the directed hypergraph theory, the topological formulas for the parameter-extraction theorem and subnetwork-extraction theorems are derived, and then the topological formulas for multiterminal feedback networks are presented. In these formulas the parameters of the feedback subnetwork are separated from that of the fundamental subnetwork, so that it is convenient to find out the effect of the feedback parameters. Furthermore, since one network is decomposed into two smaller subnetworks, the computing time complexity and space complexity can be reduced.