TOPOLOGICAL FORMULAS FOR SUBNETWORK-EXTRAC- TION THEOREMS AND MULTITERMINAL FEEDBACK NETWORKS

The concepts of modified graphs of a composite graph with respect to two vertex-pairs and a hyperedge-decomposition are introduced. By using these concepts and the directed hypergraph theory, the topological formulae for the parameter-extraction theorem and subnetwork-extraction theorems are derived, then the topological formulae for multiterminal feedback networks are presented. In these formulae 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.