Topological transformations of electrical networks

Abstract

AbstractThis paper deals with effects of modifications of network structure that may be studied without reference to the type of devices present in the network. We introduce and make systematic use of the notion of a generalized minor of a vector space. This operation generalizes the usual short and open circuit operations for a graph. Using the generalized minor operation we show how to make the equations of a given network appear to be the ‘bordered version’ of the equations of some other specified network. We also consider the decomposition of a network into several ‘multiports’ and a ‘port connection diagram’, and study the properties of a minimal decomposition (with port connection diagram having a minimum number of edges). In each case we present efficient algorithms wherever appropriate. Although the paper makes use of ideas from elementary matroid theory it is entirely self‐contained and requires no more than the knowledge of elementary linear algebra from the reader.