The Seg: A New Class of Subgraphs

Abstract

The linear graph, after a delay of about a hundred years from its conception by Kirchhoff, is today rapidly assuming a dominant position in the foundation of electric network theory. This paper is a presentation, by definition and properties deducible therefrom, of a new class of subgraphs (segs) which includes stars and cut sets as special cases. The matrix associated with the seg can be shown to be the general coefficient matrix of the Kirchhoff current equations. Hence, in addition to adding to the structure of linear graph theory, the results in this paper broaden the base of knowledge of currents in electric networks. This broadened base has already permitted the opening of a new phase of network theory and can certainly be expected to open others.