Geometrical Circuits of Electrical Networks

Abstract

If all the electrical properties are abstracted from a given electrical network, there remains a geometrical circuit, completely characterized by the sets of branches terminating at the various vertexes. In this paper, enumerations of geometrical circuits are given, classified according to two different parameters, the nullity (number of branches minus number of vertexes plus number of separate parts) and the rank (number of vertexes minus number of separate parts). There is also a partial list of geometrical circuits which are symmetrical with respect to all the branches and all the vertexes.