On the Graphicity of the Independence Structure of Linear Active Networks

Abstract

Consider a linear network composed of 2-terminal devices. Its interconnection structure is described by a graph G. The voltages or the currents of a subset of devices can independently be prescribed if and only if the subset of the corresponding edges in the graph G is circuit-free or cut set free, respectively.  This classical result of Kirchhoff can be generalized for networks containing multiterminal devices as well: the independence structure can be described by the circuits and cut sets of a more general abstract mathematical structure, a matroid M. However, these matroids will not always be graphic. Using some recent mathematical results for characterizing graphic structures among the matroids, here we give a physical characterization of subclasses of those active networks where M happens to be graphic.