Invisible Dual (n-l)-Networks Induced by Electric 1-Networks
Gabriel Kron · IEEE Transactions on Circuit Theory · 1965
Since Kirchhoff's current-law prohibits the use of "nodes," and Kirchhoff's voltage-law prohibits the use of the "planes over the meshes," the topological theory of electric networks must be based upon the utilization of "branches" only (1-network) and their surroundings. A large number of visible and invisible multidimensionalp-networks surrounding the branches can be introduced, that collectively form neither a graph nor a polyhedron, but a nonRiemannian space. All the parameters of Maxwell's field equations propagate in this space. Thus the four rectangular connection-matricesC_{0}, C_{c}, A^{°}, andA^{c}of eachp-network form the building-blocks of an asymmetric "affine connection"\Gamma_{\beta\gamma}^{\alpha}. It defines the "covariant" space-derivatives, that replace in networks the familiar gradient, divergence, and curl concepts of fields.