1Kron Reduction of Graphs with Applications to Electrical Networks

Abstract—Consider a weighted undirected graph and its corre-sponding Laplacian matrix, possibly augmented with additional diagonal elements corresponding to self-loops. The Kron reduc-tion of this graph is again a graph whose Laplacian matrix is ob-tained by the Schur complement of the original Laplacian matrix with respect to a specified subset of nodes. The Kron reduction process is ubiquitous in classic circuit theory and in related disciplines such as electrical impedance tomography, smart grid monitoring, transient stability assessment, and analysis of power electronics. Kron reduction is also relevant in other physical domains, in computational applications, and in the reduction of Markov chains. Related…