Minimizing the Hamming distance between a graph and a line-graph to discover the topology of an electrical network

Abstract

Our objective is to discover the topology of an energy distribution network modeled by a flow digraph from which we know the set of arcs without identification of their extremities. We also know possible correlations between these arcs from measurements in which errors could occur. To discover the network’s topology from the obtained correlation matrix between arcs, we consider the graph whose incidence matrix is the correlation matrix with entries rounded to zero or one. Without errors in the correlations, this graph is the line-graph of the distribution network. We propose an algorithm that given the rounded correlation matrix M, finds the incidence matrix of a line-graph with minimum Hamming distance to M. We then evaluate the performance of this approach by simulation.