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DOI: 10.7155/jgaa.00522
Minimizing the Hamming distance between a graph and a linegraph to discover the topology of an electrical network
Vol. 24, no. 3, pp. 133153, 2020. Regular paper.
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 networkâ€™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 linegraph of the distribution network. We propose an algorithm that given the rounded correlation matrix M, finds the incidence matrix of a linegraph with minimum Hamming distance to M. We then evaluate the performance of this approach by simulation.

Submitted: December 2018.
Reviewed: May 2019.
Revised: July 2019.
Reviewed: January 2020.
Revised: January 2020.
Accepted: February 2020.
Final: February 2020.
Published: March 2020.
Communicated by
William S. Evans
