  The problem of recovering the topology and cable parameters of an electrical
network from power and voltage data at all nodes is a problem of fitting both
an algebraic variety and a graph. The problem is often ill-posed. In case there
are multiple electrical networks which fit the data up to a given tolerance, we
seek a solution in which the graph and therefore the algebraic equations
associated with the electrical network are sparse, i.e. with few edges and
terms. We propose an algorithm for recovering simultaneously a sparse topology
and the cable parameters of any network, combining in an iterative procedure
the resolution of non-negative linear regression problems, which are convex,
and techniques of spectral graph sparsification. The algorithm is tested on
several electrical networks.
