  We develop methods to efficiently reconstruct the topology and line
parameters of a power grid from the measurement of nodal variables. We propose
two compressed sensing algorithms that minimize the amount of necessary
measurement resources by exploiting network sparsity, symmetry of connections
and potential prior knowledge about the connectivity. The algorithms are
reciprocal to established state estimation methods, where nodal variables are
estimated from few measurements given the network structure. Hence, they enable
an advanced grid monitoring where both state and structure of a grid are
subject to uncertainties or missing information.
