We present a methodology for efficient, robust determination of the interaction topology of networked dynamical systems using time series data collected from experiments, under the assumption that these networks are sparse, i.e., have much less edges than the full graph with the same vertex set. To achieve this, we minimize the 1-norm of the decision variables while keeping the data in close Euler fit, thus putting more emphasis on determining the interconnection pattern rather than the closeness of fit. First, we consider a networked system in which the interconnection strength enters in an affine way in the system dynamics. We demonstrate the ability of our method to identify a network structure through numerical examples. Second, we extend our approach to the case of gene regulatory networks, in which the system dynamics are much more complicated.