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We propose a novel technique to assess functional brain connectivity in electroencephalographic (EEG)/magnetoencephalographic (MEG) signals. Our method, called sparsely connected sources analysis (SCSA), can overcome the problem of volume conduction by modeling neural data innovatively with the following ingredients: 1) the EEG/MEG is assumed to be a linear mixture of correlated sources following a multivariate autoregressive (MVAR) model; 2) the demixing is estimated jointly with the source MVAR parameters; and 3) overfitting is avoided by using the group lasso penalty. This approach allows us to extract the appropriate level of crosstalk between the extracted sources and, in this manner, we obtain a sparse data-driven model of functional connectivity. We demonstrate the usefulness of SCSA with simulated data and compare it to a number of existing algorithms with excellent results.