A non-parametric technique to identify weak sources within dense sensor arrays is developed using a network approach. No knowledge about the propagation medium is needed except that signal strengths decay to insignificant levels within a scale that is shorter than the aperture. We then reinterpret the spatial covariance matrix of a wave field as a matrix whose support is a connectivity matrix of a network of vertices (sensors) connected into communities. These communities correspond to sensor clusters associated with individual sources. We estimate the support of the covariance matrix from limited-time data using a robust hypothesis test combined with a physical distance criterion. The latter ensures sufficient network sparsity to prevent vertex communities from forming by chance. We verify the approach on simulated data and quantify its reliability. The method is then applied to data from a dense 5200 element geophone array that blanketed 7$\times$10 km of the city of Long Beach (CA). The analysis exposes a helicopter traversing the array, oil production facilities, and reveals that low-frequency events tend to occur near roads.