A weighted graph thresholding method. Using biologically sound penalties and data-driven parameters, BRANE Cut improves three state-of-the-art gene regulatory network (GRN) inference methods. The proposed method generalizes standard regulatory network inference by incorporating additional terms with biological interpretation. Since their regularization parameters are estimated from gene set cardinality, it can be applied to various transcriptomic data. The computation time of our method is negligible in comparison with other model-based approaches with inference improvements. It can be used as a generic GRN post-processing with any input weights and supplementary information on transcription factors.