In this work, we introduce a novel method for compound identification in mixtures based on nuclear magnetic resonance spectra. Contrary to many other methods, our approach can be used without peak-picking the mixture spectrum and simultaneously optimizes the fit of all individual compound spectra in a given library. At the core of the method, a minimum cost flow problem is solved on a network consisting of nodes that represent spectral peaks of the library compounds and the mixture. We show that our approach can outperform other popular algorithms by applying it to a standard compound identification task for 2D ¹H,¹³C HSQC spectra of artificial mixtures and a natural sample using a library of 501 compounds. Moreover, our method retrieves individual compound concentrations with at least semiquantitative accuracy for artificial mixtures with up to 34 compounds. A software implementation of the minimum cost flow method is available on GitHub (https://github.com/GeoMetabolomics-ICBM/mcfNMR).