Models explaining network morphology and growth processes permit a wide range of phenomena to be more systematically analyzed and understood. At the same time, creating such models is often challenging and requires insights that may be counter-intuitive. We have developed an approach to automatically detect realistic decentralized network growth models from empirical data, employing a machine learning technique inspired by natural selection and defining a unified formalism to describe such models as computer programs. The proposed method can be applied “out of the box” to any given network. We were able to find programs that are simple enough to lead to an actual understanding of underlaying mechanisms, namely for a simple brain and a social network.