We study the entropy production of systems out of equilibrium using random networks. We focus on systems with a finite number of states described by a master equation close to equilibrium. The dynamics are mapped into a network of states (nodes) connected by transition rates (links). Using this framework, we analyze the entropy production of ensembles of randomly generated networks owing to specific constraints (e.g., size or symmetries) and identify the most important parameters that determine its value. This analysis gives a null-model estimation for the entropy production that can be used for comparison with specific systems.