Difunctional polymer hydrogels, such as those prepared from poly(ethylene glycol) diacrylate (PEGDA) macromers, are widely used for a number of potential applications in biotechnology and advanced materials due to their low cost, mild cross-linking conditions, and biocompatibility. The microstructure of such hydrogels is known to be heterogeneous, yet little is known about the specific structure itself, how it is impacted by the molecular parameters of the macromer, or its impact on macroscopic gel properties. Here, we determine the structure of PEGDA hydrogels using small-angle neutron scattering over a significant range of macromer molecular weights and volume fractions. From this, we propose a structural model for PEGDA hydrogels based on self-excluded, highly branched star polymers arranged into a fractal network. The primary implication of this structure is that heterogeneity arises not from defects in the cross-linking network, as is commonly assumed, but rather from a heterogeneous distribution of polymer concentration. This structural model provides a systematic explanation of the linear elasticity and swelling of PEGDA hydrogels.