The swelling pressure of randomly crosslinked polymer networks is related to the structural properties of the crosslink topology. Using the assumption that the network structure exhibits fractal properties within the correlation length xi, a scaling relation between the swelling pressure and the polymer volume fraction has been derived. The exponent obtained depends on the internal fractal dimension d(i) of the network and is in general different from the corresponding exponent for linear chains. The later can be obtained as the special case d(i)=1. As a consequence, a significant difference in mixing entropy between the networks and the corresponding uncrosslinked system is predicted. This explains the experimental results obtained by several authors, which are in contradiction to the Flory-Rehner assumption. Computer simulations based on the bond fluctuation model support the scaling predictions presented. The exponents obtained for the density dependence of the osmotic or swelling pressure are somewhat larger than expected from the theoretical work for both the linear and the crosslinked system.