The swelling responses of thin polymer networks were examined as a function of primary polymer architecture. Thin films of linear or bottlebrush polystyrene were cast on polystyrene-grafted substrates, and surface-attached networks were prepared with a radiation crosslinking reaction. The dry and equilibrated swollen thicknesses were both determined with spectroscopic ellipsometry. The dry thickness, which reflects the insoluble fraction of the film after crosslinking, depends on the primary polymer size and radiation dose but is largely independent of primary polymer architecture. When networks are synthesized with a high radiation dose, producing a high density of crosslinks, the extent of swelling is similar for all primary polymer architectures and molecular weights. However, when networks are synthesized with a low radiation dose, the extent of swelling is reduced as the primary polymer becomes larger or increasingly branched. These trends are consistent with a simple Flory model for equilibrium swelling that describes the effects of branch junctions and radiation crosslinks on network elasticity.