We present a study of the structure of Tetra-PEG model networks, using proton multiple-quantum NMR at low field in combination with computer simulations. Tetra-PEG is a novel high-performance hydrogel designed by combination of two symmetric tetra-arm macromonomers. In contrast to conventional hydrogels, which are highly heterogeneous due to fixed concentration fluctuations, Tetra-PEG exhibits a much less heterogeneous microstructure as indicated by previous light and small-angle neutron scattering studies. Here, the local-scale connectivity inhomogeneities, i.e., the sol and dangling polymer chains as well as the typical network connectivity defects resulting from the A-B reaction of four-arm macromonomers, are quantified experimentally for the first time, studying as-prepared Tetra-PEG hydrogels, cross-linked at different polymer concentrations and stoichiometries. To this end, we developed a novel approach for the analysis of double-quantum buildup curves consisting of well-distinguishable components with different segmental dynamic order parameters, benefitting from the superb large-scale homogeneity of the samples. As a model for each component we suggest different connectivity modes between the macromonomers-mainly regular single links and double links between individual stars as well as other network defects with lower order parameters. To support the model, we report results from computer simulations with the bond-fluctuation model, which confirm the concentration-dependent trends of the network and double-link fractions.