Through the use of macromolecular design and efficient chemical reactions it is now possible to control the composition of polymer networks and gels with excellent precision: In contrast, topological defects are still impossible to avoid and are generally difficult to quantify. For example, primary loops that form when a bifunctional monomer (A(2)) reacts twice with the same f functional (f> 2) monomer (B-f) during formation of an end-linked A(2) + B-f network represent a pervasive defect that has a detrimental effect on mechanical integrity. Methods for the quantitative analysis of primary loops in such materials have recently emerged; however, these methods have only been applied to the simplest network structure: A(2) + B-3. Herein, we report strategies for counting primary loops in tetrafunctional (A(2) + B-4) networks and networks with mixed tri- and tetrafunctional (A(2) + B-3/B-4) junctions. We apply these strategies to-the quantitative analysis of primary loops in a series of end-linked poly(ethylene glycol) hydrogels synthesized via copper-catalyzed azide-alkyne cydoaddition "click" chemistry. Our results show that A(2) + B-4 networks are particularly susceptible to cyclic defects compared to A(2) + B-3 networks and that higher-order cyclic species must play a significant role in the gel point of the former materials. Our experimental results were compared to rate theory and Monte Carlo simulations. This Work reveals new structural insights into a widely studied family of materials and sets the stage for the development of strategies to tune network defects in such gels.