Concept inventories are commonly used tools in physics education research (PER) for evaluating teaching methods. Student responses to concept inventories have been studied using classical test theoretical methods such as factor analysis and network methods such as module analysis. The results of these studies have been used to evaluate the instruments and to find aggregate patterns that may be used to infer how students' think about the concepts on the inventory. In this work, we apply modified model analysis using partial correlations, a network based method using partial correlations, to evaluate the Quantum Mechanics Concept Assessment (QMCA). The QMCA is designed to measure student understanding of upper-division quantum mechanics in both the spatial wave function and the spins contexts. This represents the first time a network-based analysis has been applied to an upper-division concept inventory. The modules we found are related to the structure of the instrument. There were two broad classes of modules: those that connected responses (either both correct or both incorrect) to isomorphic pairs questions written to probe the same concept in the spatial wave function and the spin contexts. The second class of modules were explain pairs, where the first question asked about a concept and the second question asked students to explain their choice, again either both correct or both incorrect. This structure resembles the structure of the Force Concept Inventory where there are a common correct and a common incorrect pair for many concepts, compared to the Force and Motion Conceptual Evaluation, which has larger and more varied communities reflecting a smaller number of topics.