Topological data analysis has been used to analyze social systems, disease spread, and polling locations, but it is not typically used in mathematics education research. In this study, university calculus students created concept maps–visual representations of connections–which were analyzed using homology groups. We argue that homology is an innovative and useful tool for analyzing concept maps, complementing previous analyses conducted via qualitative techniques or scoring systems. We further argue that topological data analysis can be a valuable tool for mathematics education research.