Network analysis is a topic in secondary mathematics education of growing importance because it offers students an opportunity to understand how to model and solve many authentic technology and engineering problems. However, very little is known about how students make sense of the algorithms typically used in network analysis. In this study, I used the Hungarian algorithm to explore how students make sense of a network algorithm and how it can be used to solve assignment problems. I report the results of a design-based research project in which eight Year 12 students participated in a teaching experiment that spanned four 60-min lessons. A hypothetical learning trajectory was developed in which students were introduced to the steps of the Hungarian algorithm incrementally. The results suggest that students made sense of the intermediate steps of the algorithm, the results of those steps, and how the algorithm works to solve assignment problems. The difficulties that students encountered are also discussed.