Abstract Visual comparison of directed acyclic graphs (DAGs) is commonly encountered in various disciplines (e.g., finance, biology). Still, knowledge about humans' perception of their similarity is currently quite limited. By similarity perception, we mean how humans perceive commonalities and differences of DAGs and herewith come to a similarity judgment. To fill this gap, we strive to identify factors influencing the DAG similarity perception. Therefore, we conducted a card sorting study employing a quantitative and qualitative analysis approach to identify (1) groups of DAGs the participants perceived as similar and (2) the reasons behind their groupings. We also did an extended analysis of our collected data to (1) reveal specifics of the influencing factors and (2) investigate which strategies are employed to come to a similarity judgment. Our results suggest that DAG similarity perception is mainly influenced by the number of levels, the number of nodes on a level, and the overall shape of the DAG. We also identified three strategies used by the participants to form groups of similar DAGs: divide and conquer, respecting the entire dataset and considering the factors one after the other, and considering a single factor. Factor specifics are, e.g., that humans on average consider four factors while judging the similarity of DAGs. Building an understanding of these processes may inform the design of comparative visualizations and strategies for interacting with them. The interaction strategies must allow the user to apply her similarity judgment strategy to the data. The considered factors bear information on, e.g., which factors are overlooked by humans and thus need to be highlighted by the visualization.