Many successful digital interfaces employ visual metaphors to convey features or data properties to users, but the characteristics that make a visual metaphor effective are not well understood. We used a theoretical conception of metaphor from cognitive linguistics to design an interactive system for viewing the citation network of the corpora of literature in the JSTOR database, a highly connected compound graph of 2 million papers linked by 8 million citations. We created 4 variants of this system, manipulating 2 distinct properties of metaphor. We conducted a between‐subjects experimental study with 80 participants to compare understanding and engagement when working with each version. We found that building on known image schemas improved response time on look‐up tasks, while contextual detail predicted increases in persistence and the number of inferences drawn from the data. Schema‐congruency combined with contextual detail produced the highest gains in comprehension. These findings provide concrete mechanisms by which designers presenting large data sets through metaphorical interfaces may improve their effectiveness and appeal with users.