Models of graph-based reasoning have typically accounted for the variation in problem solving performance with different graph types in terms of a task analysis of the problem relative to the particular visual properties of each graph type [e.g., Human Computer Interaction 8 (1993) 353; Proceedings of the Twenty-first Annual Conference of the Cognitive Science Society. Lawrence Erlbaum Associates, Mahwah, NJ (1999) 531]. This approach has been used to explain response time and accuracy differences in experimental situations where data are averaged over experimental conditions. An experiment is reported in which participants' eye movements were recorded while they were solving various problems with different graph types. The eye movement data revealed fine grained fixation patterns that are not captured by current analyses based on optimal fixation sequences. It is argued that these patterns reveal the effects of working memory limitations during the time course of problem solving. An ACT-R/PM model of the experiment is described in which a similar pattern of eye fixations is produced as a natural consequence of the decay in activation of perceptual chunks over time.