Hierarchical graphs (e.g. file system browsers, family trees) represent objects (e.g. files, folders) as graph nodes, and relations (subfolder relations) between them as lines. In three experiments, participants viewed such graphs and carried out tasks that either required search for two target nodes (Experiment 1A), reasoning about their relation (Experiment 1B), or both (Experiment 2). We recorded eye movements and used the number of fixations in different phases to identify distinct stages of comprehension. Search in graphs proceeded like search in standard visual search tasks and was mostly unaffected by graph properties. Reasoning occurred typically in a separate stage at the end of comprehension and was affected by intersecting graph lines. The alignment of nodes, together with linguistic factors, may also affect comprehension. Overall, there was good evidence to suggest that participants read graphs in a sequential manner, and that this is an economical approach of comprehension. Copyright © 2010 John Wiley & Sons, Ltd.