A graph is an abstract model that represents relations among entities, for example, the interactions between characters in a novel. A background story endows entities and relations with real-world meanings and describes the semantics and context of the abstract model, for example, the actual story that the novel presents. Considering practical experience and prior research, human viewers who are familiar with the background story of a graph and those who do not know the background story may perceive the same graph differently. However, no previous research has adequately addressed this problem. This research article thus presents an evaluation that investigated the effects of background stories on graph perception. Three hypotheses that focused on the role of visual focus areas, graph structure identification, and mental model formation on graph perception were formulated and guided three controlled experiments that evaluated the hypotheses using real-world graphs with background stories. An analysis of the resulting experimental data, which compared the performance of participants who read and did not read the background stories, obtained a set of instructive findings. First, having knowledge about a graph's background story influences participants' focus areas during interactive graph explorations. Second, such knowledge significantly affects one's ability to identify community structures but not high degree and bridge structures. Third, this knowledge influences graph recognition under blurred visual conditions. These findings can bring new considerations to the design of storytelling visualizations and interactive graph explorations.