During a disaster, social media can be both a source of help and of danger: Social media has a potential to diffuse rumors, and officials involved in disaster mitigation must react quickly to the spread of rumor on social media. In this paper, we investigate how topic diversity (i.e., homogeneity of opinions in a topic) depends on the truthfulness of a topic (whether it is a rumor or a non-rumor) and how the topic diversity changes in time after a disaster. To do so, we develop a method for quantifying the topic diversity of the tweet data based on text content. The proposed method is based on clustering a tweet graph using Data polishing that automatically determines the number of subtopics. We perform a case study of tweets posted after the East Japan Great Earthquake on March 11, 2011. We find that rumor topics exhibit more homogeneity of opinions in a topic during diffusion than non-rumor topics. Furthermore, we evaluate the performance of our method and demonstrate its improvement on the runtime for data processing over existing methods.