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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. 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