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Recent years have witnessed the great success of social media websites. Tag-based image search is an important approach to accessing the image content on these websites. However, the existing ranking methods for tag-based image search frequently return results that are irrelevant or not diverse. This paper proposes a diverse relevance ranking scheme that is able to take relevance and diversity into account by exploring the content of images and their associated tags. First, it estimates the relevance scores of images with respect to the query term based on both the visual information of images and the semantic information of associated tags. Then, we estimate the semantic similarities of social images based on their tags. Based on the relevance scores and the similarities, the ranking list is generated by a greedy ordering algorithm which optimizes average diverse precision, a novel measure that is extended from the conventional average precision. Comprehensive experiments and user studies demonstrate the effectiveness of the approach. We also apply the scheme for web image search reranking, and it is shown that the diversity of search results can be enhanced while maintaining a comparable level of relevance.