With the explosive growth of digital cameras and online media, it has become crucial to design efficient methods that help users browse and search large image collections. The recent VisualRank algorithm  employs visual similarity to represent the link structure in a graph so that the classic PageRank algorithm can be applied to select the most relevant images. However, measuring visual similarity is difficult when there exist diversified semantics in the image collection, and the results from VisualRank cannot supply good visual summarization with diversity. This paper proposes to rank the images in a structural fashion, which aims to discover the diverse structure embedded in photo collections, and rank the images according to their similarity among local neighborhoods instead of across the entire photo collection. We design a novel algorithm named RankCompete, which generalizes the PageRank algorithm for the task of simultaneous ranking and clustering. The experimental results show that RankCompete outperforms VisualRank and provides an efficient but effective tool for organizing web photos.