Abstract: The explosive growth of social networks has created numerous exciting research opportunities. A central concept in the analysis of social networks is a proximity measure, which captures the closeness or similarity between nodes in the network. Despite much research on proximity measures, there is a lack of techniques to efciently and accurately compute proximity measures for largescale social networks. In this paper, we embed the original massive social graph into a much smaller graph, using a novel dimensionality reduction technique termed Clustered Spectral Graph Embedding. We showthat the embedded graph captures the essential clustering and spectral structure of the original graph and allow a wide range of analysis to be performed on massive social graphs. Applying the clustered embedding to proximity measurement of social networks, we develop accurate, scalable, and exible solutions to three important social network analysis tasks: proximity estimation, missing link inference, and link prediction. We demonstrate the effectiveness of our solutions to the tasks in the context of large real-world social network datasets: Flickr, LiveJournal, and My- Space with up to 2 million nodes and 90 million links.