Proximity measures quantify the closeness or similarity between nodes in a social network and form the basis of a range of applications in social sciences, business, information technology, computer networks, and cyber security. It is challenging to estimate proximity measures in online social networks due to their massive scale (with millions of users) and dynamic nature (with hundreds of thousands of new nodes and millions of edges added daily). To address this challenge, we develop two novel methods to efficiently and accurately approximate a large family of proximity measures. We also propose a novel incremental update algorithm to enable near real-time proximity estimation in highly dynamic social networks. Evaluation based on a large amount of real data collected in five popular online social networks shows that our methods are accurate and can easily scale to networks with millions of nodes.To demonstrate the practical values of our techniques, we consider a significant application of proximity estimation: link prediction, i.e., predicting which new edges will be added in the near future based on past snapshots of a social network. Our results reveal that (i) the effectiveness of different proximity measures for link prediction varies significantly across different online social networks and depends heavily on the fraction of edges contributed by the highest degree nodes, and (ii) combining multiple proximity measures consistently yields the best link prediction accuracy.

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-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 efciently 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 show that 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 MySpace with up to 2 million nodes and 90 million links.

No 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 efciently 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 show that 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 MySpace with up to 2 million nodes and 90 million links.