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Increasing research on social networks stresses the urgency for producing effective means of ensuring user privacy. Represented ubiquitously as graphs, social networks have a myriad of recently developed techniques to prevent identity disclosure, but the equally important attribute disclosure attacks have been neglected. To address this gap, we introduce an approach to anonymize social networks that have labeled nodes, α-proximity, which requires that the label distribution in every neighbourhood of the graph be close to that throughout the entire network. We present an effective greedy algorithm to achieve α-proximity and experimentally validate the quality of the solutions it derives.