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In this paper we present a novel approach for anonymizing Online SocialNetwork graphs which can be used in conjunction with existing perturbationapproaches such as clustering and modification. The main insight of this paperis that by imposing additional constraints on which nodes can be selected wecan reduce the information loss with respect to key structural metrics, whilemaintaining an acceptable risk. We present and evaluate two constraints,'local1' and 'local2' which select the most similar subgraphs within the samecommunity while excluding some key structural nodes. To this end, we introducea novel distance metric based on local subgraph characteristics and which iscalibrated using an isomorphism matcher. Empirical testing is conducted withthree real OSN datasets, six information loss measures, five adversary queriesas risk measures, and different levels of k-anonymity. The results show thatoverall, the methods with constraints give the best results for informationloss and risk of disclosure.

The effect of constraints on information loss and risk for clustering and modification based graph anonymization methods