Motivated by a real life problem of sharing social network data that contain sensitive personal information, we propose a novel approach to release and analyse synthetic graphs to protect privacy of individual relationships captured by the social network while maintaining the validity of statistical results. A case-study using a version of the Enron e-mail corpus data set demonstrates the application and usefulness of the proposed techniques in solving the challenging problem of maintaining privacy and supporting open access to network data to ensure reproducibility of existing studies and discovering new scientific insights that can be obtained by analysing such data. We use a simple yet effective randomized response mechanism to generate synthetic networks under ε-edge differential privacy and then use likelihood-based inference for missing data and Markov chain Monte Carlo techniques to fit exponential family random-graph models to the generated synthetic
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