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We present a new workflow for differentially-private publication of graph topologies. First, we produce differentially-private measurements of interesting graph statistics using our new version of the PINQ programming language, Weighted PINQ, which is based on a generalization of differential privacy to weighted sets. Next, we show how to generate graphs that fit any set of measured graph statistics, even if they are inconsistent (due to noise), or if they are only indirectly related to actual statistics that we want our synthetic graph to preserve. We combine the answers to Weighted PINQ queries with an incremental evaluator (Markov Chain Monte Carlo (MCMC)) to synthesize graphs where the statistic of interest aligns with that of the protected graph. This paper presents our preliminary results; we show how to cast a few graph statistics (degree distribution, edge multiplicity, joint degree distribution) as queries in Weighted PINQ, and then present experimental results synthesizing graphs generated from answers to these queries.
Proserpio et al. (Fri,) studied this question.