De-Anonymizing Social Networks With Overlapping Community Structure

The advent of social networks poses severe threats on user privacy as adversaries can de-anonymize users’ identities by mapping them to correlated cross-domain networks. Without ground-truth mapping, prior literature proposes various cost functions in hope of measuring the quality of mappings. However, their cost functions, whose minimizers may remain algorithmically unknown, usually bring imponderable mapping errors when the true mapping cannot minimize these cost functions. We jointly tackle above concerns under a more practical social network model parameterized by overlapping communities, which, neglected by prior art, can serve as side information for de-anonymization. Regarding the unavailability of ground-truth mapping to adversaries, by virtue of the Minimum Mean Square Error (MMSE), our first contribution is a well-justified cost function minimizing the expected number of mismatched users over all possible true mappings. While proving the NP-hardness of minimizing MMSE, we validly transform it into the weighted-edge matching problem (WEMP), which, as disclosed theoretically, resolves the tension between optimality and complexity: 1) WEMP asymptotically returns a negligible mapping error in large network size under mild conditions facilitated by higher overlapping strength; 2) WEMP can be algorithmically characterized via the convex-concave based de-anonymization algorithm (CBDA), effectively finding the optimum of WEMP. Extensive experiments further confirm the effectiveness of CBDA under overlapping communities: 90% users are re-identified averagely in a series of networks when communities overlap densely, and the re-identification ratio is enhanced about 70% compared to non-overlapping cases.