Social network analysis (SNA) is increasingly attracting attentions from both academia and industrial areas. While revealing interesting properties and inferences from social network data is important, the protection of sensitive information of individuals is at the meanwhile a serious concern. In this paper, we study privacy preservation in interactive SNA settings, where the access to data is restricted to interactive queries, and the privacy of individuals is guaranteed by output perturbation. In particular, we dig into the problem of noisy answering of sub graph counting queries, while defending against the graph reconstruction attack that utilizes adaptive, incremental such queries to reconstruct the social graph. For the queries that we concern, applying the existing output perturbation mechanisms introduce too much noise to render the outputs useful. We solve this paradox by introducing ``seamless privacy'', a new notion of privacy that is shown to best fit the problem. Also, we propose a mechanism that achieves seamless privacy, and prove its correctness. Experiments on both real and synthetic data show that seamless privacy requires significantly less noise than its predecessors.
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