Triangle Counting Over Signed Graphs with Differential Privacy

Triangle counting serves as a foundational operator in graph analysis. Since graph data often contain sensitive information about entities, the release of triangle counts poses privacy concerns. While recent studies have addressed privacy-preserving triangle counting, they mainly concentrate on unsigned graphs. In this paper, we investigate a new problem of developing triangle counting algorithms for signed graphs that adhere to centralized differential privacy and local differential privacy, respectively. The inclusion of edge signs and more classes of triangles leads to increased complexity and overwhelms the statistics with noise. To overcome these problems, we first propose a novel algorithm for smooth-sensitivity computation to achieve differential privacy under the centralized model. In addition, to handle large signed graphs, we devise a computationally efficient function that calculates a smooth upper bound on local sensitivity. Finally, we release the approximate triangle counts after the introduction of Laplace noise, which is calibrated to the smooth upper bound on local sensitivity. In the local model, we propose a two-phase framework tailored for balanced and unbalanced triangle counting. The first phase utilizes the Generalized Randomized Response mechanism to perturb data, followed by a novel response mechanism in the second phase. Extensive experiments conducted over real-world datasets demonstrate that our proposed methods can achieve an excellent trade-off between privacy and utility.

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