Publishing Below-Threshold Triangle Counts under Local Weight Differential Privacy

Abstract: We propose an algorithm for counting below-threshold triangles in weighted graphs under local weight differential privacy. While prior work focused on unweighted graphs, many real-world networks naturally include edge weights. We study the setting where the graph topology is public known and the privacy of the influence of an individual on the edge weights is protected. This captures realistic scenarios such as road networks and telecommunication networks. Our approach consists of two rounds of communication. In the first round, each node publishes their incident weight information under local weight differential privacy while in the second round, the nodes locally count below-threshold triangles, for which we introduce a biased and unbiased variant. We further propose two different improvements. We present a pre-computation step that reduces the covariance and thereby lowers the expected error. Secondly, we develop an algorithm for computing the smooth-sensitivity, which significantly reduces the running time compared to a straightforward approach. Finally, we provide experimental results that demonstrate the differences between the biased and unbiased variants and the effectiveness of the proposed improvements.