Privacy-Preserving Triangle Counting in Directed Graphs

In directed graphs, the relationship between users is asymmetric, resulting in two types of triangles: cycle triangles and flow triangles. This paper studies the problem of privacy-preserving triangle counting in directed graphs. Based on different applications, we consider two scenarios, i.e., trusted and untrusted servers. In the literature, privacy-preserving triangle counting in undirected graphs has been widely studied. However, directly applying these algorithms to address our problem suffers from many issues. Concretely, for the trusted server scenario, the differentially private triangle counting algorithms, designed for undirected graphs, exhibit suboptimal performance when applied to directed graphs. Hence, we propose a new centralized differentially private algorithm that adds Laplacian noise to the exact numbers by analyzing global sensitivity. Furthermore, for the untrusted server scenario, the existing techniques cannot be used to count cycle and flow triangles with differential privacy because the local view of each user in directed graphs is limited to out-neighbors rather than all neighbors. Therefore, we design a novel locally differentially private algorithm to provide local unbiased estimation, which implies that after aggregating all the local estimations on the central server side, an unbiased estimation for the numbers of cycle and flow triangles is deduced. Empirical experiments on six real-world graph datasets demonstrate that our proposed algorithms achieve high efficiency and utility.