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.

Ideology detection (ID) is important for gaining insights about peoples' opinions and stances on our world and society, which can find many applications in politics, economics and social sciences.It is not uncommon that a piece of text can contain descriptions of various issues.It is also widely accepted that a person can take different ideological stances in different facets.However, existing datasets for the ID task only label a text as ideologically left-or right-leaning as a whole, regardless whether the text containing one or more different issues.Moreover, most prior work annotates texts from data resources with known ideological bias through distant supervision approaches, which may result in many false labels.With some theoretical help from social sciences, this work first designs an ideological schema containing five domains and twelve facets for a new multifaceted ideology detection (MID) task to provide a more complete and delicate description of ideology.We construct a MITweet dataset for the MID task, which contains 12,594 English Twitter posts, each annotated with a Relevance and an Ideology label for all twelve facets.We also design and test a few of strong baselines for the MID task under in-topic and cross-topic settings, which can serve as benchmarks for further research.