On learning cluster coefficient of private networks

Enabling accurate analysis of social network data while preserving differential privacy has been challenging since graph features such as clustering coefficient or modularity often have high sensitivity, which is different from traditional aggregate functions (e.g., count and sum) on tabular data. In this paper, we treat a graph statistics as a function f and develop a divide and conquer approach to enforce differential privacy. The basic procedure of this approach is to first decompose the target computation f into several less complex unit computations $$f_1,\ldots,f_m$$f1,…,fm connected by basic mathematical operations (e.g., addition, subtraction, multiplication, division), then perturb the output of each fi with Laplace noise derived from its own sensitivity value and the distributed privacy threshold $$\epsilon_i,$$ϵi, and finally combine those perturbed fi as the perturbed output of computation f. We examine how various operations affect the accuracy of complex computations. When unit computations have large global sensitivity values, we enforce the differential privacy by calibrating noise based on the smooth sensitivity, rather than the global sensitivity. By doing this, we achieve the strict differential privacy guarantee with smaller magnitude noise. We illustrate our approach using clustering coefficient, which is a popular statistics used in social network analysis. Empirical evaluations on five real social networks and various synthetic graphs generated from three random graph models show that the developed divide and conquer approach outperforms the direct approach.