PGB: Benchmarking Differentially Private Synthetic Graph Generation Algorithms

Differentially private graph analysis is a powerful tool for deriving insights from diverse graph data while protecting individual information. Designing private analytic algorithms for different graph queries often requires starting from scratch. In contrast, differentially private synthetic graph generation offers a general paradigm that supports one-time generation for multiple queries. Although various differentially private graph generation algorithms have been proposed, comparing them effectively remains challenging due to various factors, including differing privacy definitions, diverse graph datasets, varied privacy requirements, and multiple utility metrics. To this end, we propose PGB (Private Graph Benchmark), a comprehensive benchmark designed to enable researchers to compare differentially private graph generation algorithms fairly. We begin by identifying four essential elements of existing works as a 4-tuple: mechanisms, graph datasets, privacy requirements, and utility metrics. We discuss principles regarding these elements to ensure the comprehensiveness of a benchmark. Next, we present a benchmark instantiation that adheres to all principles, establishing a new method to evaluate existing and newly proposed graph generation algorithms. Through extensive theoretical and empirical analysis, we gain valuable insights into the strengths and weaknesses of prior algorithms. Our results indicate that there is no universal solution for all possible cases. Finally, we provide guidelines to help researchers select appropriate mechanisms for various scenarios.