Differentially Private Guarantees for Analytics and Machine Learning on Graphs: A Survey of Results

We study the applications of differential privacy (DP) in the context of graph-structured data and discuss the formulations of DP applicable to the publication of graphs and their associated statistics as well as machine learning on graph-based data, including graph neural networks (GNNs). Interpreting DP guarantees in the context of graph-structured data can be challenging, as individual data points are interconnected (often non-linearly or sparsely). This connectivity complicates the computation of individual privacy loss in differentially private learning. The problem is exacerbated by an absence of a single, well-established formulation of DP in graph settings. This issue extends to the domain of GNNs, rendering private machine learning on graph-structured data a challenging task. A lack of prior systematisation work motivated us to study graph-based learning from a privacy perspective. In this work, we systematise different formulations of DP on graphs, discuss challenges and promising applications, including the GNN domain. We compare and separate works into graph analytics tasks and graph learning tasks with GNNs. We conclude our work with a discussion of open questions and potential directions for further research in this area.