How do we interpret the differential privacy (DP) guarantee for network data? We take a deep dive into a popular form of network DP (ε--edge DP) to find that many of its common interpretations are flawed. Drawing on prior work for privacy with correlated data, we interpret DP through the lens of adversarial hypothesis testing and demonstrate a gap between the pairs of hypotheses actually protected under DP (tests of complete networks) and the sorts of hypotheses implied to be protected by common claims (tests of individual edges). We demonstrate some conditions under which this gap can be bridged, while leaving some questions open. While some discussion is specific to edge DP, we offer selected results in terms of abstract DP definitions and provide discussion of the implications for other forms of network DP.
@article{arxiv.2504.12520,
title = {Interpreting Network Differential Privacy},
author = {Jonathan Hehir and Xiaoyue Niu and Aleksandra Slavkovic},
journal= {arXiv preprint arXiv:2504.12520},
year = {2025}
}