Consistent Spectral Clustering of Network Block Models under Local Differential Privacy

Main Article Content

Jonathan Hehir
Aleksandra Slavkovic
Xiaoyue Niu


The stochastic block model (SBM) and degree-corrected block model (DCBM) are network models often selected as the fundamental setting in which to analyze the theoretical properties of community detection methods. We consider the problem of spectral clustering of SBM and DCBM networks under a local form of edge differential privacy. Using a randomized response privacy mechanism called the edge-flip mechanism, we develop theoretical guarantees for differentially private community detection, demonstrating conditions under which this strong privacy guarantee can be upheld while achieving spectral clustering convergence rates that match the known rates without privacy. We prove the strongest theoretical results are achievable for dense networks (those with node degree linear in the number of nodes), while weak consistency is achievable under mild sparsity (node degree greater than $\sqrt{n}$). We empirically demonstrate our results on a number of network examples.

Article Details

How to Cite
Hehir, Jonathan, Aleksandra Slavkovic, and Xiaoyue Niu. 2022. “Consistent Spectral Clustering of Network Block Models under Local Differential Privacy”. Journal of Privacy and Confidentiality 12 (2).
TPDP 2021
Author Biographies

Aleksandra Slavkovic, Penn State University

Professor of Statistics, Penn State University

Xiaoyue Niu, Penn State University

Associate Research Professor, Department of Statistics, Penn State University