2022/11/28 by Calvin Hawkins, Hawkins, Calvin, Bo Chen +5 · 5 citations
Computer Science · Mathematics · #FOS: Mathematics #Internet Traffic Analysis and Secure E-voting #Optimization and Control (math.OC) #Privacy-Preserving Technologies in Data #Random Matrices and Applications #math.OC
paper · pdf · doi:10.48550/arxiv.2211.15366
arXiv admin note: text overlap with arXiv:2104.00654
arxiv created 2022/11/28 · openalex publication_date 2022/11/28 · arxiv updated 2022/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper develops a framework for privatizing the spectrum of the graph Laplacian of an undirected graph using differential privacy. We consider two privacy formulations. The first obfuscates the presence of edges in the graph and the second obfuscates the presence of nodes. We compare these two privacy formulations and show that the privacy formulation that considers edges is better suited to most engineering applications. We use the bounded Laplace mechanism to provide differential privacy to the eigenvalues of a graph Laplacian, and we pay special attention to the algebraic connectivity, which is the Laplacian's second smallest eigenvalue. Analytical bounds are presented on the the accuracy of the mechanisms and on certain graph properties computed with private spectra. A suite of numerical examples confirms the accuracy of private spectra in practice.