{"ID":2863936,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.25431","arxiv_id":"2509.25431","title":"Generating Differentially Private Networks with a Modified Erdős-Rényi Model","abstract":"Differential privacy has been used to privately calculate numerous network properties, but existing approaches often require the development of a new privacy mechanism for each property of interest. Therefore, we present a framework for generating entire networks in a differentially private way. Differential privacy is immune to post-processing, which allows for any network property to be computed and analyzed for a private output network, without weakening its protections. We consider undirected networks and develop a differential privacy mechanism that takes in a sensitive network and outputs a private network by randomizing its edge set. We prove that this mechanism does provide differential privacy to a network's edge set, though it induces a complex distribution over the space of output graphs. We then develop an equivalent privacy implementation using a modified Erdős-Rényi model that constructs an output graph edge by edge, and it is efficient and easily implementable, even on large complex networks. Experiments implement $\\varepsilon$-differential privacy with $\\varepsilon=2.5$ when computing graph Laplacian spectra, and these results show the proposed mechanism incurs $49.34\\%$ less error than the current state of the art.","short_abstract":"Differential privacy has been used to privately calculate numerous network properties, but existing approaches often require the development of a new privacy mechanism for each property of interest. Therefore, we present a framework for generating entire networks in a differentially private way. Differential privacy is...","url_abs":"https://arxiv.org/abs/2509.25431","url_pdf":"https://arxiv.org/pdf/2509.25431v1","authors":"[\"Huaiyuan Rao\",\"Calvin Hawkins\",\"Alexander Benvenuti\",\"Matthew Hale\"]","published":"2025-09-29T19:40:34Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}