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Analysis of centrality measures under differential privacy models

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  • Laeuchli, Jesse
  • Ramírez-Cruz, Yunior
  • Trujillo-Rasua, Rolando

Abstract

This article provides the first analysis of the differentially private computation of three centrality measures, namely eigenvector, Laplacian and closeness centralities, on arbitrary weighted graphs, using the smooth sensitivity approach. We do so by finding lower bounds on the amounts of noise that a randomised algorithm needs to add in order to make the output of each measure differentially private. Our results indicate that these computations are either infeasible, in the sense that there are large families of graphs for which smooth sensitivity is unbounded; or impractical, in the sense that even for the cases where smooth sensitivity is bounded, the required amounts of noise result in unacceptably large utility losses.

Suggested Citation

  • Laeuchli, Jesse & Ramírez-Cruz, Yunior & Trujillo-Rasua, Rolando, 2022. "Analysis of centrality measures under differential privacy models," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    • Handle: RePEc:eee:apmaco:v:412:y:2022:i:c:s0096300321006305
    DOI: 10.1016/j.amc.2021.126546
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    References listed on IDEAS

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    1. Aaron Clauset & Cristopher Moore & M. E. J. Newman, 2008. "Hierarchical structure and the prediction of missing links in networks," Nature, Nature, vol. 453(7191), pages 98-101, May.
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    1. Almaraz Luengo, Elena & Leiva Cerna, Marcos Brian & García Villalba, Luis Javier & Hernandez-Castro, Julio, 2022. "A new approach to analyze the independence of statistical tests of randomness," Applied Mathematics and Computation, Elsevier, vol. 426(C).

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