Analysis of centrality measures under differential privacy models

TL;DR

This paper analyzes the challenges of computing eigenvector, Laplacian, and closeness centralities under differential privacy, revealing fundamental limitations and impractical noise requirements for arbitrary weighted graphs.

Contribution

First analysis of differentially private centrality measures on weighted graphs using smooth sensitivity, highlighting feasibility and utility challenges.

Findings

Smooth sensitivity can be unbounded for many graphs.

Required noise levels often cause significant utility loss.

Computing these measures privately is generally infeasible or impractical.

Abstract

This paper 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.