Estimating Power-Law Exponent with Edge Differential Privacy

TL;DR

This paper introduces new edge differential privacy algorithms to accurately estimate the power-law exponent of graph degree distributions without revealing individual edge information.

Contribution

It proposes privatizing low-dimensional sufficient statistics instead of the entire degree distribution, improving estimation accuracy under privacy constraints.

Findings

Effective algorithms for both centralized and local DP models.

Comparison shows advantages of degree release versus log-statistics release.

Evaluation on multiple datasets demonstrates practical utility across privacy budgets.

Abstract

Many real-world graphs have degree distributions that are well approximated by a power-law, and the corresponding scaling parameter $\alpha$ provides a compact summary of that structure which is useful for graph analysis and system optimization. When graphs contain sensitive relationship data, $\alpha$ must be estimated without revealing information about individual edges. This paper studies power-law exponent estimation under edge differential privacy. Instead of first releasing a noisy degree distribution and then fitting a power-law model, we propose privatizing only the low-dimensional sufficient statistics needed to estimate $\alpha$, thereby avoiding the high distortion introduced by traditional approaches. Using these released statistics, we support both discrete approximation and likelihood-based numerical optimization for efficient parameter estimation. We develop edge-DP algorithms for both centralized and local DP models, compare degree release and log-statistic release in the local setting, and evaluate the resulting methods on various graph datasets across multiple privacy budgets and tail-cutoff settings.