Many real-world graphs have degree distributions that are well approximated by a power-law, and the corresponding scaling parameter $α$ provides a compact summary of that structure which is useful for graph analysis and system optimization. When graphs contain sensitive relationship data, $α$ 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 $α$, 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.

翻译：许多真实世界图的度分布可由幂律很好地近似，对应的标度参数α为图分析与系统优化提供了该结构的紧凑总结。当图包含敏感关系数据时，需在不泄露单条边信息的前提下估计α。本文研究边差分隐私下的幂律指数估计。不同于先发布带噪度分布再拟合幂律模型，我们提出仅对估计α所需的低维充分统计量进行私有化，从而避免传统方法引入的高噪声。利用发布的统计量，我们支持离散近似与基于似然的数值优化以实现高效参数估计。针对中心化与本地化两种差分隐私模型，我们开发了边差分隐私算法，在本地场景下比较了度发布与对数统计量发布，并在多种隐私预算与尾部截断设置下，使用不同图数据集评估了所提方法。