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都能很好地近似为幂律分布，其缩放参数$α$提供了该结构的紧凑摘要，有助于图分析与系统优化。当图包含敏感关系数据时，必须在不泄露个体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。不同于先发布带噪声的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隐私化处理，从而避免传统方法引入的高失真。利用这些发布的统计量，我们支持离散近似和基于似然的数值优化两种高效参数估计方法。我们为集中式与本地差分隐私模型设计了边差分隐私算法，在本地设置下比较了度发布与对数统计量发布两种方式，并在多种图数据集上评估了所提方法在不同隐私预算与尾部截断阈值设定下的性能。