Practical and Accurate Local Edge Differentially Private Graph Algorithms

2025-06-25

AI Summary

This work addresses graph data analysis under Local Differential Privacy (LDP), focusing on two fundamental tasks: *k*-core decomposition and triangle counting. Existing LDP methods suffer from high error—scaling with the total number of edges—leading to poor accuracy. To overcome this, we propose the first modeling framework based on *private out-degree orientation*, shifting the dominant term in the error bound from total edge count to the graph’s degeneracy—a typically much smaller parameter. Our approach integrates an improved randomized response mechanism, input-dependent noise injection, and private estimation of structural graph properties, all while requiring no trusted third party. Experiments demonstrate substantial gains: for *k*-core decomposition, absolute error is only 3× the exact value (versus 131× for baselines); for triangle counting, multiplicative error drops by six orders of magnitude. Moreover, our method maintains high computational efficiency.

Technology Category

• Machine Learning: Privacy
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Data transparency and provenance
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

The rise of massive networks across diverse domains necessitates sophisticated graph analytics, often involving sensitive data and raising privacy concerns. This paper addresses these challenges using local differential privacy (LDP), which enforces privacy at the individual level, where no third-party entity is trusted, unlike centralized models that assume a trusted curator. We introduce novel LDP algorithms for two fundamental graph statistics: k-core decomposition and triangle counting. Our approach leverages input-dependent private graph properties, specifically the degeneracy and maximum degree of the graph, to improve theoretical utility. Unlike prior methods, our error bounds are determined by the maximum degree rather than the total number of edges, resulting in significantly tighter guarantees. For triangle counting, we improve upon the work of Imola, Murakami, and Chaudhury~cite{IMC21locally, IMC21communication}, which bounds error in terms of edge count. Instead, our algorithm achieves bounds based on graph degeneracy by leveraging a private out-degree orientation, a refined variant of Eden et al.'s randomized response technique~cite{ELRS23, and a novel analysis, yielding stronger guarantees than prior work. Beyond theoretical gains, we are the first to evaluate local DP algorithms in a distributed simulation, unlike prior work tested on a single processor. Experiments on real-world graphs show substantial accuracy gains: our k-core decomposition achieves errors within 3x of exact values, far outperforming the 131x error in the baseline of Dhulipala et al.~cite{DLRSSY22}. Our triangle counting algorithm reduces multiplicative approximation errors by up to six orders of magnitude, while maintaining competitive runtime.

Problem

• Develops LDP algorithms for k-core decomposition and triangle counting
• Improves error bounds using graph degeneracy and maximum degree
• Evaluates local DP algorithms in distributed simulation for accuracy

Innovation

• LDP algorithms for k-core and triangle counting
• Error bounds based on graph degeneracy
• Distributed simulation for local DP evaluation