Differentially Private Synthetic Graphs Preserving Triangle-Motif Cuts
Pan Peng, Hangyu Xu

TL;DR
This paper introduces a differentially private mechanism for generating synthetic graphs that accurately approximate triangle-motif sizes across all cuts, balancing privacy with utility in complex network analysis.
Contribution
It presents the first $(,)$-DP algorithm for approximating triangle-motif cuts in graphs, with proven lower bounds and extensions to weighted graphs and larger motifs.
Findings
Achieves polynomial-time synthetic graph generation with bounded additive error.
Provides a lower bound on the error for DP algorithms answering triangle-motif queries.
Extends the approach to weighted graphs and larger motifs.
Abstract
We study the problem of releasing a differentially private (DP) synthetic graph that well approximates the triangle-motif sizes of all cuts of any given graph , where a motif in general refers to a frequently occurring subgraph within complex networks. Non-private versions of such graphs have found applications in diverse fields such as graph clustering, graph sparsification, and social network analysis. Specifically, we present the first -DP mechanism that, given an input graph with vertices, edges and local sensitivity of triangles , generates a synthetic graph in polynomial time, approximating the triangle-motif sizes of all cuts of the input graph up to an additive error of . Additionally, we provide a lower bound of…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Privacy-Preserving Technologies in Data · Advanced Graph Theory Research
