Graph representation learning (GRL) is critical for extracting insights from complex network structures, but it also raises security concerns due to potential privacy vulnerabilities in these representations. This paper investigates the structural vulnerabilities in graph neural models where sensitive topological information can be inferred through edge reconstruction attacks. Our research primarily addresses the theoretical underpinnings of cosine-similarity-based edge reconstruction attacks (COSERA), providing theoretical and empirical evidence that such attacks can perfectly reconstruct sparse Erdos Renyi graphs with independent random features as graph size increases. Conversely, we establish that sparsity is a critical factor for COSERA's effectiveness, as demonstrated through analysis and experiments on stochastic block models. Finally, we explore the resilience of (provably) private graph representations produced via noisy aggregation (NAG) mechanism against COSERA. We empirically delineate instances wherein COSERA demonstrates both efficacy and deficiency in its capacity to function as an instrument for elucidating the trade-off between privacy and utility.

翻译：图表示学习对于从复杂网络结构中提取关键信息至关重要，但其潜在隐私脆弱性也引发了安全担忧。本文研究了图神经模型中可通过边重建攻击推断敏感拓扑信息的结构脆弱性。研究主要聚焦于基于余弦相似度的边重建攻击的理论基础，通过理论推导与实验验证表明：当图规模增大时，此类攻击能够完美重建具有独立随机特征的稀疏埃尔德什-雷尼图。同时，我们通过随机块模型的分析与实验证明，稀疏性是决定COSERA有效性的关键因素。最后，我们探究了通过噪声聚合机制产生的（可证明）隐私保护图表示对COSERA的鲁棒性，并实证划分了COSERA在阐明隐私-效用权衡中兼具有效性与局限性的典型场景。