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.

通过对余弦相似度为基础的边重建攻击（COSERA）进行理论和实证研究，本文揭示了图神经模型中结构性漏洞的存在，这些漏洞导致了敏感拓扑信息的推测，同时还探讨了通过噪声聚合机制（NAG）生成的（可证明的）私有图表示对 COSERA 攻击的弹性，以及 COSERA 在隐私和效用之间权衡的表现。