Many real-world interconnections among entities can be characterized as graphs. Collecting local graph information with balanced privacy and data utility has garnered notable interest recently. This paper delves into the problem of identifying and protecting critical information of entity connections for individual participants in a graph based on cohesive subgraph searches. This problem has not been addressed in the literature. To address the problem, we propose to extract the critical connections of a queried vertex using a fortress-like cohesive subgraph model known as $p$-cohesion. A user's connections within a fortress are obfuscated when being released, to protect critical information about the user. Novel merit and penalty score functions are designed to measure each participant's critical connections in the minimal $p$-cohesion, facilitating effective identification of the connections. We further propose to preserve the privacy of a vertex enquired by only protecting its critical connections when responding to queries raised by data collectors. We prove that, under the decentralized differential privacy (DDP) mechanism, one's response satisfies $(\varepsilon, \delta)$-DDP when its critical connections are protected while the rest remains unperturbed. The effectiveness of our proposed method is demonstrated through extensive experiments on real-life graph datasets.

翻译：许多现实世界中实体间的相互连接可以刻画为图。如何在平衡隐私与数据效用的前提下收集局部图信息，近期引起了广泛关注。本文研究基于凝聚子图搜索的图中个体参与者实体连接关键信息的识别与保护问题。该问题在现有文献中尚未得到解决。为此，我们提出采用一种名为$p$-凝聚的堡垒式凝聚子图模型提取查询顶点的关键连接。用户在其堡垒内部的连接在对外发布时将进行混淆处理，以保护用户的关键信息。我们设计了新颖的收益与惩罚得分函数，用于度量最小$p$-凝聚中每个参与者的关键连接，从而有效识别这些连接。我们进一步提出通过仅保护数据收集者查询时用户回答中的关键连接，来实现对查询顶点的隐私保护。我们证明，在去中心化差分隐私（DDP）机制下，当用户的关键连接受到保护而其余部分保持不变时，其回答满足$(\varepsilon, \delta)$-DDP。通过在真实图数据集上的大量实验，验证了所提方法的有效性。