The structural stability of a network reflects the ability of the network to maintain a sustainable service. As the leave of some users will significantly break network stability, it is critical to discover these key users for defending network stability. The model of k-core, a maximal subgraph where each vertex has at least k neighbors in the subgraph, is often used to measure the stability of a network. Besides, the coreness of a vertex, the largest k such that the k-core contains the vertex, is validated as the “best practice” for measuring the engagement of the vertex. In this paper, we propose and study the collapsed coreness problem: finding b vertices (users) s.t. the deletion of these vertices leads to the largest coreness loss (the total decrease of coreness from every vertex). We prove that the problem is NP-hard and hard to approximate. We show that the collapsed coreness is more effective and challenging than the existing models. An efficient greedy algorithm is proposed with powerful pruning rules. The algorithm is adapted to find the key users within a given time limit. Extensive experiments on 12 real-life graphs demonstrate the effectiveness of our model and the efficiency of the proposed method.

网络的结构稳定性反映了网络维持可持续服务的能力。由于部分用户的离开会严重破坏网络稳定性，因此发现这些关键用户对于维护网络稳定性至关重要。k -core模型是一个最大子图，其中每个顶点在子图中至少有k 个邻居，通常用于衡量网络的稳定性。此外，一个顶点的核数，最大ķ使得ķ -core包含了顶点，被确认为“最佳实践”，用于测量顶点的参与。在本文中，我们提出并研究了坍缩核心问题：找到bvertices (users) st 这些顶点的删除导致最大的coreness loss（每个顶点的coreness 总减少）。我们证明该问题是 NP-hard 且难以近似的。我们表明，折叠的核心比现有模型更有效和更具挑战性。提出了一种具有强大剪枝规则的高效贪婪算法。该算法适用于在给定的时间限制内找到关键用户。对 12 个真实图的大量实验证明了我们模型的有效性和所提出方法的效率。