In social networks, the strength of relationships between users can significantly affect the stability of the network. Two users are more likely to build the friendship if they share some common friends. Meanwhile, the breakdown or enhancement of critical connections may lead to a cascaded phenomenon and cause the social network collapsed or reinforced. In this paper, we leverage the k-truss model to measure the stability of a social network. To identify the critical edges, we propose two novel problems named k-truss minimization problem and k-truss maximization problem. Given a social network G, a positive integer k and a budget b, it aims to find b edges for deletion (resp. addition), which can lead to the maximum number of edges collapsed (resp. added) in the k-truss of G. We prove that both problems are NP-hard. To accelerate the computation, novel pruning rules and searching paradigms are developed for the corresponding problem. Comprehensive experiments are conducted over 9 real-life networks to demonstrate the effectiveness and efficiency of our proposed models and approaches.

在社交网络中，用户之间关系的强度可以显着影响网络的稳定性。如果两个用户分享一些共同的朋友，他们更有可能建立友谊。同时，关键连接的破坏或增强可能导致级联现象，导致社交网络崩溃或加强。在本文中，我们利用k- truss 模型来衡量社交网络的稳定性。为了识别关键边，我们提出了两个新问题，分别是k- truss 最小化问题和k- truss 最大化问题。给定一个社交网络G，一个正整数k和一个预算b，它的目标是找到b删除边（相应地添加），这会导致G的k桁架中折叠（相应地添加）边的最大数量。我们证明这两个问题都是 NP 难的。为了加速计算，针对相应的问题开发了新颖的剪枝规则和搜索范式。在 9 个真实网络上进行了综合实验，以证明我们提出的模型和方法的有效性和效率。