The concept of k-core in complex networks plays a key role in many applications, e.g., understanding the global structure, or identifying central/critical nodes, of a network. A malicious attacker with jamming ability can exploit the vulnerability of the k-core structure to attack the network and invalidate the network analysis methods, e.g., reducing the k-shell values of nodes can deceive graph algorithms, leading to the wrong decisions. In this paper, we investigate the robustness of the k-core structure under adversarial attacks by deleting edges, for the first time. Firstly, we give the general definition of targeted k-core attack, map it to the set cover problem which is NP-hard, and further introduce a series of evaluation metrics to measure the performance of attack methods. Then, we propose $Q$ index theoretically as the probability that the terminal node of an edge does not belong to the innermost core, which is further used to guide the design of our heuristic attack methods, namely COREATTACK and GreedyCOREATTACK. The experiments on a variety of real-world networks demonstrate that our methods behave much better than a series of baselines, in terms of much smaller Edge Change Rate (ECR) and False Attack Rate (FAR), achieving state-of-the-art attack performance. More impressively, for certain real-world networks, only deleting one edge from the k-core may lead to the collapse of the innermost core, even if this core contains dozens of nodes. Such a phenomenon indicates that the k-core structure could be extremely vulnerable under adversarial attacks, and its robustness thus should be carefully addressed to ensure the security of many graph algorithms.
翻译:复杂网络中的 k- 核心概念在许多应用中发挥着关键作用, 比如, 理解全球结构, 或者确定网络的中央/ 关键节点。 具有干扰能力的恶意攻击者可以利用 k- 核心结构的脆弱性攻击网络, 并否定网络分析方法。 例如, 降低节点的K- 壳值可以欺骗图形算法, 导致错误的决定。 本文首次通过删除边缘来调查对抗性攻击下的 k- 核心结构的稳健性。 首先, 我们给出了目标的 k- 核心攻击的一般定义, 将它映射为NP- 硬的一组覆盖问题, 并进一步推出一系列评估指标来衡量攻击方法的性能。 然后, 我们从理论上提出 $ 指数, 因为边缘的终端值可能不属于最核心的算法 。 本文中, 我们用来指导我们疯狂攻击方法的设计, 即 COREATACK 和 Greedy COARTACK 。 各种真实网络的实验显示, 真实- 核心网络的稳定性, 因此, 核心- 核心 水平 水平 可能比 核心 核心 核心 核心 核心 更能 更明显地 。