Defending core-periphery structure in networks against multiple localized attacks

The core-periphery structure is a typical representative of the mesoscale structure in networks, which dominates the basic and potential function of the networked systems. In reality, networks inevitably face attacks, among which localized attacks have received much increasing attention since they provide efficient models for typical disruptive scenarios. However, the existing research primarily focuses on a single localized attack, with limited studies addressing multiple localized attacks, particularly regarding the impact on core-periphery structures. Here, we propose a framework for multiple localized attacks and introduce a new index to assess the vulnerability of core-periphery structure within our framework. Enhancing algorithm based on the proposed framework and index is exquisitely designed. Experimental results indicate that the algorithm can effectively measure and enhance the robustness of core-periphery structure within a limited defense budget. Furthermore, we discover the structural characteristics of the network that influence its core-periphery vulnerability. The interesting differences in defense strategies when optimizing various networks are also discussed.