Robustness analysis of k-core percolation on asymmetric interdependent networks

Asymmetric interdependency phenomenon is widely present in real networks, but the vast majority of the existing researches are on symmetric interdependent networks, in which when one party is failed and the other one will be failed as well. While in the asymmetric interdependent networks (AINs), the dependency relationships are unidirectional, the failure for one part may not necessarily result in that for the other part. Consequently, the exploration on the robustness of AINs is very important and meaningful. While k-core percolation theory provides an effective tool on the analysis of network performance, for this paper, we aims to the analysis on robustness of AINs with use of it. A scale gap threshold θ is defined to analyze the tolerance between dependent nodes. Then the k-core percolation equation for AINs is derived to analyze the types of phase transition. The simulations on different networks imply that the robustness of networks is improved after the introduction of asymmetric relation. It can be obtained that the reduction of θ can make the network robustness further improved, and the network exists continuous phase transition only when k=1,2, while it has a discontinuous phase transition with square root behavior at the critical point when k≥3. Finally, based on the characteristics of k-core structure and asymmetric dependency, and with consideration of the effect upon node failure, an improved edge attack strategy is put forward. Compared with several other attack strategies, the significance for the proposed strategy is proved by experimental simulation. This study will be beneficial for understanding the hierarchical structure of AINs and optimizing the network design, and it also provides a basis for further identifying the key nodes and vulnerable links of AINs.