Volume 133, Number 4, February 2021
|Number of page(s)||7|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||29 March 2021|
k-core percolation on interdependent and interconnected multiplex networks
1 School of Computer Science, Southwest Petroleum University - Chengdu 610500, China
2 Cybersecurity Research Institute, Sichuan University - Chengdu 610065, China
Received: 10 December 2020
Accepted: 27 January 2021
Many real-world networks are coupled together to maintain their normal functions. Here we study the robustness of multiplex networks with interdependent and interconnected links under k -core percolation, where a node fails when it connects to less than k neighbors. By deriving the self-consistent equations, we solve the key quantities of interests such as the critical threshold and size of the giant component and validate the theoretical predictions by numerical simulations. We find a rich phase transition phenomenon as we tune the inter-layer coupling strength. Specifically speaking, in the ER-ER multiplex networks, with the increase of coupling strength, the size of the giant component in each layer first undergoes a first-order transition and then a second-order transition and finally a first-order transition. This is due to the nature of inter-layer links with both connectivity and dependency. The system is more robust if the dependency on the initially robust network is strong and more vulnerable if the dependency on the initial attacked network is strong. These effects are even amplified in the cascading process. When applying our model to the SF-SF multiplex networks, the type of transition changes. The system undergoes a first-order phase transition first only when the two layers' mutually coupling is very strong and a second-order transition in all other conditions.
PACS: 89.75.Fb – Structures and organization in complex systems / 87.23.Ge – Dynamics of social systems / 89.75.-k – Complex systems
© 2021 EPLA
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