k-core percolation on interdependent and interconnected multiplex networks

TL;DR

This paper analyzes the robustness of interdependent multiplex networks under k-core percolation, revealing complex phase transitions influenced by inter-layer coupling strength and network type, with theoretical and simulation validation.

Contribution

It introduces an analytical framework for k-core percolation on multiplex networks with interdependence and interconnected links, uncovering diverse phase transition behaviors.

Findings

Giant component size exhibits first- and second-order transitions depending on coupling strength.

System robustness increases with stronger dependency on initially robust networks.

Transition types differ between ER-ER and SF-SF multiplex networks under varying coupling conditions.

Abstract

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 a threshold of less than k neighbors. By deriving the self-consistency equations, we solve the key quantities of interests such as the critical threshold and size of the giant component analytically and validate the theoretical results with 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 simultaneously. The system is more robust if the dependency on the initial 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 other conditions.