Group percolation in interdependent networks

TL;DR

This paper introduces a new group percolation model in interdependent networks, showing that group formation enhances network resilience but results in only first-order phase transitions, with implications for network robustness.

Contribution

The study develops a theoretical framework for group percolation in interdependent networks and demonstrates the impact of group formation on network resilience and phase transition nature.

Findings

Group formation improves network robustness.

Percolation transition remains first order regardless of group size distribution.

Mapping to inter-similarity structures confirms non-continuous phase transitions.

Abstract

In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under attacks. In this model, nodes belonging to the same group survive or fail together. We develop a theoretical framework for this novel group percolation and find that the formation of groups can improve the resilience of interdependent networks significantly. However, the percolation transition is always of first order, regardless of the distribution of group sizes. As an application, we map the interdependent networks with inter-similarity structures, which attract many attentions very recently, onto the group percolation and confirm the non-existence of continuous phase transitions.