Core Percolation in Interdependent Networks

Abstract

Core percolation, as a fundamental structural transition resulting from preserving core nodes in the network, is crucial in the network controllability and robustness. Prior art has investigated single, non-interacting complex networks where core structure plays an important role in ensuring the network robustness. In contrast, real networks are usually composed of multiple interdependent layers. Under this circumstance, the network robustness is influenced by not only the intra-layer connections, which represents the structural attributes such as node degree within the same layer, but also the inter-layer dependencies where interdependent nodes across different layers can be preserved or removed in company. In this paper, we take a first look at core percolation in multi-layer networks. For investigation, we start from the double-layer networks and propose an extended algorithm, called Correlated Greedy Leaf Removal (CGLR) procedure, that aims to preserve core nodes by recursively switching among layers in removing leaves in one layer and disenabling their interdependent nodes in other layers. Along with empirical observations, we show that intra-layer connections are manifested to be dominating in determining the existence of core nodes. But more notably, the presence of core structure with strong inter-layer dependencies always exhibits a first order phase transition at the critical point while it undergoes a continuous phase transition in the single-layer undirected networks. These findings are also extendable to networks with more layers, and is of significance in better construction and control of real-life networks.