Interdependent networks with redundant and dependent interconnections

For complex systems, the effect of increasing the complexity may either enhance the robustness or aggravate the fragility of the systems. In order to understand the two-fold effect of the complexity, in this paper we use interdependent networks to represent the complex systems, and introduce the redundant and dependent connections across different layers (interconnections) to study how the complexity influence the robustness and fragility of the systems. Specifically, we consider the redundant and dependent interconnections from two aspects which are the number of the layers and the number of multiple connections among nodes in different layers. By adopting a message-passing approach, we show that the addition of redundant interlayer connections could enhance the robustness of the systems, and conversely, the fragility of the systems aggravates with additional dependent interlayer connections. Furthermore, we find that the influence from the aspect of the number of multiple connections among nodes are stronger than the aspect from the number of layers.