Hybrid-radius spatial network model and its robustness analysis

In many real-world complex networks, their nodes are constrained by spatial positions, which we call spatial networks. Transmission delay and energy consumption are two key performance indicators to make the spatial network work normally, and they exist certain contradictions, i.e., reducing the transmission delay will increase energy consumption, and vice versa. In this paper, a new spatial network model named hybrid-radius spatial network is proposed to balance these two indicators. In this model, the connectivity radii of nodes have two types – the small radius and large radius. First, we study two performance indicators of the hybrid-radius spatial network to make sure that the generated network has a relatively smaller transmission delay and lower energy consumption. Then, we study cascading failures in the hybrid-radius spatial network and compare it with the small-radius spatial network and the large-radius spatial network. On this basis, we further analyze the relationship between the topological characteristics and robustness of this model. Our results show that this model has a heterogeneous betweenness distribution, which leads to its "robust yet fragile" property. In general, the robustness of the hybrid-radius spatial network is between the small-radius spatial network and the large-radius spatial network. The hybrid-radius spatial network model proposed in this paper can provide a simple but effective tool for the study of spatial networks, and the research on the robustness of it can also provide reference for the planning of real-world spatial networks.