The resilience of interdependent transportation networks under targeted attack

Modern world builds on the resilience of interdependent infrastructures characterized as complex networks. Recently, a framework for analysis of interdependent networks has been developed to explain the mechanism of resilience in interdependent networks. Here we extend this interdependent network model by considering flows in the networks and study the system’s resilience under different attack strategies. In our model, nodes may fail due to either overload or loss of interdependency. Under the interaction between these two failure mechanisms, it is shown that interdependent scale-free networks show extreme vulnerability. The resilience of interdependent SF networks is found in our simulation much smaller than single SF network or interdependent SF networks without flows. Introduction. – Over the past decade, network theory has become one of the major tools in studying complex systems, and has been proved useful for the description and analysis of complex systems in various fields [1–11]. As one of the most fundamental questions, the resilience of networks has been studied intensively, which helps to provide efficient solutions to protect real networks against faults or attacks [12–16]. However, most of these studies are based on the assumption that networks are isolated, neglecting the interdependency between them. Recently, Buldyrev et al. presented a theory of interdependent networks. In their work, a mutual percolation model is proposed to study the vulnerability of network of networks where the links between the networks are interdependency links [17]. This has initiated a series of studies about various interdependent networks. Parshani et al. proposed a theoretical framework for studying the case of partially interdependent networks by defining the coupling strength q. Their findings showed that reducing the coupling strength (a)[email protected] (b)[email protected] leads to a change from first to second order percolation transition [18]. Gao et al. has generalized the theory on network of networks, showing that the percolation theory of a single network is a limiting case of this generalization [19–21]. Interdependency does exist between various networks for transferring flows including airlines, urban road networks, Internet and power grid [22–28]. The failure of network components, either by random breakdown or intentional attacks, could change the balance of flows causing overloads and trigger the cascading failures, which probably ends up with catastrophes [12, 13, 29–33]. In single networks, Motter et al. presented a model to consider a cascade of overload failures [12,13]. In this paper, we generalize it to interdependent networks, study their resilience against cascading failures caused by both overloads and by loss of interdependency under random or intentional attack strategies. Firstly we study the resilience of interdependent scale-free networks under different attacks and explore in detail how the resilience depend on scaling exponent γ of degree distributions. Secondly, we study how the interdependent Erdős-Rényi networks respond to dif-