Catastrophic cascade of failures in interdependent networks

Power outages: catastrophic failure of linked networks On 28 September 2003, Italy suffered a near-nationwide power cut (Sicily was spared) that also brought down the Internet. Buldyrev et al . take this event, typical of a number that have occurred worldwide in recent years, and examine how such a cascade of failures involving independent networks can occur. They find that, surprisingly, a broader degree of distribution increases the vulnerability of interdependent networks to random failure — the opposite of what happens in a single network. This highlights the need to consider interdependent network properties when designing robust networks if a random failure is not to have catastrophic results. Modern networks are rarely independent, instead being coupled together with many others. Thus the failure of a small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. Here, a framework is developed for understanding the robustness of interacting networks subject to such 'cascading' failures. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure. Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 . Modern systems are coupled together 15 , 16 , 17 , 18 , 19 and therefore should be modelled as interdependent networks. A fundamental property of interdependent networks is that failure of nodes in one network may lead to failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. A dramatic real-world example of a cascade of failures (‘concurrent malfunction’) is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations 20 . Here we develop a framework for understanding the robustness of interacting networks subject to such cascading failures. We present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two inte