Avoiding cascading failures in correlated networks of networks

Networks in nature do not act in isolation, but instead exchange information and depend on one another to function properly. Theory has shown that connecting random networks may very easily result in abrupt failures. Many organisms and biological systems in nature often interact with each other, exchanging information in a very efficient way. However, networks built by humans are more prone to cascading failures due to small perturbations, as in blackouts in power grids. Here we provide a solution to this conundrum, showing that the stability of a system of networks relies on the relation between the internal structure of a network and its pattern of connections to other networks. Specifically, we demonstrate that if interconnections are provided by network hubs, and the connections between networks are moderately convergent, the system of networks is stable and robust to failure. We test this theoretical prediction on two independent experiments of functional brain networks (in task and resting states), which show that brain networks are connected with a topology that maximizes stability according to the theory. Our results provide not only an answer to the question of why natural networks are more stable than artificial ones, but they also provide a prediction of how structured networks, whether natural or man-made, should be organized in order to acquire stability.