Correlated network of networks enhances robustness against catastrophic failures.

Networks in nature rarely function in isolation but instead interact with one another with a form of network of networks (NoN). Network of networks with interdependency between distinct networks contains instabilities of abrupt collapse related to the global rule of activation. As a remedy of the collapse instability, here we investigate a model of correlated NoN and find that the collapse instabilities can be removed with a specific pattern of correlated connectivity. We find that when hubs provide majority of interconnections and interconnections are convergent, a system of networks becomes stable systematically. Our study identifies a stable structure of correlated NoN against catastrophic failures. Our result further suggests a plausible way to enhance network robustness by manipulating connection patterns, along with other methods such as controlling the state of node based on local rule.