Networks in nature rarely function in isolation but instead interact with oneanother with a form of network of networks (NoN). Network of networks withinterdependency between distinct networks contains instabilities of abruptcollapse related to the global rule of activation. As a remedy of the collapseinstability, here we investigate a model of correlated NoN and find that thecollapse instabilities can be removed with a specific pattern of correlatedconnectivity. We find that when hubs provide majority of interconnections andinterconnections are convergent, a system of networks becomes stablesystematically. Our study identifies a stable structure of correlated NoNagainst catastrophic failures. Our result further suggests a plausible way toenhance network robustness by manipulating connection patterns, along withother methods such as controlling the state of node based on local rule.
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