Avoiding catastrophic failure in correlated networks of networks

Abstract

Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in abrupt failures. This theoretical finding bares an intrinsic paradox: If natural systems organize in interconnected networks, how can they be so stable? 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 network inter-connections are provided by hubs of the network and if there is a moderate degree of convergence of inter-network connection the systems of network are stable and robust to failure. We test this theoretical prediction in 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.

40 pages, 7 figures

References in corpus (5)

• Power-law distributions in empirical data
• Scale-free brain functional networks
• Percolation on interacting networks
• Scaling of degree correlations and the influence on diffusion in scale-free networks
• Brain modularity controls the critical behavior of spontaneous activity

Cited by in corpus (14)

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• Redundant interdependencies boost the robustness of multilayer networks
• Cascading Failures in Complex Networks
• Epidemic spreading and bond percolation in multilayer networks
• Cascading failures in scale-free interdependent networks
• Clustering determines the dynamics of complex contagions in multiplex networks
• Asymmetry in interdependence makes a multilayer system more robust against cascading failures
• Diverse types of percolation transitions
• Supersymmetric multiplex networks described by coupled Bose and Fermi statistics
• Abrupt transition due to non-local cascade propagation in multiplex systems
• Identification of highly susceptible individuals in complex networks
• Enhanced robustness of single-layer networks with redundant dependencies
• Vitality of Neural Networks under Reoccurring Catastrophic Failures
• The State of the Art in Multilayer Network Visualization