Percolation in real interdependent networks

Abstract

The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network layers has been extensively studied in recent years. However, the theoretical frameworks developed so far apply only to special models in the limit of infinite sizes. These methods are therefore of little help in practical contexts, given that real interconnected networks have finite size and their structures are generally not compatible with those of graph toy models. Here, we introduce a theoretical method that takes as inputs the adjacency matrices of the layers to draw the entire phase diagram for the interconnected network, without the need of actually simulating any percolation process. We demonstrate that percolation transitions in arbitrary interdependent networks can be understood by decomposing these system into uncoupled graphs: the intersection among the layers, and the remainders of the layers. When the intersection dominates the remainders, an interconnected network undergoes a continuous percolation transition. Conversely, if the intersection is dominated by the contribution of the remainders, the transition becomes abrupt even in systems of finite size. We provide examples of real systems that have developed interdependent networks sharing a core of "high quality" edges to prevent catastrophic failures.

7 pages, 4 figures

References in corpus (31)

• Error and attack tolerance of complex networks
• Epidemic spreading in scale-free networks
• Catastrophic cascade of failures in interdependent networks
• The spread of epidemic disease on networks
• Network robustness and fragility: Percolation on random graphs
• Spatial Networks
• Resilience of the Internet to random breakdowns
• Critical phenomena in complex networks
• The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles
• Prediction and predictability of global epidemics: the role of the airline transportation network
• Efficient Immunization Strategies for Computer Networks and Populations
• Mitigation of Malicious Attacks on Networks
• Multirelational Organization of Large-scale Social Networks in an Online World
• Spectral redemption: clustering sparse networks
• Random Walks on Multiplex Networks
• MuxViz: A Tool for Multilayer Analysis and Visualization of Networks
• Abrupt transition in the structural formation of interconnected networks
• Percolation on sparse networks
• Avoiding catastrophic failure in correlated networks of networks
• Percolation Theory on Interdependent Networks Based on Epidemic Spreading
• Percolation in Multiplex Networks with Overlap
• Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
• Self-organized adaptation of a simple neural circuit enables complex robot behaviour
• Percolation of Interdependent Networks with Inter-similarity
• The unreasonable effectiveness of tree-based theory for networks with clustering
• How to make a fragile network robust and vice versa
• Link overlap, viability, and mutual percolation in multiplex networks
• Percolation on dense graph sequences
• Tight lower bound for percolation threshold on a quasi-regular graph
• Efficient algorithm to compute mutually connected components in interdependent networks
• Efficient algorithm to study interconnected networks

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• Dynamic interdependence and competition in multilayer networks
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• Machine learning dismantling and early-warning signals of disintegration in complex systems
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• Cascading Failures in Complex Networks
• Eradicating Catastrophic Collapse in Interdependent Networks via Reinforced Nodes
• Message passing theory for percolation models on multiplex networks with link overlap
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• Bond percolation on multiplex networks
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• Irreducibility of multilayer network dynamics: the case of the voter model
• Leveraging percolation theory to single out influential spreaders in networks
• The influence of the broadness of the degree distribution on network's robustness: comparing localized attack and random attack
• Optimal resource diffusion for suppressing disease spreading in multiplex networks
• From the origin of life to pandemics: Emergent phenomena in complex systems
• $k$-core percolation on complex networks: Comparing random, localized and targeted attacks
• The dynamic nature of percolation on networks with triadic interactions
• Breaking of the site-bond percolation universality in networks
• The interdependent network of gene regulation and metabolism is robust where it needs to be
• Cascading failures in interdependent systems under a flow redistribution model
• Epidemic spreading and bond percolation in multilayer networks
• Rare events and discontinuous percolation transitions
• Beyond the locally tree-like approximation for percolation on real networks
• Characterizing the analogy between hyperbolic embedding and community structure of complex networks
• Fluctuations in percolation of sparse complex networks
• Social contagions on time-varying community networks
• Controlling the uncertain response of real multiplex networks to random damage
• Percolation in real multiplex networks
• How does bond percolation happen in coloured networks?
• Nonbacktracking expansion of finite graphs
• Clustering determines the dynamics of complex contagions in multiplex networks
• Multilayer Network Science: from Cells to Societies
• Large deviation theory of percolation on multiplex networks
• Asymmetry in interdependence makes a multilayer system more robust against cascading failures
• Correlated network of networks enhances robustness against catastrophic failures
• History-dependent percolation on multiplex networks
• k-core percolation on interdependent and interconnected multiplex networks
• Evolution Features and Behavior Characters of Friendship Networks on Campus Life
• Robustness of flow networks against cascading failures under partial load redistribution
• Percolation and the effective structure of complex networks
• Optimal percolation in correlated multilayer networks with overlap
• Shortest-path percolation on random networks
• k-core structure of real multiplex networks
• Spreading of localized attacks on spatial multiplex networks with a community structure
• Deep-learning-aided dismantling of interdependent networks
• Interdependent transport via percolation backbones in spatial networks
• Explosive percolation in thresholded networks
• Assessing Percolation Threshold Based on High-Order Non-Backtracking Matrices
• Vitality of Neural Networks under Reoccurring Catastrophic Failures
• Observability transition in real networks
• Topological Convergence of Urban Infrastructure Networks
• Observability transition in multiplex networks
• Analysis and Optimization of Robustness in Multiplex Flow Networks Against Cascading Failures
• Modeling resource consumption in the US air transportation system via minimum-cost percolation
• On the accuracy of message-passing approaches to percolation in complex networks
• Deep Learning Super-Diffusion in Multiplex Networks
• Combinatorial approach to spreading processes on networks
• Analysing Motifs in Multilayer Networks
• Random growth lattice filling model of percolation: a crossover from continuous to discontinuous transition
• The healing strategy by prioritizing minimum degree against localized attacks on interdependent spatially embedded networks
• Cascading failures in anisotropic interdependent networks of spatial modular structures