Robustness and resilience of complex networks

Abstract

Complex networks are ubiquitous: a cell, the human brain, a group of people and the Internet are all examples of interconnected many-body systems characterized by macroscopic properties that cannot be trivially deduced from those of their microscopic constituents. Such systems are exposed to both internal, localized, failures and external disturbances or perturbations. Owing to their interconnected structure, complex systems might be severely degraded, to the point of disintegration or systemic dysfunction. Examples include cascading failures, triggered by an initially localized overload in power systems, and the critical slowing downs of ecosystems which can be driven towards extinction. In recent years, this general phenomenon has been investigated by framing localized and systemic failures in terms of perturbations that can alter the function of a system. We capitalize on this mathematical framework to review theoretical and computational approaches to characterize robustness and resilience of complex networks. We discuss recent approaches to mitigate the impact of perturbations in terms of designing robustness, identifying early-warning signals and adapting responses. In terms of applications, we compare the performance of the state-of-the-art dismantling techniques, highlighting their optimal range of applicability for practical problems, and provide a repository with ready-to-use scripts, a much-needed tool set.

References in corpus (125)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Error and attack tolerance of complex networks
• Assortative mixing in networks
• Catastrophic cascade of failures in interdependent networks
• The architecture of complex weighted networks
• Functional cartography of complex metabolic networks
• Epidemic processes in complex networks
• Random graphs with arbitrary degree distributions and their applications
• Synchronization in complex networks
• Multilayer Networks
• Mixing patterns in networks
• Benchmark graphs for testing community detection algorithms
• The structure and dynamics of multilayer networks
• Network robustness and fragility: Percolation on random graphs
• Critical phenomena in complex networks
• Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
• Hierarchical structure and the prediction of missing links in networks
• Hierarchical Organization in Complex Networks
• Cascade-based attacks on complex networks
• Attack vulnerability of complex networks
• Community detection in networks: A user guide
• Breakdown of the Internet under intentional attack
• Influence maximization in complex networks through optimal percolation
• Mitigation of Malicious Attacks on Networks
• Mathematical Formulation of Multi-Layer Networks
• The physics of higher-order interactions in complex systems
• Scale-free networks are rare
• Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
• Cascade control and defense in complex networks
• Modeling Cascading Failures in the North American Power Grid
• k-core organization of complex networks
• Robustness of a Network of Networks
• Betweenness Centrality in Large Complex Networks
• The physics of spreading processes in multilayer networks
• Assessing the risks of "infodemics" in response to COVID-19 epidemics
• Universal behavior in a generalized model of contagion
• Clique percolation in random networks
• Suppressing cascades of load in interdependent networks
• Random graphs with clustering
• Efficiency of Scale-Free Networks: Error and Attack Tolerance
• Vulnerability and Protection of Critical Infrastructures
• Oscillators that sync and swarm
• Percolation on complex networks: Theory and application
• Cascade Dynamics of Multiplex Propagation
• Small vulnerable sets determine large network cascades in power grids
• Percolation Critical Exponents in Scale-Free Networks
• Inter-similarity between coupled networks
• The extreme vulnerability of interdependent spatially embedded networks
• Percolation on sparse networks
• Network dismantling
• Dynamically induced cascading failures in power grids
• Avoiding catastrophic failure in correlated networks of networks
• "Explosive Percolation" Transition is Actually Continuous
• The Physics of Financial Networks
• The Anatomy of a Scientific Rumor
• Sandpile on Scale-Free Networks
• Percolation Theory on Interdependent Networks Based on Epidemic Spreading
• Interdependent networks with correlated degrees of mutually dependent nodes
• Percolation in real interdependent networks
• Network resilience
• Network Geometry
• Multiplexity-facilitated cascades in networks
• Generalized Network Dismantling
• Bootstrap Percolation on Complex Networks
• Optimization of Robustness of Complex Networks
• Critical load and congestion instabilities in scale-free networks
• Explosive Phenomena in Complex Networks
• Percolation and Epidemic Thresholds in Clustered Networks
• 20 years of network community detection
• Towards designing robust coupled networks
• Exact solution of site and bond percolation on small-world networks
• Explosive Percolation is Continuous, but with Unusual Finite Size Behavior
• Identifying optimal targets of network attack by belief propagation
• Early-warning signals of topological collapse in interbank networks
• Scale-free Networks Well Done
• Fast and simple decycling and dismantling of networks
• Percolation on correlated networks
• Recent advances and open challenges in percolation
• Modeling sequences and temporal networks with dynamic community structures
• Systemic risk analysis in reconstructed economic and financial networks
• Machine learning dismantling and early-warning signals of disintegration in complex systems
• Immunization and targeted destruction of networks using explosive percolation
• Clustering in complex networks. II. Percolation properties
• Cascading Failures in Complex Networks
• Threshold model of cascades in temporal networks
• Multiscale unfolding of real networks by geometric renormalization
• Cascades on a class of clustered random networks
• Predicting percolation thresholds in networks
• Optimal percolation on multiplex networks
• Multiple Tipping Points and Optimal Repairing in Interacting Networks
• Cascading Dynamics in Modular Networks
• The dynamical structure of political corruption networks
• True scale-free networks hidden by finite size effects
• Collective influence in evolutionary social dilemmas
• Sandpile avalanche dynamics on scale-free networks
• Optimizing spread dynamics on graphs by message passing
• Breaking of the site-bond percolation universality in networks
• Effects of temporal correlations on cascades: Threshold models on temporal networks
• Tight lower bound for percolation threshold on a quasi-regular graph
• Beyond the locally tree-like approximation for percolation on real networks
• Analysis of a threshold model of social contagion on degree-correlated networks
• A Nonconservative Earthquake Model of Self-Organized Criticality on a Random Graph
• Early warning signs in social-ecological networks
• The nested structural organization of the worldwide trade multi-layer network
• Testing statistical laws in complex systems
• Diffusion geometry unravels the emergence of functional clusters in collective phenomena
• Fundamental difference between superblockers and superspreaders in networks
• Modeling Structure and Resilience of the Dark Network
• Non-Markovian recovery makes complex networks more resilient against large-scale failures
• Early warning signs for saddle-escape transitions in complex networks
• Message passing methods on complex networks
• Multilayer Network Science: from Cells to Societies
• Unraveling the effects of multiscale network entanglement on disintegration of empirical systems
• Asymmetric percolation drives a double transition in sexual contact networks
• Cavity analysis on the robustness of random networks against targeted attacks: Influences of degree-degree correlations
• Quantifying efficient information exchange in real network flows
• Percolation on feature-enriched interconnected systems
• Smeared phase transitions in percolation on real complex networks
• Network Overload due to Massive Attacks
• Effectiveness of dismantling strategies on moderated vs. unmoderated online social platforms
• Abrupt transition due to non-local cascade propagation in multiplex systems
• Non-Markovian random walks characterize network robustness to nonlocal cascades
• Degree-targeted cascades in modular, degree-heterogeneous networks

Cited by in corpus (30)

• Reputation in public goods cooperation under double Q-learning protocol
• Path Percolation in Quantum Communication Networks
• Multi-Species Cohesion: Humans, machinery, AI and beyond
• Shortest-path percolation on random networks
• Deep-learning-aided dismantling of interdependent networks
• Can Large Language Models Be Trusted as Evolutionary Optimizers for Network-Structured Combinatorial Problems?
• Higher-order triadic percolation on random hypergraphs
• General theory for extended-range percolation on simple and multiplex networks
• Effect of clustering on Turing instability in complex networks
• Universal vulnerability in strong modular networks with various degree distributions between inequality and equality
• Robustness of Decentralised Learning to Nodes and Data Disruption
• Understanding Trends, Patterns, and Dynamics in Global Company Acquisitions: A Network Perspective
• Triadic percolation on multilayer networks
• The behavior of rich-club coefficient in scale-free networks
• Efficient and faithful reconstruction of dynamical attractors using homogeneous differentiators
• A statistical mechanics investigation of Unfolded Protein Response across organisms
• Mixed strategy approach destabilizes cooperation in finite populations with clustering coefficient
• Coprime networks of the composite numbers: pseudo-randomness and synchronizability
• gPC-based robustness analysis of neural systems through probabilistic recurrence metrics
• Identifying Central Nodes in Multiplex Networks by Embracing Layer-Specific Heterogeneity via DomiRank
• Ordinal language of antipersistent binary walks
• Superexponential growth of epidemics in networks with cliques
• A Compounded Burr Probability Distribution for Fitting Heavy-Tailed Data with Applications to Biological Networks
• Nonlinear dynamics of information overload: Impact on source localization in complex networks
• Irregular Metamaterial Networks
• Nonmonotonic percolation threshold in correlated networks and hypergraphs
• Modeling Epidemic Dynamics of Mutant Strains with Evolutionary Game-based Vaccination Behavior
• Robustness of complexity estimation in event-driven signals against accuracy of event detection method
• Shortest-path percolation on scale-free networks
• Starvation suppression in dense scale-free metabolic networks: Dynamical mean-field analysis of catalytic reaction networks