Error and attack tolerance of complex networks

Abstract

Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. In this paper we demonstrate that error tolerance is not shared by all redundant systems, but it is displayed only by a class of inhomogeneously wired networks, called scale-free networks. We find that scale-free networks, describing a number of systems, such as the World Wide Web, Internet, social networks or a cell, display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected by even unrealistically high failure rates. However, error tolerance comes at a high price: these networks are extremely vulnerable to attacks, i.e. to the selection and removal of a few nodes that play the most important role in assuring the network's connectivity.

14 pages, 4 figures, Latex

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• The effect of randomness for dependency map on the robustness of interdependent lattices
• Optimal transport on supply-demand networks
• Oscillations of complex networks
• Collective effects of link failures in linear flow networks
• Preferential attachment with information filtering - node degree probability distribution properties
• Thermodynamic forces, flows, and Onsager coefficients in complex networks
• Growing networks of overlapping communities with internal structure
• Scale-free networks resistant to intentional attacks
• Bond and site color-avoiding percolation in scale free networks
• Dynamical robustness of complex networks subject to long-range connectivity
• The structure of networks that evolve under a combination of growth, via node addition and random attachment, and contraction, via random node deletion
• Optimal Stabilization of Boolean Networks through Collective Influence
• The Immunity of Polymer-Microemulsion Networks
• REACT: REActive resilience for critical infrastructures using graph-Coloring Techniques
• A quantitative method for determining the robustness of complex networks
• Aftershocks in Modern Perspectives: Complex Earthquake Network, Aging, and Non-Markovianity
• Quantum Internet under random breakdowns and intentional attacks
• Optimizing and controlling functions of complex networks by manipulating rich-club connections
• Cyber Network Resilience against Self-Propagating Malware Attacks
• Deep-learning-aided dismantling of interdependent networks
• An analytically solvable model of probabilistic network dynamics
• Effects of aging and links removal on epidemic dynamics in scale-free networks
• Optimal cost for strengthening or destroying a given network
• Spectral estimation of the percolation transition in clustered networks
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• Continuous variables graph states shaped as complex networks: optimization and manipulation
• Critical phenomena of a hybrid phase transition in cluster merging dynamics
• Randomly Evolving Idiotypic Networks: Structural Properties and Architecture
• How Does the Vulnerability of an Evolving Power Grid Change?
• Measuring the importance of individual units in producing the collective behavior of a complex network
• Probabilistic generation of random networks taking into account information on motifs occurrence
• Fragmenting networks by targeting collective influencers at a mesoscopic level
• Stability of glassy hierarchical networks
• Geographical networks stochastically constructed by a self-similar tiling according to population
• An optimal network for passenger traffic
• Convexity in complex networks
• Emergence of Robust and Efficient Networks in a Family of Attachment Models
• Percolation transition and distribution of connected components in generalized random network ensembles
• Balancing building and maintenance costs in growing transport networks
• Evolutionary Construction of Geographical Networks with Nearly Optimal Robustness and Efficient Routing Properties
• Fragmentation properties of two-dimensional Proximity Graphs considering random failures and targeted attacks
• Impact of noise and damage on collective dynamics of scale-free neuronal networks
• Diluted antiferromagnet in a ferromagnetic enviroment
• Understanding the temporal pattern of spreading in heterogeneous networks: Theory of the mean infection time
• Failure mechanisms of load sharing complex systems
• Bypass rewiring and robustness of complex networks
• Site and bond percolation thresholds in $K_{n,n}$-based lattices: Vulnerability of quantum annealers to random qubit and coupler failures on chimera topologies
• Identification of highly susceptible individuals in complex networks
• Tuning degree distributions of scale-free networks
• A Local Optima Network View of Real Function Fitness Landscapes
• Fundamental Structural Constraint of Random Scale-Free Networks
• Clarifying How Degree Entropies and Degree-Degree Correlations Relate to Network Robustness
• Binary dynamics on star networks under external perturbations
• Robustness of community structure under edge addition
• Estimating Properties of Social Networks via Random Walk considering Private Nodes
• Nanoporous Metallic Network as a Largescale 3D Source of Second Harmonic Light
• Non-Markovian random walks characterize network robustness to nonlocal cascades
• Link deletion in directed complex networks
• Comparison of Modules of Wild Type and Mutant Huntingtin and TP53 Protein Interaction Networks: Implications in Biological Processes and Functions
• Complex systems: features, similarity and connectivity
• Critical behaviors of high-degree adaptive and collective-influence percolation
• Percolation of networks with directed dependency links
• Control of excitable systems is optimal near criticality
• A Study on the Effects of Diffusion of Information on Epidemic Spread
• Understanding Communication Patterns in MOOCs: Combining Data Mining and qualitative methods
• Criticality and Continuity of Explosive Site Percolation in Random Networks
• Two faces of greedy leaf removal procedure on graphs
• Robustness of correlated networks against propagating attacks
• Exact solution of bond percolation on small arbitrary graphs
• Random node reinforcement and $K$-core structure of complex networks
• When is a scale-free graph ultra-small?
• Integrating fluctuations into distribution of resources in transportation networks
• Network topology of the Argentine interbank money market
• Statistical analysis of edges and bredges in configuration model networks
• Radial Structure of the Internet
• Kauffman Boolean model in undirected scale free networks
• Discovering universal statistical laws of complex networks
• Variability Analysis of Complex Networks Measures based on Stochastic Distances
• Duality between preferential attachment and static random networks on hyperbolic spaces
• Selective pressure on metabolic network structures as measured from the random blind-watchmaker network
• "Clumpiness" Mixing in Complex Networks
• Multi-layer network approach in modeling epidemics in an urban town
• Impact of random and targeted disruptions on information diffusion during outbreaks
• Lattice splitting under intermittent flows
• Maximal switchability of centralized networks
• Correlations between thresholds and degrees: An analytic approach to model attacks and failure cascades
• Static Pairwise Annihilation in Complex Networks
• Degree-targeted cascades in modular, degree-heterogeneous networks
• Preservation of network Degree Distributions from non-uniform failures
• Diophantine Networks
• Weighted projected networks: mapping hypergraphs to networks
• Why are probabilistic laws governing quantum mechanics and neurobiology?
• Learning the mechanisms of network growth
• Generalized $k$-core pruning process on directed networks
• Scaling properties of scale-free networks in degree-thresholding renormalization flows
• Epidemics in networks: A master equation approach
• Centralities in complex networks
• Performance of attack strategies on modular networks
• The Fate of Articulation Points and Bredges in Percolation
• Bounding robustness in complex networks under topological changes through majorization techniques
• Enhanced robustness of evolving open systems by the bidirectionality of interactions between elements
• Robustness of networks against propagating attacks under vaccination strategies
• War pact model of shrinking networks
• Degree-ordered percolation on hierarchical scale-free network
• Equilibrium properties of disordered spin models with two scale interactions
• Impact of shocks to economies on the efficiency and robustness of the international pesticide trade networks
• Tutte polynomial of pseudofractal scale-free web
• Degree and component size distributions in generalized uniform recursive tree
• Dynamical network stability analysis of multiple biological ages provides a framework for understanding the aging process
• Rank-based model for weighted network with hierarchical organization and disassortative mixing
• A Statistical Mechanical Load Balancer for the Web
• P2P-PL: A Pattern Language to Design Efficient and Robust Peer-to-Peer Systems
• Spatially self-organized resilient networks by a distributed cooperative mechanism
• Network Inoculation: Heteroclinics and phase transitions in an epidemic model
• Universal vulnerability in strong modular networks with various degree distributions between inequality and equality
• Optimal Control of Networks in the presence of Attackers and Defenders
• Random Walk Sampling in Social Networks Involving Private Nodes
• Biology helps to construct weighted scale free networks
• Invited review: Epidemics on social networks
• A Monte-Carlo Approach to Lifespan Failure Performance Analysis of the Network Fabric in Modular Data Centers
• A compartmental model for cyber-epidemics
• Robustness Assessment of Complex Networks using the Idle Network
• Centralities for Networks with Consumable Resources
• Faster calculation of the percolation correlation length on spatial networks
• Extinction-induced community reorganization in bipartite networks
• Spin-glass model for the C-dismantling problem
• Node Diversification in Complex Networks by Decentralized Coloring
• Constraints and Entropy in a Model of Network Evolution
• Log-periodic oscillations due to discrete effects in complex networks
• Economy importance and structural robustness of the international pesticide trade networks
• The Impact of Imperfect Information on Network Attack
• Vulnerable Connectivity Caused by Local Communities in Spatial Networks
• Robustness of Random Networks with Selective Reinforcement against Attacks
• Phase transition in evolving networks that combine preferential attachment and random node deletion
• Synchronization in an evolving network
• Design of endurable networks in the presence of aging
• Redefinition of site percolation in light of entropy and the second law of thermodynamics
• A Fast Monte Carlo algorithm for evaluating matrix functions with application in complex networks
• Network resilience in the presence of non-equilibrium dynamics
• Robustness of Decentralised Learning to Nodes and Data Disruption
• Prediction of lethal and synthetically lethal knock-outs in regulatory networks
• Random Walks in Local Dynamics of Network Losses
• Modeling resource consumption in the US air transportation system via minimum-cost percolation
• Comparing the sensitivity of social networks, web graphs, and random graphs with respect to vertex removal
• Self-organized network design by link survivals and shortcuts
• Quantitative modeling of degree-degree correlation in complex networks
• Scale-free networks are not robust under neutral evolution
• Asymptotic behavior of the node degrees in the ensemble average of adjacency matrix
• Network structure and fragmentation of the Argentinean interbank markets
• Preferential attachment renders an evolving network of populations robust against crashes
• $K$-selective percolation: A simple model leading to a rich repertoire of phase transitions
• A hybrid percolation transition at a finite transition point in scale-free networks
• Disorder Induced Limited Path Percolation
• No-exclaves percolation on random networks
• Dynamical processes on metric networks
• Quantifying the temporal stability of international fertilizer trade networks
• Degree-Ordered-Percolation on uncorrelated networks
• Degree distributions under general node removal: Power-law or Poisson?
• Universality class of explosive percolation in Barabási-Albert networks
• Critical Network Cascades with Re-excitable nodes: Why tree-like approximations usually work, when they breakdown, and how to correct them
• Scaling Properties of Human Brain Functional Networks
• Optimal shattering of complex networks
• Structural Properties of Networks Grown via an Achlioptas Process
• Ising model for distribution networks
• More Tolerant Reconstructed Networks by Self-Healing against Attacks in Saving Resource
• Analytic Solution to Clustering Coefficients on Weighted Networks
• Revisiting small-world network models: Exploring technical realizations and the equivalence of the Newman-Watts and Harary models
• The network structure of mathematical knowledge according to the Wikipedia, MathWorld, and DLMF online libraries
• Critical line in undirected Kauffman boolean networks - the role of percolation
• Interplay between degree and Boolean rules in the stability of Boolean networks
• Large deviations of connected components in the stochastic block model
• Multidomain Evolutionary Optimization on Combinatorial Problems in Complex Networks
• Conformation-networks of two-dimensional lattice homopolymers
• Identifying influential subpopulations in metapopulation epidemic models using message-passing theory
• A Network Epidemic Model for Online Community Commissioning Data
• A subset selection based approach to finding important structure of complex networks
• Ising Model on Edge-Dual of Random Networks
• Phase transitions in atypical systems induced by a condensation transition on graphs
• Towards Limited Scale-free Topology with Dynamic Peer Participation
• Usage leading to an abrupt collapse of connectivity
• D-chain tomography of networks: a new structure spectrum and an application to the SIR process
• Range-based attacks on links in random scale-free networks
• Temporal Correlations of Local Network Losses
• Influence Robustness of Nodes in Multiplex Networks against Attacks
• Core Influence Mechanism on Vertex-Cover Problem through Leaf-Removal-Core Breaking
• On the complexity of color-avoiding site and bond percolation
• An almost-solvable model of complex network dynamics
• Deductive Way of Reasoning about the Internet AS Level Topology
• Tinnitus, lucid dreaming and awakening. An online survey and theoretical implications
• Color-avoiding percolation in edge-colored Erdős-Rényi graphs
• Understanding How Network Geometry Influences Diffusion Processes in Complex Networks: A Focus on Cryptocurrency Blockchains and Critical Infrastructure Networks
• Modified Lomax Model: A heavy-tailed distribution for fitting large-scale real-world complex networks
• Robustness of planar random graphs to targeted attacks
• Stationary States of a Random Copying Mechanism over a Complex Networks
• Fault Tolerance of Random Graphs with respect to Connectivity: Mean-field Approximation for Semi-dense Random Graphs
• A resource- and computationally-efficient protocol for multipartite entanglement distribution in Bell-pair networks
• Inferring financial stock returns correlation from complex network analysis
• Polynomial Observables in the Graph Partitioning Problem
• Global decomposition of networks into multiple cores formed by local hubs
• Vulnerability of Transport through Evolving Spatial Networks
• Anti-correlation network among China A-shares
• Ad-hoc Limited Scale-Free Models for Unstructured Peer-to-Peer Networks
• Multiple predator based capture process on complex networks
• Universality in percolation of arbitrary Uncorrelated Nested Subgraphs
• The All-Pairs Vitality-Maximization (VIMAX) Problem
• A machine learning procedure to detect network attacks
• How network properties and epidemic parameters influence stochastic SIR dynamics on scale-free random networks
• The effects of inhibitory and excitatory neurons on the dynamics and control of avalanching neural networks
• Miuz: measuring the impact of disconnecting a node
• Six General Ecosystem Properties are more Intense in Biogeochemical Cycling Networks than Food Webs
• Shortest-path percolation on scale-free networks
• The effect of preferential node deletion on the structure of networks that evolve via preferential attachment
• Spectral Gradient Iterative Edge Attack for Synchronization Suppression in Complex Networks
• Connectivity jamming game for physical layer attack in peer to peer networks
• Random Walks on Complex Networks
• Permutation Tests for Infection Graphs
• Metanetworks of artificially evolved regulatory networks
• Bilinear effect in complex systems
• Predicting the cascading dynamics in complex networks via the bimodal failure size distribution
• Some Combinatorial Problems in Power-law Graphs
• Spatio-Temporal Graphical Counterfactuals: An Overview
• The effect of temporal pattern of injury on disability in learning networks
• Measuring Centralization of Online Platforms Through Size and Interconnection of Communities
• A Taxonomy of Causality-Based Biological Properties
• Italian Business-to-Business Invoicing Data: A Network Analysis
• Link Cascades in Complex Networks: A Mean-field Approach
• Network growth under opportunistic attachment
• Overcoming the complexity barrier of the dynamic message-passing method in networks with fat-tailed degree distributions
• Thermodynamic stability and structural transitions in virus-host networks
• Starvation suppression in dense scale-free metabolic networks: Dynamical mean-field analysis of catalytic reaction networks
• Trade-Off Between Multiplicity and Specificity in the Inter-layer Connectivity of non-identical Multilayer Networks
• Manageable to unmanageable transition in a fractal model of project networks
• The local Gaussian correlation networks among return tails in the Chinese stock market