Stability and topology of scale-free networks under attack and defense strategies.

We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an intentional attack with insufficient knowledge of the network. We determine, for all strategies, the critical fraction p(c) of nodes that must be removed for disintegrating the network. We find that, for an intentional attack, little knowledge of the well-connected sites is sufficient to strongly reduce p(c). At criticality, the topology of the network depends on the removal strategy, implying that different strategies may lead to different kinds of percolation transitions.

• Publication year

  2005

• Venue

  Physical Review Letters

• Publication date

  2005-03-21

• Fields of study

  Mathematics, Physics, Computer Science, Medicine

• Identifiers
  DOI 10.1103/PhysRevLett.94.188701arXiv cond-mat/0505201PMID 15904414
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Evolution and Structure of the Internet: A Statistical Physics Approach

  2005cited by this paper
• Weighted evolving networks: coupling topology and weight dynamics.

  2004cited by this paper
• Evolution of Networks: From Biological Nets to the Internet and WWW

  2004cited by this paper
• The Structure and Function of Complex Networks

  2003cited by this paper
• The architecture of complex weighted networks.

  2003cited by this paper
• Evolution of Networks: From Biological Nets to the Internet and WWW (Physics)

  2003cited by this paper
• Critical load and congestion instabilities in scale-free networks

  2002cited by this paper
• Cascade-based attacks on complex networks.

  2002cited by this paper
• The web of human sexual contacts

  2001cited by this paper
• ACM SIGCOMM computer communication review

  2001cited by this paper
• Statistical mechanics of complex networks

  2001cited by this paper
• Halting viruses in scale-free networks.

  2001cited by this paper
• correction: Error and attack tolerance of complex networks

  2001cited by this paper
• Resilience of the internet to random breakdowns

  2000cited by this paper
• Connectivity of growing random networks.

  2000cited by this paper
• Topology of evolving networks: local events and universality

  2000cited by this paper
• Breakdown of the internet under intentional attack.

  2000cited by this paper
• Error and attack tolerance of complex networks

  2000cited by this paper
• Emergence of Scaling in Random Networks

  1999cited by this paper
• Emergence of scaling in random networks

  1999cited by this paper
• Gravitational force distribution in fractal structures

  1998cited by this paper
• Nature (London

  1975cited by this paper

• Robustness of spatial interdependent networks under extreme geographically localized attacks

  2026cites this paper
• Percolation with Distance-Dependent Site Occupational Probabilities

  2026cites this paper
• Analytics solution for the robustness of incomplete information scale-free networks

  2025cites this paper
• Robustness of infrastructure networks with cascading overload failures under extreme geographically localized attacks.

  2025cites this paper
• Limited Improvement of Connectivity in Scale-Free Networks by Increasing the Power-Law Exponent

  2025cites this paper
• River networks in the framework of complex network theory.

  2025cites this paper
• UniqueRank: Identifying Important and Difficult-to-Replace Nodes in Attributed Graphs

  2025cites this paper
• Assessing the robustness of physical networks under attack uncertainty

  2025cites this paper
• Toward the resilience of UAV swarms with percolation theory under attacks

  2024cites this paper
• Scaling and universality for percolation in random networks: A unified view.

  2024cites this paper
• Hierarchical multi-task deep learning-assisted construction of human gut microbiota reactive oxygen species-scavenging enzymes database

  2024cites this paper
• Targeting attack activity-driven networks.

  2024cites this paper
• A Tiny Viral Protein, SARS-CoV-2-ORF7b: Functional Molecular Mechanisms

  2024cites this paper
• Towards the analysis of errors in centrality measures in perpetuated networks

  2024cites this paper
• An Enhanced Resilience and Throughput BBV-based Method for UAV Networks

  2024cites this paper
• Exact analysis of generalized degree-based percolation without memory

  2024cites this paper
• Node and Edge Removal on Complex Networks in Labor Market Research and their Influence on Centrality Measures

  2024cites this paper
• Decentralizing the lightning network: a score-based recommendation strategy for the autopilot system

  2023cites this paper
• Identification of Relevant Protein Interactions with Partial Knowledge: A Complex Network and Deep Learning Approach

  2023cites this paper
• The all-pairs vitality-maximization (VIMAX) problem

  2023cites this paper
• Percolation of interlayer feature-correlated multiplex networks

  2023cites this paper
• Acquaintance immunization with limited knowledge of network structure

  2023cites this paper
• A possible quadruple point in networks of directed networks under targeted attacks

  2023cites this paper
• Extended SPR for Evolving Networks with Nodes Preferential Deletion

  2023cites this paper
• Efficient network intervention with sampling information

  2023cites this paper
• Study on the relationship between ecological spatial network structure and regional carbon use Efficiency: A case study of the Wuding river basin

  2023cites this paper
• On Edge Pruning of Communication Networks under an Age-of-Information Framework

  2022cites this paper
• Throughput of Hybrid UAV Networks With Scale-Free Topology

  2022cites this paper
• Characteristics of edge-based interdependent networks

  2022cites this paper
• Targeting attack hypergraph networks.

  2022cites this paper
• Percolation behaviors of finite components on complex networks

  2022cites this paper
• Degree distributions under general node removal: Power-law or Poisson?

  2022cites this paper
• How teams adapt to exogenous shocks: Experimental evidence with node knockouts of central members

  2022cites this paper
• Network structure revelation and airport role evaluation under three different COVID-19 pandemic periods: Evidence from a Chinese airline

  2022cites this paper
• Percolation behaviors of a network of networks under intentional attack with limited information

  2022cites this paper
• Three Decades in Econophysics—From Microscopic Modelling to Macroscopic Complexity and Back

  2022cites this paper
• Network structure revelation and airport role evaluation under three different COVID-19 pandemic periods: Evidence from a Chinese airline

  2022cites this paper
• A Novel Approach to Climate Resilience of Infrastructure Networks

  2022cites this paper
• Network structure revelation and airport role evaluation under three different COVID-19 pandemic periods: Evidence from a Chinese airline

  2022cites this paper
• Disrupting networks of hate: characterising hateful networks and removing critical nodes

  2022cites this paper
• Dynamical Recovery of Complex Networks under a Localised Attack

  2021cites this paper
• THE RESILIENCE OF COMPLEX NETWORK: AN APPROACH FOR RELEVANT NODES EXTRACTION

  2021cites this paper
• Mathematical Problems of Managing the Risks of Complex Systems under Targeted Attacks with Known Structures

  2021cites this paper
• Defense strategies against cascading failures in networks: “Too-big-to-fail” and “too-small-to-fail”

  2021cites this paper
• Feasibility study of PRA for critical infrastructure risk analysis

  2021cites this paper
• Risk-opportunity analysis for transformative policy design and appraisal

  2021cites this paper
• Generalized k-cores of networks under attack with limited knowledge

  2021cites this paper
• Cascading Failure Dynamics against Intentional Attack for Interdependent Industrial Internet of Things

  2021cites this paper
• Percolation on complex networks: Theory and application

  2021cites this paper
• Dynamics of Epidemic Spreading in the Group-Based Multilayer Networks

  2020cites this paper
• Security Assessment for Cascading Failures of Cyber-Physical Systems Under Target Attack Strategy

  2020cites this paper
• Geodesic Vulnerability Approach for Identification of Critical Buses in Power Systems

  2020cites this paper
• Impact of Immunization Strategies on the Dynamics of Social Contagions

  2020cites this paper
• The Reliability Analysis of a Complex Electromechanical System from a Complex Network Perspective

  2020cites this paper
• An Early Stage Researcher's Primer on Systems Medicine Terminology

  2020cites this paper
• Link and Node Removal in Real Social Networks: A Review

  2020cites this paper
• Degree-ordered-percolation on uncorrelated networks

  2020cites this paper
• Pseudo-Darwinian evolution of physical flows in complex networks

  2020cites this paper
• Efficient network immunization under limited knowledge

  2020cites this paper
• Impacts of malicious attacks on robustness of knowledge networks: a multi-agent-based simulation

  2020cites this paper
• The responsiveness of criminal networks to intentional attacks: Disrupting darknet drug trade

  2020influential citation
• Robustness of multi-agent formation based on natural connectivity

  2020cites this paper
• Edge attack strategies in interdependent scale-free networks

  2020cites this paper
• Classification of Literary Works: Fractality and Complexity of the Narrative, Essay, and Research Article

  2020cites this paper
• A comparative analysis of link removal strategies in real complex weighted networks

  2020cites this paper
• Service Reliability Assurance Technology Based on N-X Analysis

  2020cites this paper
• Subgraph Robustness of Complex Networks Under Attacks

  2019cites this paper
• Robustness of partially interdependent networks under combined attack.

  2019cites this paper
• Extinction-induced community reorganization in bipartite networks

  2019cites this paper
• Cumulative Merging Percolation and the Epidemic Transition of the Susceptible-Infected-Susceptible Model in Networks

  2019cites this paper
• Average hopcount of the shortest path in tree-like components with finite size

  2019cites this paper
• Robustness analysis of partially interdependent networks with different coupling preferences and multicluster functional nodes in VCMS

  2019cites this paper
• Analysis on topological features of deterministic hierarchical complex network

  2019cites this paper
• A pedestrian review of games on structured populations

  2019cites this paper
• A pedestrian review of games on structured populations

  2019cites this paper
• New Robustness Measures of Communication Networks Against Virus Attacks

  2019cites this paper
• Universal behavior of cascading failures in interdependent networks

  2019cites this paper
• A new information dimension of complex network based on Rényi entropy

  2019cites this paper
• Localized attack on networks with clustering

  2019cites this paper
• Review of the network risk propagation research

  2019cites this paper
• Security Assessment for Cascading Failures of Cyber-Physical Systems Under Target Attack Strategy

  2019cites this paper
• An improved node algorithm based on the evaluation of weighted network node importance

  2018cites this paper
• Mathematical Modeling and Inference for Degree-capped Egocentric Network Sampling

  2018cites this paper
• Multiple robustness assessment method for understanding structural and functional characteristics of the power network

  2018cites this paper
• A multiple perspective method for urban subway network robustness analysis

  2018cites this paper
• Geographical interdependent robustness measures in transportation networks

  2018influential citation
• Robustness of Link Prediction Under Network Attacks

  2018cites this paper
• Optimal resource allocation for network functionality

  2018cites this paper
• Is city traffic damaged by torrential rain?

  2018cites this paper
• Effects of time-delays in the dynamics of social contagions

  2018cites this paper
• Statistical Analysis of Underground Pipeline Typical Accidents and Numerical Simulation Research

  2018cites this paper
• Multi-node attack strategy of complex networks due to cascading breakdown

  2018cites this paper
• Resilience of networks to environmental stress: From regular to random networks.

  2017cites this paper
• Percolation and reinforcement on complex networks

  2017cites this paper
• A Study on Effectiveness of Network Attack Using Analysis of Eigenvalue

  2017cites this paper
• Robustness of multiple interdependent networks under shell attack

  2017cites this paper
• Graph-based modelling on the robustness of interconnected networks under attack

  2017influential citation
• Optimal cost for strengthening or destroying a given network.

  2017cites this paper
• False Positive and False Negative Effects on Network Attacks

  2017cites this paper
• Robustness of Dengue Complex Network under Targeted versus Random Attack

  2017cites this paper