Percolation on correlated networks

Abstract

We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for degree-degree correlations to be irrelevant for critical singularities. We present examples of networks in which assortative and disassortative mixing leads to unusual percolation properties and new critical exponents.

14 pages, 6 figures

References in corpus (30)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Error and attack tolerance of complex networks
• Assortative mixing in networks
• Random graphs with arbitrary degree distributions and their applications
• Evolution of networks
• Specificity and stability in topology of protein networks
• Network robustness and fragility: Percolation on random graphs
• Critical phenomena in complex networks
• Dynamical and correlation properties of the Internet
• Universal Behavior of Load Distribution in Scale-free Networks
• Organization of Growing Random Networks
• Large-scale topological and dynamical properties of Internet
• Epidemic spreading in correlated complex networks
• Are randomly grown graphs really random?
• Pattern Detection in Complex Networks: Correlation Profile of the Internet
• Percolation Critical Exponents in Scale-Free Networks
• Resilience to damage of graphs with degree correlations
• Epidemic spreading in complex networks with degree correlations
• The entropy of randomized network ensembles
• Infinite-Order Percolation and Giant Fluctuations in a Protein Interaction Network
• Critical phenomena in networks
• Anomalous percolating properties of growing networks
• Rate equation approach for correlations in growing network models
• Clustering of correlated networks
• Percolation transition in networks with degree-degree correlation
• Intrinsic degree-correlations in static model of scale-free networks
• Universal Properties of Growing Networks
• Asymmetric evolving random networks
• A simple asymmetric evolving random network

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• Degree Correlations Amplify the Growth of Cascades in Networks
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• Hierarchical scale-free network is fragile against random failure
• Observability transitions in correlated networks
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• Unifying continuous, discrete, and hybrid susceptible-infected-recovered processes on networks
• Spectral estimation of the percolation transition in clustered networks
• Percolation transition and distribution of connected components in generalized random network ensembles
• Robustness analysis of bimodal networks in the whole range of degree correlation
• Robustness of correlated networks against propagating attacks
• Enhanced robustness of single-layer networks with redundant dependencies
• Characterizing the intrinsic correlations of scale-free networks
• Synergistic epidemic spreading in correlated networks
• Degree-ordered percolation on hierarchical scale-free network
• Identification of intrinsic long-range degree correlations in complex networks
• Optimizing spreading dynamics in interconnected networks
• Percolation on a maximally disassortative network
• Scaling and universality for percolation in random networks: A unified view
• Degree-dependent network growth: From preferential attachment to explosive percolation
• Generating functions for message-passing on weighted networks: directed bond percolation and SIR epidemics
• Detecting Structure of Complex Network by Quantum Bosonic Dynamics
• Finite-size scaling of percolation on scale-free networks
• Coarse-grained Monte Carlo simulations of the phase transition of Potts model on weighted networks
• Quantitative modeling of degree-degree correlation in complex networks
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• Simple model of fractal networks formed by self-organized critical dynamics
• Structural instability of large-scale functional networks
• Universality in percolation of arbitrary Uncorrelated Nested Subgraphs
• Revisiting finite size effect of percolation in degree correlated networks
• How universal is the mean-field universality class for percolation in complex networks?
• Discontinuous emergence of a giant cluster in assortative scale-free networks
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• Continuum Percolation on Disoriented Surfaces: the Problem of Permeable Disks on a Klein Bottle
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