Percolation and Epidemic Thresholds in Clustered Networks

Abstract

We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant connected component, it cannot restore a finite percolation threshold. In turn, this implies the absence of an epidemic threshold in this class of networks extending, thus, this result to a wide variety of real scale-free networks which shows a high level of transitivity. Our findings are in good agreement with numerical simulations.

4 Pages and 3 Figures. Final version to appear in PRL

References in corpus (16)

• Statistical mechanics of complex networks
• Epidemic spreading in scale-free networks
• Assortative mixing in networks
• The spread of epidemic disease on networks
• Defining and identifying communities in networks
• Resilience of the Internet to random breakdowns
• k-core organization of complex networks
• Absence of epidemic threshold in scale-free networks with connectivity correlations
• Properties of highly clustered networks
• Percolation Critical Exponents in Scale-Free Networks
• Cut-offs and finite size effects in scale-free networks
• Resilience to damage of graphs with degree correlations
• Generalized percolation in random directed networks
• Tuning clustering in random networks with arbitrary degree distributions
• Random Networks with Tunable Degree Distribution and Clustering
• Epidemics, disorder, and percolation

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