Clustering in complex networks. II. Percolation properties

Abstract

The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows to find the critical threshold and the size of the giant component. Numerical simulations confirm the accuracy of our results. In more general terms, we show that weak clustering hinders the onset of the giant component whereas strong clustering favors its appearance. This is a direct consequence of the differences in the $k$-core structure of the networks, which are found to be totally different depending on the level of clustering. An empirical analysis of a real social network confirms our predictions.

Updated reference list

References in corpus (16)

• Assortative mixing in networks
• Random graphs with arbitrary degree distributions and their applications
• The spread of epidemic disease on networks
• Network robustness and fragility: Percolation on random graphs
• 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
• Resilience to damage of graphs with degree correlations
• Percolation and Epidemic Thresholds in Clustered Networks
• Generalized percolation in random directed networks
• Clustering in complex networks. I. General formalism
• Tuning clustering in random networks with arbitrary degree distributions
• Epidemics, disorder, and percolation

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