Clustering in complex networks. II. Percolation properties

Details Clustering in complex networks. II. Percolation properties Clustering in complex networks. II. Percolation properties

2006-08-15

arxiv.org/abs/cond-mat/0608337v2

Physical Review E 74, 056115 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Updated reference list

Scientific paper

10.1103/PhysRevE.74.056115

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.

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