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Percolation in Hierarchical Scale-Free Nets

Hernán D. Rozenfeld·Daniel ben-Avraham
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Abstract

We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size), assortative or disassortative (a measure of the tendency of like-degree nodes to be connected to one another), or possess various degrees of clustering. The percolation phase transition can be analyzed exactly in all these cases, due to the self-similar structure of the hierarchical nets. We find different types of criticality, illustrating the crucial effect of other structural properties besides the scale-free degree distribution of the nets.

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BibTeXRIS

Hernán D. Rozenfeld, Daniel ben-Avraham. 2007-05-18. Percolation in Hierarchical Scale-Free Nets. https://doi.org/10.1103/physreve.75.061102

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