Percolation in Hierarchical Scale-Free Nets
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.
Cite
@article{arxiv.cond-mat/0703155,
title = {Percolation in Hierarchical Scale-Free Nets},
author = {Hernán D. Rozenfeld and Daniel ben-Avraham},
journal= {arXiv preprint arXiv:cond-mat/0703155},
year = {2009}
}
Comments
9 Pages, 11 figures. References added and minor corrections to manuscript. In press