Percolation in Hierarchical Scale-Free Nets

Details Percolation in Hierarchical Scale-Free Nets Percolation in Hierarchical Scale-Free Nets

2007-03-06

arxiv.org/abs/cond-mat/0703155v3

Phys. Rev. E 75, 061102 (2007)

Physics

Condensed Matter

Statistical Mechanics

9 Pages, 11 figures. References added and minor corrections to manuscript. In press

Scientific paper

10.1103/PhysRevE.75.061102

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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