Percolation in Hierarchical Scale-Free Nets

TL;DR

This paper investigates the percolation phase transition in hierarchical scale-free networks, revealing how structural properties like fractality, small-world characteristics, and assortativity influence critical behavior.

Contribution

It provides an exact analysis of percolation transitions across various hierarchical scale-free network structures, highlighting the impact of structural differences.

Findings

Different types of criticality depending on network structure

Exact solutions for percolation thresholds in hierarchical nets

Structural properties affect percolation behavior beyond degree distribution

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.