Different thresholds of bond percolation in scale-free networks with identical degree sequence

Generally, the threshold of percolation in complex networks depends on the underlying structural characterization. However, what topological property plays a predominant role is still unknown, despite the speculation of some authors that degree distribution is a key ingredient. The purpose of this paper is to show that power-law degree distribution itself is not sufficient to characterize the threshold of bond percolation in scale-free networks. To achieve this goal, we first propose a family of scale-free networks with the same degree sequence and obtain by analytical or numerical means several topological features of the networks. Then, by making use of the renormalization group technique we determine the threshold of bond percolation in our networks. We find an existence of non-zero thresholds and demonstrate that these thresholds can be quite different, which implies that power-law degree distribution does not suffice to characterize the percolation threshold in scale-free networks.

Finite epidemic thresholds in fractal scale-free `large-world networks

It is generally accepted that scale-free networks is prone to epidemic spreading allowing the onset of large epidemics whatever the spreading rate of the infection. In the paper, we show that disease propagation may be suppressed in particular fractal scale-free networks. We first study analytically the topological characteristics of a network model and show that it is simultaneously scale-free, highly clustered, large-world, fractal and disassortative. Any previous model does not have all the properties as the one under consideration. Then, by using the renormalization group technique we analyze the dynamic susceptible-infected-removed (SIR) model for spreading of infections. Interestingly, we find the existence of an epidemic threshold, as compared to the usual epidemic behavior without a finite threshold in uncorrelated scale-free networks. This phenomenon indicates that degree distribution of scale-free networks does not suffice to characterize the epidemic dynamics on top of them. Our results may shed light in the understanding of the epidemics and other spreading phenomena on real-life networks with similar structural features as the considered model.