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

TL;DR

This paper investigates how the bond percolation threshold in scale-free networks is influenced by topological features beyond degree distribution, showing that identical degree sequences can have different percolation thresholds.

Contribution

It introduces a family of scale-free networks with identical degree sequences and analyzes their percolation thresholds, revealing the importance of network topology beyond degree distribution.

Findings

Different thresholds exist for networks with the same degree sequence.

Power-law degree distribution alone does not determine the percolation threshold.

Topological features significantly influence percolation behavior.

Abstract

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.