Attack Vulnerability Of Fractal Scale-Free Network

An in-depth analysis of the attack vulnerability of fractal scale-free networks is of great significance for designing robust networks. Previous studies have mainly focused on the impact of fractal property on attack vulnerability of scale-free networks under static node attacks, while we extend the study to the cases of various types of targeted attacks, and explore the relationship between the attack vulnerability of fractal scale-free networks and the fractal dimension. A hierarchical multiplicative growth model is first proposed to generate scale-free networks with the same structural properties except for the fractal dimension. Furthermore, the fractal dimension of the network is calculated using two methods, namely, the box-covering method and the cluster-growing method, to exclude the possibility of differences in conclusions caused by the methods of calculating the fractal dimension for the subsequent relationship analysis. Finally, four attack strategies are used to attack the network, and the network performance is quantitatively measured by three structural indicators. Results on model networks show that compared to non-fractal modular networks, fractal scale-free networks are more robust to both static and dynamic targeted attacks on nodes and links, and the robustness of the network increases as the fractal dimension decreases. However, there is a cost in that as the fractal dimension decreases, the network becomes less efficient and more vulnerable to random failures on links. These findings contribute to a deeper understanding of the impact of fractal property on scale-free network performance and may be useful for designing resilient infrastructures.