An improved vulnerability index of complex networks based on fractal dimension

TL;DR

This paper introduces an enhanced vulnerability index for complex networks that incorporates fractal dimension to better capture structural and physical properties, improving vulnerability assessment accuracy.

Contribution

The paper proposes a novel vulnerability evaluation model based on fractal dimension, integrating network structure and covering ability for more physically meaningful assessments.

Findings

The new model effectively characterizes network vulnerability.

Numerical and real-world examples demonstrate improved evaluation accuracy.

Abstract

With an increasing emphasis on network security, much more attention has been attracted to the vulnerability of complex networks. The multi-scale evaluation of vulnerability is widely used since it makes use of combined powers of the links' betweenness and has an effective evaluation to vulnerability. However, how to determine the coefficient in existing multi-scale evaluation model to measure the vulnerability of different networks is still an open issue. In this paper, an improved model based on the fractal dimension of complex networks is proposed to obtain a more reasonable evaluation of vulnerability with more physical significance. Not only the structure and basic physical properties of networks is characterized, but also the covering ability of networks, which is related to the vulnerability of the network, is taken into consideration in our proposed method. The numerical examples and real applications are used to illustrate the efficiency of our proposed method.