Evaluating Topological Vulnerability Based on Fuzzy Fractal Dimension

Complex networks have been widely applied in many complex systems existed in nature and society because of its rapid development. Many methods have been proposed to evaluate the vulnerability of the complex networks because of the high security requirements of the network. In this paper, a novel method is proposed to evaluate network’s vulnerability, which is based on fuzzy fractal dimension and average edge betweenness. Fuzzy fractal dimension can reflect the dynamic structure and topological structure of complex network, which is important to the vulnerability of complex network. So this proposed method can overcome the shortcomings of previous works by replacing the key coefficient p by fuzzy fractal dimension. In order to show this proposed method’s accuracy and effectiveness, six USAir networks in different years are applied in this paper. Three common methods are used to compare the results with this proposed method, and the RB attack strategy is used to analyze the vulnerability of dynamic characteristic. The fuzzy fractal dimension of randomly selecting largest connected subset which is close to the initial fuzzy fractal dimension shows the reliability and stability of this proposed method. The vulnerability order obtained by this proposed method is more realistic, because the Pearson correlation coefficient r about this method equals to 0.9805, which shows a extremely strong correlation with the reality.