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

An improved vulnerability index of complex networks based on fractal dimension