Centre including eccentricity algorithm for complex networks

In this work, the authors propose a new centre including eccentricity algorithm, to define the fractal dimension of networks. The authors did the fractal analysis of the real Escherichia coli network and a model UV-flower network and confirmed that these networks are fractals . The fractal dimensions (D$D$) of these networks are calculated and D$D$ = 2.485 for the real E. coli network and D$D$ = 2.1 for the UV-flower network is obtained. Also, the authors defined the fractal dimensions of real social networks and compared their method with Song's, Zhang's and Zheng's methods. Furthermore, the authors' algorithm can solve situations with single-node boxes at the edges of the network and can cover networks with minimum number of boxes. The authors believe that centre including eccentricity algorithm is competitive among existing algorithms and can be used to evaluate fractal properties of complex networks.