Generalization of the Information Dimension of Complex Networks

The information dimension is a common quality to measure the fractal property of complex networks from the perspective of information content. Based on the existed definition of information dimension of complex networks, we consider further the difference between network nodes, and define firstly the probability of information containing the box as the ratio of the sum of nodes degree in that box to the sum of nodes degree in the network. Then we propose a new information dimension of complex networks according to the probability of information containing the box. The proposed method was applied to calculate the fractal dimensions of five real-world complex networks. The simulation results show that the fractal dimensions obtained by the proposed method are very close to the existed information dimension method and the classical box-covering method, which demonstrate that the proposed method can dealing with the fractal dimension problem of complex networks effectively.