Tsallis information dimension of complex networks

• A generalized information dimension of the complex networks is proposed based on the Tsallis entropy.
• The information dimension of the complex networks is changed according to the scale.
• We show the relation between the information dimension and the nonextensivity parameter qq.

The fractal and self-similarity properties are revealed in many complex networks. The information dimension is a useful method to describe the fractal and self-similarity properties of the complex networks. In order to show the influence of different parts in the complex networks to the information dimension, we have proposed a new information dimension based on the Tsallis entropy namely the Tsallis information dimension. The proposed information dimension is changed according to the scale which is described by the nonextensivity parameter qq, and it is inverse with the nonextensivity parameter qq. The existing information dimension is a special case of the Tsallis information dimension when q=1q=1. The Tsallis information dimension is a generalized information dimension of the complex networks.