A new information dimension of complex network based on Rényi entropy

Abstract

With the development of high technology and artificial intelligence, it evolves into an open issue to calculate the dimension of the complex network. In this paper, a new dimension — Rényi dimension, combined with Rényi entropy and information dimension is proposed. A modified box-covering algorithm is introduced to calculate the minimum number and the length of the boxes needed to cover the whole network. Additionally, the self weight factor (SWF) and the positive weight factor (PWF) are defined to illustrate the change of the dimension value based on the perspective of both topology structure and dynamic property. The concept of attractors is proposed to illuminate the physical meaning of the weighted parameter in the formula of Rényi entropy — α, PWF and SWF. Finally, to demonstrate the efficiency of our method, it is applied to calculate the dimension of Sierpinski weighted fractal network, BA networks and many real-world networks. The results show that attractors exist in the network researched and α can access the attractiveness of attractors as a criterion. The SWF quantifies the total attractiveness of attractors. The comparison results with Tsallis dimension indicate the stability of the Rényi dimension.