Measuring the complexity of complex network by Tsallis entropy

Measuring the complexity degree of complex network has been an important issue of network theory. A number of complexity measures like structure entropy have been proposed to address this problem. However, these existing structure entropies are based on Shannon entropy which only focuses on global structure or local structure. To break the limitation of existing method, a novel structure entropy which is based on Tsallis entropy is introduced in this paper. This proposed measure combines the fractal dimension and local dimension which are both the significant property of network structure, and it would degenerate to the Shannon entropy based on the local dimension when fractal dimension equals to 1. This method is based on the dimension of network which is a different approach to measure the complexity degree compared with other methods. In order to show the performance of this proposed method, a series of complex networks which are grown from the simple nearest-neighbor coupled network and five real-world networks have been applied in this paper. With comparing with several existing methods, the results show that this proposed method performs well.