Nonextensive analysis on the local structure entropy of complex networks

The local structure entropy is a new method which is proposed to identify the influential nodes in the complex networks. In this paper a new form of the local structure entropy of the complex networks is proposed based on the Tsallis entropy. The value of the entropic index q will influence the property of the local structure entropy. When the value of q is equal to 0, the nonextensive local structure entropy is degenerated to a new form of the degree centrality. When the value of q is equal to 1, the nonextensive local structure entropy is degenerated to the existing form of the local structure entropy. We also have find a nonextensive threshold value in the nonextensive local structure entropy. When the value of q is bigger than the nonextensive threshold value, change the value of q will has no influence on the property of the local structure entropy, and different complex networks have different ∗Corresponding author: Yong Deng, School of Computer and Information Science, Southwest University, Chongqing, 400715, China. Email address: [email protected], [email protected] (Yong Deng) Preprint submitted to Physica A February 3, 2015 nonextensive threshold value. The results in this paper show that the new nonextensive local structure entropy is a generalised of the local structure entropy. It is more reasonable and useful than the existing one.