Node similarity measuring in complex networks with relative entropy

Measuring the similarity of nodes in complex network has been significant research in the analysis of complex characteristic. Several existing methods have been proposed to address this problem, but most of them have their own limitations and shortcomings. So a novel method based on relative entropy is proposed to solve the problems above. The proposed entropy combines the fractal dimension of the whole network and the local dimension of each node on the basis of Tsallis entropy. When the fractal dimension equals to 1, the relative entropy would degenerate to classic form based on Shannon entropy. In addition, relevance matrix and similarity matrix are used to show the difference of structure and the similarity of each pair of nodes. The ranking results show the similarity degree of each node. In order to show the effectiveness of this method, four real-world complex networks are applied to measure the similarity of nodes. After comparing four existing methods, the results demonstrate the superiority of this method by employing susceptible-infected (SI) model and the ratio of mutual similar nodes.