Complex network comparison based on communicability sequence entropy

Identification and quantification of the structural dissimilarities between complex networks is a very important and challenging problem in network science. A simple and efficient way to quantify network differences remains unexplored. Although the methods for network comparison based on the probability distribution of a network descriptor have been shown to be effective for specific purposes, the information they provide is often limited or incomplete. In order to overcome the defect of the methods, here we use the communicability between two nodes to define the communicability sequence entropy of networks, and on the basis of this entropy measure, we propose a Jensen-Shannon divergence of two networks which can be used as natural distance measure between complex networks. By the extensive experiments, we find that the measure can accurately quantify the structural dissimilarities between synthetic networks. Most importantly, the measure can be able to identify the critical percolation probability of the random network in the evolution process, and it can also effectively guide us to choose a more suitable model to simulate real systems.