A method of characterizing network topology based on the breadth-first search tree

A method based on the breadth-first search tree is proposed in this paper to characterize the hierarchical structure of network. In this method, a similarity coefficient is defined to quantitatively distinguish networks, and quantitatively measure the topology stability of the network generated by a model. The applications of the method are discussed in ER random network, WS small-world network and BA scale-free network. The method will be helpful for deeply describing network topology and provide a starting point for researching the topology similarity and isomorphism of networks.