Generating function technique in complex networks

Abstract

Complex network is a useful tool in describing the interactions between different agents of a complex system, and has attracted considerable interest recently. There are various approaches to studying the structure and dynamic of complex networks for the diverse and complicated connectivity structure. One more applicable theoretical approach is the generating function technique, which is useful for the studies of network structure and dynamic, especially for tree-like networks. In this paper, we will give a summary of the basic ideas of this approach, and explore the structure of networks. A cascading failures model we have proposed before will also be presented as an application of this approach.