Dynamical properties of diffusion process on complex networks with arbitrary degree distribution

Dynamical properties of diffusion process on complex networks with arbitrary degree distribution are investigated. The rule of the diffusion process encompasses both the structural characteristics and the information processing dynamics. Considering the influence of a node on the global dynamical behavior, the dynamical generating function of the process, which is deeply reflecting the basic characteristic of the process and mutually decided with the dynamical process, is proposed. Based on the analysis of the dynamical generating function we introduce dynamical centrality for each node, which determines the relative importance of nodes and the capability of the given node to collect and communicate information with its neighbouring environment in the network via the diffusion process. Furthermore, a new parameter, dynamical entropy, is proposed to measure the interplay between dynamical centrality and diffusion dynamics. The experimental results on large-scale complex networks with Poisson distribution confirm our analytical prediction.