Asymptotic Degree Distribution of a Kind of Asymmetric Evolving Network

Abstract

We propose a kind of evolving network which shows tree structure. The model is a combination of preferential attachment model and uniform model. We show that the proportional degree sequence ${\left\{p_k\right\}}_{k>1}$ obeys power law, exponential distribution, and other forms according to the relation of $k$ and parameter $m$.