Asymptotic degree distribution in a homogeneous evolving network model.

In this paper we propose an evolving network model, which is a randomized version of the pseudofractal graphs by introducing an evolutionary parameter 0 < p < 1. Our network model grows exponentially over time, and can be generated in an iterative manner: at each time step, with probability p each existing edge recruits independently a new node and connects to it with both endpoints. We first briefly discuss the network size, which can correspond to a supercritical branching process. Then, it shows that the asymptotic degree distribution in our network model can be uniquely determined by a functional equation of its probability generating function. [ABSTRACT FROM AUTHOR]