An evolving pseudofractal network model

In this work, we consider a randomized version of the deterministic pseudofractal graph model, which was first proposed in the physical literature. Our model is a sequence of dynamic networks, in which the increment of network size at each time depends on the current size and a sequence of evolving parameters. We first show that the network size is closely related to a branching process in the varying environment. Under a mild assumption, we then prove that the asymptotic degree distribution in our model obeys the power law with an exponent three. Based on this asymptotic degree distribution, we show that the clustering coefficient of our network model converges to a given constant in probability.