Tail Flexibility in the Degrees of Preferential Attachment Networks

Abstract: Devising the underlying generating mechanism of a real-life network is difficult as, more often than not, only its snapshots are available, but not its full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest form, results in a degree distribution that follows the power law. Consequently, the growth of real-life networks that roughly display such power-law behaviour is commonly modelled by preferential attachment. However, the validity of the power law has been challenged by the presence of alternatives with comparable performance, as well as the recent findings that the right tail of the degree distribution is often lighter than implied by the body, whilst still being heavy. In this paper, we study a modified version of the model with a flexible preference function that allows super/sub-linear behaviour whilst also guaranteeing that the limiting degree distribution has a heavy tail. We relate the distributions tail index directly to the model parameters, allowing direct inference of the parameters from the degree distribution alone.