Evidencing preferential attachment in dependency network evolution

Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable practices of determining scale-freeness and when only snapshots of the degree distribution are observed. In the presence of the evolution history of the network, modelling the increments of the evolution allows us to measure preferential attachment directly. Therefore, we propose a generalised linear model for such purpose, where the in-degrees and their increments are the covariate and response, respectively. Not only are the parameters that describe the preferential attachment directly incorporated, they also ensure that the tail heaviness of the asymptotic degree distribution is realistic. The Bayesian approach to inference enables the hierarchical version of the model to be implemented naturally. The application to the dependency network of R packages reveals subtly different behaviours between new dependencies by new and existing packages, and between addition and removal of dependencies.