A spliced preferential attachment model for degree distributions in networks
Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is the general preferential attachment (GPA), in which existing nodes gain new connections at a rate governed by a preference function of their current degree, which, in its simplest form, results in a degree distribution that follows the power law. However, the ubiquity of the power law in real-life networks has been challenged on two fronts: alternative distributions often fit comparably well, and recent works using extreme value methods have shown that the tail of the degree distribution, while still regularly varying, tends to be lighter than the body implies. In this paper, we propose a GPA model with a flexible preference function. Using methods for discrete extremes, we characterise the tail behaviour of the limiting degree distribution directly by the preference function. This direct connection facilitates the inference of the model parameters using snapshot data alone, and sidesteps the need of traditional threshold-based extreme value methods, which lack interpretability and suffer from identifiability issues. Comprehensive simulation studies show that our model recovers the parameters well, while applications to real-life networks demonstrate comparable performance to established alternatives and provide insights into the growth dynamics of the networks.