Nonparametric estimation of the preferential attachment function from one network snapshot

Measuring preferential attachment in growing networks is an important topic in network science, since the experimental confirmation of assumptions about the generative processes that give rise to heavy-tail degree distributions characteristic of real-world networks depends on it. Multiple methods have been devised for measuring preferential attachment in time-resolved networks. However, many real-world network datasets are available as only single snapshots. We propose a novel nonparametric method, called PAFit-oneshot, for estimating the preferential attachment function for a growing network from one snapshot. The PAFit-oneshot method corrects for a bias that arises when estimating preferential attachment values only for degrees observed in the single snapshot. This bias, which had previously gone unnoticed, has a connection with a recently developed conditional inference approach called post-selection inference. Extensive experiments show that our method recovers the true preferential attachment function in simulated as well as real-world networks. Our work opens up a new path for network scientists to measure preferential attachment in a large number of one-snapshot networks that have been out-of-reach until now. As a demonstration, we nonparametrically estimated the preferential attachment function in three such networks and found all are sub-linear. The PAFit-oneshot method is implemented in the R package PAFit.