  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.
