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 areavailable 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 .
Measuring preferential attachment in growing networks has received considerable attention, not only for understanding how heavy-tail degree distributions emerge in real-world networks , but also for gaining insight into various rich-get-richer effects that arise in diverse fields. Conventional estimation methods require that a network be observed across at least two snapshots in time. Numerous real-world datasets are, however, available only as single snapshots, rendering most conventional methods inapplicable of estimating a general preferential attachment function . We propose a nonparametric method, called PAFit-oneshot, for estimating preferential attachment in a growing network from one snapshot. PAFit-oneshot corrects for a previously unnoticed bias that arises when estimating preferential attachment values only for degrees observed in the snapshot. Our work provides scientists with a means of measuring preferential attachment in a large number of publicly available one-snapshot networks . As a demonstration, we estimated preferential attachment in three such networks , and found sublinear preferential attachment in all cases .
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