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Preferential attachment is commonly invoked to explain the emergence of thoseheavy-tailed degree distributions characteristic of growing networkrepresentations of diverse real-world phenomena. Experimentally confirming thishypothesis in real-world growing networks is an important frontier in networkscience research. Conventional preferential attachment estimation methodsrequire that a growing network be observed across at least two snapshots intime. Numerous publicly available growing network datasets are, however, onlyavailable as single snapshots, leaving the applied network scientist with nomeans of measuring preferential attachment in these cases. We propose anonparametric method, called PAFit-oneshot, for estimating preferentialattachment in a growing network from one snapshot. PAFit-oneshot corrects for apreviously unnoticed bias that arises when estimating preferential attachmentvalues only for degrees observed in the single snapshot. Our work provides ameans of measuring preferential attachment in a large number of publiclyavailable one-snapshot networks. As a demonstration, we estimated preferentialattachment in three such networks, and found sublinear preferential attachmentin all cases. PAFit-oneshot is implemented in the R package PAFit.

Nonparametric estimation of the preferential attachment function from one network snapshot