Nonparametric estimation of the preferential attachment function from one network snapshot

TL;DR

This paper introduces PAFit-oneshot, a nonparametric method to estimate preferential attachment from a single network snapshot, enabling analysis of many real-world networks where multiple snapshots are unavailable.

Contribution

The paper presents a novel bias-corrected nonparametric estimator for preferential attachment from one snapshot, expanding analysis capabilities for single-snapshot networks.

Findings

Estimated sublinear preferential attachment in three real-world networks.

Corrected bias in single-snapshot preferential attachment estimation.

Enabled analysis of many publicly available networks with one snapshot.

Abstract

Preferential attachment is commonly invoked to explain the emergence of those heavy-tailed degree distributions characteristic of growing network representations of diverse real-world phenomena. Experimentally confirming this hypothesis in real-world growing networks is an important frontier in network science research. Conventional preferential attachment estimation methods require that a growing network be observed across at least two snapshots in time. Numerous publicly available growing network datasets are, however, only available as single snapshots, leaving the applied network scientist with no means of measuring preferential attachment in these cases. 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 single snapshot. Our work provides 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. PAFit-oneshot is implemented in the R package PAFit.