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Degree distributions in networks: Beyond the power law

Lookup NU author(s): Dr Clement LeeORCiD

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Abstract

The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been criticisms of the power law, for example, that a threshold needs to be preselected without its uncertainty quantified, that the power law is simply inadequate, and that subsequent hypothesis tests are required to determine whether the data could have come from the power law. We propose a modeling framework that combines two different generalizations of the power law, namely the generalized Pareto distribution and the Zipf-polylog distribution, to resolve these issues. The proposed mixture distributions are shown to fit the data well and quantify the threshold uncertainty in a natural way. A model selection step embedded in the Bayesian inference algorithm further answers the question whether the power law is adequate.

Publication metadata

Author(s): Lee C, Eastoe E, Farrell A

Publication type: Article

Publication status: Published

Journal: Statistica Neerlandica

Year: 2024

Pages: epub ahead of print

Online publication date: 23/07/2024

Acceptance date: 08/07/2024

Date deposited: 23/07/2024

ISSN (print): 0039-0402

ISSN (electronic): 1467-9574

Publisher: Wiley

URL: https://doi.org/10.1111/stan.12355

DOI: 10.1111/stan.12355

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