Degree distributions in networks: Beyond the power law

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 nee...

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Bibliographic Details
Published in:Statistica Neerlandica Vol. 78; no. 4; pp. 702 - 718
Main Authors: Lee, Clement, Eastoe, Emma F., Farrell, Aiden
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.11.2024
Subjects:
Algorithms
Bayesian analysis
Bayesian model selection
degree distribution
generalized Pareto
Markov analysis
Markov chain Monte Carlo
Monte Carlo simulation
polyalgorithm
Power law
Statistical inference
threshold uncertainty
Uncertainty
ISSN:0039-0402, 1467-9574
Online Access:Get full text
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Summary: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.
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ISSN:0039-0402
1467-9574
DOI:10.1111/stan.12355