Paper ID: 2311.11200 • Published Nov 19, 2023
Beyond the Power Law: Estimation, Goodness-of-Fit, and a Semiparametric Extension in Complex Networks
Nixon Jerez-Lillo, Francisco A. Rodrigues, Paulo H. Ferreira, Pedro L. Ramos
TL;DR
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Scale-free networks play a fundamental role in the study of complex networks
and various applied fields due to their ability to model a wide range of
real-world systems. A key characteristic of these networks is their degree
distribution, which often follows a power-law distribution, where the
probability mass function is proportional to x-\alpha, with α
typically ranging between 2 < α < 3. In this paper, we introduce
Bayesian inference methods to obtain more accurate estimates than those
obtained using traditional methods, which often yield biased estimates, and
precise credible intervals. Through a simulation study, we demonstrate that our
approach provides nearly unbiased estimates for the scaling parameter,
enhancing the reliability of inferences. We also evaluate new goodness-of-fit
tests to improve the effectiveness of the Kolmogorov-Smirnov test, commonly
used for this purpose. Our findings show that the Watson test offers superior
power while maintaining a controlled type I error rate, enabling us to better
determine whether data adheres to a power-law distribution. Finally, we propose
a piecewise extension of this model to provide greater flexibility, evaluating
the estimation and its goodness-of-fit features as well. In the complex
networks field, this extension allows us to model the full degree distribution,
instead of just focusing on the tail, as is commonly done. We demonstrate the
utility of these novel methods through applications to two real-world datasets,
showcasing their practical relevance and potential to advance the analysis of
power-law behavior.