Parameter specification for the degree distribution of simulated Barabási–Albert graphs

Fairul Mohd-Zaid, Christine M. Schubert Kabban, Richard F. Deckro and Edward D. White

Physica A: Statistical Mechanics and its Applications, 2017, vol. 465, issue C, 141-152

Abstract: The degree distribution of a simulated Barabási–Albert graph under linear preferential attachment is investigated. Specifically, the parameters of the power law distribution are estimated and compared against the theoretical values derived using mean field theory. Least squares method and MLE-nonparametric method were utilized to estimate the distribution parameters on 1000 simulated Barabási–Albert graphs for edge parameter m∈{2,4,6} and size n∈{2k:k=5,6,…,14,15}. Goodness of fit metrics were computed on a second set of simulated graphs for the median of the estimated parameters and other hypothetical values for the distribution parameters. The results suggest that the distribution of the parameters from simulated graphs are significantly different from the theoretical distribution and is also dependent on m. Further results confirm the finding that the parameter of the power law distribution, β, increases as m increases.

Keywords: Barabási–Albert; Degree distribution; Parameter estimation; Pareto distribution; Yule–Simon distribution; Goodness of fit (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:465:y:2017:i:c:p:141-152

DOI: 10.1016/j.physa.2016.07.024

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