کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
974204 | 1480108 | 2017 | 12 صفحه PDF | دانلود رایگان |
• Least squares method is not appropriate for estimating β of Barabási–Albert graphs.
• A modified version of Clauset et al. (2009) is more preferable for estimation.
• Simulated graphs show that exponent is not the theoretical β = 2 for small graphs.
• Value of β is also dependent on number of edges added, mm, for small graphs.
• Smaller value of m results in larger value of β for all graph sizes.
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 10001000 simulated Barabási–Albert graphs for edge parameter m∈{2,4,6}m∈{2,4,6} and size n∈{2k:k=5,6,…,14,15}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 mm. Further results confirm the finding that the parameter of the power law distribution, ββ, increases as mm increases.
Journal: Physica A: Statistical Mechanics and its Applications - Volume 465, 1 January 2017, Pages 141–152