For a family of linear preferential attachment graphs, we provide rates of convergence for the total variation distance between the degree of a randomly chosen vertex and an appropriate power law distribution as the number of vertices tends to ∞. Our proof uses a new formulation of Stein's method for the negative binomial distribution, which stems from a distributional transformation that has the negative binomial distributions as the only fixed points.
Nathan Ross. "Power laws in preferential attachment graphs and Stein's method for the negative binomial distribution." Adv. in Appl. Probab. 45 (3) 876 - 893, September 2013. https://doi.org/10.1239/aap/1377868543