The Asymptotic Mandelbrot Law of Some Evolution Networks

Details The Asymptotic Mandelbrot Law of Some Evolution Networks The Asymptotic Mandelbrot Law of Some Evolution Networks

2011-06-19

arxiv.org/abs/1106.3740v2

Physics

Data Analysis, Statistics and Probability

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Scientific paper

In this letter, we study some evolution networks that grow with linear preferential attachment. Based upon some recent results on the quotient Gamma function, we give a rigorous proof of the asymptotic Mandelbrot law for the degree distribution $p_k \propto (k + c)^{-\gamma}$ in certain conditions. We also analytically derive the best fitting values for the scaling exponent $\gamma$ and the shifting coefficient $c$.

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