The Asymptotic Mandelbrot Law of Some Evolution Networks

TL;DR

This paper proves the asymptotic Mandelbrot law for degree distributions in evolution networks with linear preferential attachment, providing analytical derivations for key parameters.

Contribution

It offers a rigorous proof of the Mandelbrot law in certain evolution networks and derives optimal parameters for the degree distribution.

Findings

Proves the asymptotic Mandelbrot law for specific networks.

Derives analytical formulas for the scaling exponent and shift coefficient.

Provides best-fitting values for the degree distribution parameters.

Abstract

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 $c$.