Asymptotic Mandelbrot Law for Some Evolving Networks  

作　　者：Jiyuan Tan Li Li Yi Zhang 

机构地区：[1]Tsinghua National Laboratory for Information Science and Technology,Department of Automation,Tsinghua University,Beijing 100084,China

出　　处：《Tsinghua Science and Technology》2012年第3期310-312,共3页清华大学学报（自然科学版（英文版）

基　　金：Partially supported by the National Natural Science Foundation of China (Nos. 60774034 and 60721003);the Scientific Research Foundation for Returned Overseas Chinese Scholars, Education Ministry of China

摘　　要：Complex networks are now the focus of many branches of research. Particularly, the scale-free property of some networks is of great interest, due to their importance and pervasiveness. Recent studies have shown that in some complex networks, e.g., transportation networks and social collaboration networks, the degree distribution follows the so-called ＂shifted power law＂ （or Mandelbrot law） P（k）oc （k ＋cyy. This study analyzes some evolving networks that grow with linear preferential attachments. Recent results for the quotient Gamma function are used to prove the asymptotic Mandelbrot law for the degree distribution in certain conditions. The best fit values for the scaling exponent, y, and the shifting coefficient, c, can be directly calculated using Bernoulli polynomial functions. The study proves that the degree distribution of some complex networks follows an asymptotic Mandelbrot law with linear preferential attachment depicted by p（k） .Complex networks are now the focus of many branches of research. Particularly, the scale-free property of some networks is of great interest, due to their importance and pervasiveness. Recent studies have shown that in some complex networks, e.g., transportation networks and social collaboration networks, the degree distribution follows the so-called ＂shifted power law＂ （or Mandelbrot law） P（k）oc （k ＋cyy. This study analyzes some evolving networks that grow with linear preferential attachments. Recent results for the quotient Gamma function are used to prove the asymptotic Mandelbrot law for the degree distribution in certain conditions. The best fit values for the scaling exponent, y, and the shifting coefficient, c, can be directly calculated using Bernoulli polynomial functions. The study proves that the degree distribution of some complex networks follows an asymptotic Mandelbrot law with linear preferential attachment depicted by p（k） .

关 键 词：complex networks SCALE-FREE asymptotic Mandelbrot law 

分 类 号：TP393.08[自动化与计算机技术—计算机应用技术] TN929.5[自动化与计算机技术—计算机科学与技术]