Open AccessAverage path length of Internet with power law degree distribution
Author(s) -
Ying Li,
Shan Xiu-Ming,
YongXiang Ren
Publication year - 2004
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.53.3695
Subject(s) - path (computing) , degree (music) , path length , average path length , degree distribution , distribution (mathematics) , work (physics) , the internet , relation (database) , combinatorics , power (physics) , mathematics , computer science , discrete mathematics , shortest path problem , physics , mathematical analysis , complex network , computer network , graph , data mining , quantum mechanics , world wide web , acoustics , thermodynamics
The average path length of Internet with power law degree distribution is stud ied in this paper. The main work is to give a formula to compute the average pat h length . The essential of Internet or many other complex networks is to realize the least cost (the smallest total number of edges) and the best benefi t (the short average path length), which can be expressed as two optimization fa ctors to minimize the average degree and the average path length . By analyzing the main factor affecting , we find the main property of p ath length distribution P(l), and then give a formula of P(l) only inclu ding one parameter α. This work shows that P(l) and a direct relation with P(k),and α represent the effective link between nodes and the tota l number of networks on . This formula makes it possible that if we get the α of P(k)k-α, we can calculate easily. The simulati on shows the formula is quite exact. Our method is successful. In the end, we di scuss that the parameter αis very important for Internet design.