Does the average path length grow in the Internet?

Abstract

In this paper we focus on the trend of the average path length of the AS-level Internet, which is one of the most important parameters to measure the efficiency of the Internet. The conclusion drawn by the power-law and small world models is that the average path length of network scales as ln(n) or ln(ln(n)), n is the number of nodes in network. But through analyzing the data of BGP tables in recent 5 years, we find that the average path length of the Internet is descending and the descending rate is about 0.00025 which is much different from the result induced from the theories. We anatomize the reason and find many factors will affect the value of path length, like multi-homing, commercial relationships and so on. Besides, the trend of the average path length is also drawn with mathematics. © 2008 Springer Berlin Heidelberg.