Phase changes in the evolution of the IPv4 and IPv6 AS-Level Internet topologies

  • Authors:
  • Guoqiang Zhang;Bruno Quoitin;Shi Zhou

  • Affiliations:
  • Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China;Networking Lab, Université de Mons, Place du Parc, 20, 7000 Mons, Belgium;Department of Computer Science, University College London, United Kingdom

  • Venue:
  • Computer Communications
  • Year:
  • 2011

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In this paper, we investigate the evolution of the IPv4 and IPv6 Internet topologies at the autonomous system (AS) level over a long period of time. We provide abundant empirical evidence that there is a phase transition in the growth trend of the two networks. For the IPv4 network, the phase change occurred in 2001. Before then the network's size grew exponentially, and thereafter it followed a linear growth. Changes are also observed around the same time for the maximum node degree, the average node degree and the average shortest path length. For the IPv6 network, the phase change occurred in late 2006. It is notable that the observed phase transitions in the two networks are different, for example the size of IPv6 network initially grew linearly and then shifted to an exponential growth. Our results show that following decades of rapid expansion up to the beginning of this century, the IPv4 network has now evolved into a mature, steady stage characterised by a relatively slow growth with a stable network structure; whereas the IPv6 network, after a slow startup process, has just taken off to a full speed growth. We also provide insight into the possible impact of IPv6-over-IPv4 tunnelling deployment scheme on the evolution of the IPv6 network. The Internet topology generators so far are based on an inexplicit assumption that the evolution of Internet follows non-changing dynamic mechanisms. This assumption, however, is invalidated by our results. Our work reveals insights into the Internet evolution and provides inputs to future AS-Level Internet models.