On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
On inferring autonomous system relationships in the internet
IEEE/ACM Transactions on Networking (TON)
Towards capturing representative AS-level Internet topologies
SIGMETRICS '02 Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Network topology generators: degree-based vs. structural
Proceedings of the 2002 conference on Applications, technologies, architectures, and protocols for computer communications
Towards an accurate AS-level traceroute tool
Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications
Internet connectivity at the AS-level: an optimization-driven modeling approach
MoMeTools '03 Proceedings of the ACM SIGCOMM workshop on Models, methods and tools for reproducible network research
A first-principles approach to understanding the internet's router-level topology
Proceedings of the 2004 conference on Applications, technologies, architectures, and protocols for computer communications
Collecting the internet AS-level topology
ACM SIGCOMM Computer Communication Review
Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
The internet AS-level topology: three data sources and one definitive metric
ACM SIGCOMM Computer Communication Review
Graph mining: Laws, generators, and algorithms
ACM Computing Surveys (CSUR)
Building an AS-topology model that captures route diversity
Proceedings of the 2006 conference on Applications, technologies, architectures, and protocols for computer communications
In search for an appropriate granularity to model routing policies
Proceedings of the 2007 conference on Applications, technologies, architectures, and protocols for computer communications
Observing the evolution of internet as topology
Proceedings of the 2007 conference on Applications, technologies, architectures, and protocols for computer communications
On the impact of route monitor selection
Proceedings of the 7th ACM SIGCOMM conference on Internet measurement
Modeling internet topology dynamics
ACM SIGCOMM Computer Communication Review
In search of the elusive ground truth: the internet's as-level connectivity structure
SIGMETRICS '08 Proceedings of the 2008 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Ten years in the evolution of the internet ecosystem
Proceedings of the 8th ACM SIGCOMM conference on Internet measurement
Basic properties of the IPv6 AS-level topology
ACM SIGMETRICS Performance Evaluation Review
Measuring the Impacts of Sampling Bias on Internet AS-Level Topology Inference
CMC '09 Proceedings of the 2009 WRI International Conference on Communications and Mobile Computing - Volume 03
Lord of the links: a framework for discovering missing links in the internet topology
IEEE/ACM Transactions on Networking (TON)
Network topologies: inference, modeling, and generation
IEEE Communications Surveys & Tutorials
Detecting and assessing the hybrid IPv4/IPv6 as relationships
Proceedings of the ACM SIGCOMM 2011 conference
HDLBR: A name-independent compact routing scheme for power-law networks
Computer Communications
Understanding IPv6 internet background radiation
Proceedings of the 2013 conference on Internet measurement conference
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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.