On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Collecting the internet AS-level topology
ACM SIGCOMM Computer Communication Review
Building an AS-topology model that captures route diversity
Proceedings of the 2006 conference on Applications, technologies, architectures, and protocols for computer communications
AS relationships: inference and validation
ACM SIGCOMM Computer Communication Review
Testing the reachability of (new) address space
Proceedings of the 2007 SIGCOMM workshop on Internet network management
A systematic framework for unearthing the missing links: measurements and impact
NSDI'07 Proceedings of the 4th USENIX conference on Networked systems design & implementation
Internet optometry: assessing the broken glasses in internet reachability
Proceedings of the 9th ACM SIGCOMM conference on Internet measurement conference
Proceedings of the 9th ACM SIGCOMM conference on Internet measurement conference
Pitfalls for testbed evaluations of internet systems
ACM SIGCOMM Computer Communication Review
The (in)completeness of the observed internet AS-level structure
IEEE/ACM Transactions on Networking (TON)
Towards an AS-to-organization map
IMC '10 Proceedings of the 10th ACM SIGCOMM conference on Internet measurement
Scalable and systematic Internet-wide path and delay estimation from existing measurements
Computer Networks: The International Journal of Computer and Telecommunications Networking
Twelve years in the evolution of the internet ecosystem
IEEE/ACM Transactions on Networking (TON)
Mixing biases: structural changes in the AS topology evolution
TMA'10 Proceedings of the Second international conference on Traffic Monitoring and Analysis
On the incompleteness of the AS-level graph: a novel methodology for BGP route collector placement
Proceedings of the 2012 ACM conference on Internet measurement conference
Inferring multilateral peering
Proceedings of the ninth ACM conference on Emerging networking experiments and technologies
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Study of the Internet's high-level structure has for some time intrigued scientists. The AS-graph (showing interconnections between Autonomous Systems) has been measured, studied, modelled and discussed in many papers over the last decade. However, the quality of the measurement data has always been in question. It is by now well known that most measurements of the AS-graph are missing some set of links. Many efforts have been undertaken to correct this, primarily by increasing the set of measurements, but the issue remains: how much is enough? When will we know that we have enough measurements to be sure we can see all (or almost all) of the links. This paper aims to address the problem of estimating how many links are missing from our measurements. We use techniques pioneered in biostatistics and epidemiology for estimating the size of populations (for instance of fish or disease carriers). It is rarely possible to observe entire populations, and so sampling techniques are used. We extend those techniques to the domain of the AS-graph. The key difference between our work and the biological literature is that all links are not the same, and so we build a stratified model and specify an EM algorithm for estimating its parameters. Our estimates suggest that a very significant number of links (many of thousands) are missing from standard route monitor measurements of the AS-graph. Finally, we use the model to derive the number of monitors that would be needed to see a complete AS-graph with high-probability. We estimate that 700 route monitors would see 99.9% of links.