# On the bias of traceroute sampling: or, power-law degree distributions in regular graphs

@article{Achlioptas2005OnTB, title={On the bias of traceroute sampling: or, power-law degree distributions in regular graphs}, author={Dimitris Achlioptas and Aaron Clauset and David Kempe and Cristopher Moore}, journal={J. ACM}, year={2005}, volume={56}, pages={21:1-21:28} }

Understanding the structure of the Internet graph is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining its graph structure is a surprisingly difficult task, as edges cannot be explicitly queried. Instead, empirical studies rely on traceroutes to build what are essentially single-source, all-destinations, shortest-path trees. These trees only sample a fraction of the network's edges, and a recent paper by Lakhina et…

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## References

SHOWING 1-10 OF 56 REFERENCES

Sampling biases in IP topology measurements

- Computer ScienceIEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428)
- 2003

It is shown that when graphs are sampled using traceroute-like methods, the resulting degree distribution can differ sharply from that of the underlying graph, and why this effect arises is explored.

Accuracy and scaling phenomena in Internet mapping.

- Mathematics, MedicinePhysical review letters
- 2005

It is found that in order to accurately estimate alpha, one must use a number of sources which grows linearly in the mean degree of the underlying graph, and comment on the accuracy of the published values of alpha for the Internet.

Exploring networks with traceroute-like probes: theory and simulations

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2006

An analytical approximation for the probability of edge and vertex detection is derived that exploits the role of the number of sources and targets and allows us to relate the global topological properties of the underlying network with the statistical accuracy of the sampled graph.

Bias Reduction in Traceroute Sampling - Towards a More Accurate Map of the Internet

- Computer Science, PhysicsWAW
- 2007

A new estimator for the degree of a node in a traceroute-sampled graph is developed and validated theoretically in Erdos-Renyi graphs and, through computer experiments, for a wider range of graphs; and it is applied to produce a new picture of the degree distribution of the autonomous system graph.

Issues with inferring Internet topological attributes

- Computer ScienceComput. Commun.
- 2004

This study uses multiple views of the same data to demonstrate that some topological attributes, such as the average path length, are relatively consistent across a variety of data sources, and illustrates how using the same methodology to model other attributes can produce substantially misleading results.

On the marginal utility of network topology measurements

- Computer ScienceIMW '01
- 2001

This paper characterize the observable topology in terms of nodes, links, node degree distribution, and distribution of end-to-end flows using statistical and information-theoretic techniques and shows that the utility of adding destinations is constant for interfaces, node, links and node degree indicating that it is more important to add destinations than sources.

On power-law relationships of the Internet topology

- Computer ScienceSIGCOMM '99
- 1999

These power-laws hold for three snapshots of the Internet, between November 1997 and December 1998, despite a 45% growth of its size during that period, and can be used to generate and select realistic topologies for simulation purposes.

Distance distribution in random graphs and application to network exploration.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

This work introduces a different way of computing the distribution of distances between nodes that leads to estimates that coincide remarkably well with numerical simulations and allows us to characterize the phase transitions appearing when the connectivity probability varies.

The origin of power laws in Internet topologies revisited

- Computer Science, MathematicsProceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies
- 2002

Re-examine the BGP (border gateway protocol) measurements that form the basis for the results reported by Faloutsos et al. and find that while the vertex degree distributions resulting from the extended maps are heavy-tailed, they deviate significantly from a strict power law.

The Web as a Graph: Measurements, Models, and Methods

- Computer ScienceCOCOON
- 1999

This paper describes two algorithms that operate on the Web graph, addressing problems from Web search and automatic community discovery, and proposes a new family of random graph models that point to a rich new sub-field of the study of random graphs, and raises questions about the analysis of graph algorithms on the Internet.