Article

Traceroute-like exploration of unknown networks: a statistical analysis

Authors:

Luca Dall'Asta,

Ignacio Alvarez-Hamelin,

Alexei Vázquez,

Alessandro VespignaniAuthors Info & Claims

CAAN'04: Proceedings of the First international conference on Combinatorial and Algorithmic Aspects of Networking

Pages 140 - 153

https://doi.org/10.1007/11527954_13

Published: 05 August 2004 Publication History

Abstract

Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology has been argued to introduce uncontrolled sampling biases that might produce statistical properties of the sampled graph which sharply differ from the original ones. Here we explore these biases and provide a statistical analysis of their origin. We derive a mean-field analytical approximation for the probability of edge and vertex detection that allows us to relate the global topological properties of the underlying network with the statistical accuracy of the sampled graph. In particular we show that shortest path routed sampling allows a clear characterization of underlying graphs with scale-free topology. We complement the analytical discussion with a throughout numerical investigation of simulated mapping strategies in different network models.

References

[1]

The National Laboratory for Applied Network Research (NLANR), sponsored by the National Science Foundation. (see http://moat.nlanr.net/).

[2]

The Cooperative Association for Internet Data Analysis (CAIDA), located at the San Diego Supercomputer Center. (see http://www.caida.org/home/).

[3]

Topology project, Electric Engineering and Computer Science Department, University of Michigan (http://topology.eecs.umich.edu/).

[4]

SCAN project, Information Sciences Institute (http://www.isi.edu/div7/scan/).

[5]

Internet mapping project at Lucent Bell Labs (http://www.cs.belllabs.com/who/ches/map/).

[6]

M. Faloutsos, P. Faloutsos, and C. Faloutsos, "On Power-law Relationships of the Internet Topology," ACM SIGCOMM '99, Comput. Commun. Rev. 29, 251-262 (1999).

Digital Library

[7]

R. Govindan and H. Tangmunarunkit, "Heuristics for Internet Map Discovery," Proc. of IEEE Infocom 2000, Volume 3, 1371-1380, (2000).

[8]

A. Broido and K. C. Claffy, "Internet topology: connectivity of IP graphs," San Diego Proceedings of SPIE International symposium on Convergence of IT and Communication. Denver, CO. 2001.

[9]

G. Caldarelli, R. Marchetti, and L. Pietronero, "The Fractal Properties of Internet," Europhys. Lett. 52, 386 (2000).

[10]

R. Pastor-Satorras, A. Vázquez, and A. Vespignani, "Dynamical and Correlation Properties of the Internet," Phys. Rev. Lett. 87, 258701 (2001); A. Vázquez, R. Pastor-Satorras, and A. Vespignani, "Large-scale topological and dynamical properties of the Internet," Phys. Rev. E .65, 066130 (2002).

[11]

Q. Chen, H. Chang, R. Govindan, S. Jamin, S. J. Shenker, and W. Willinger, "The Origin of Power Laws in Internet Topologies Revisited," Proceedings of IEEE Infocom 2002, New York, USA.

[12]

A. Medina and I. Matta, "BRITE: a flexible generator of Internet topologies," Tech. Rep. BU-CS-TR-2000-005, Boston University, 2000.

Digital Library

[13]

C. Jin, Q. Chen, and S. Jamin, "INET: Internet topology generators," Tech. Rep. CSE-TR-433-00, EECS Dept., University of Michigan, 2000.

[14]

S. N. Dorogovtsev and J. F. F. Mendes, Evolution of networks: From biological nets to the Internet and WWW (Oxford University Press, Oxford, 2003).

Digital Library

[15]

P. Baldi, P. Frasconi and P. Smyth, Modeling the Internet and the Web: Probabilistic methods and algorithms (Wiley, Chichester, 2003).

[16]

R. Pastor-Satorras and A. Vespignani, Evolution and structure of the Internet: A statistical physics approach (Cambridge University Press, Cambridge, 2004).

Digital Library

[17]

H. Burch and B. Cheswick, "Mapping the internet," IEEE computer, 32(4), 97-98 (1999).

Digital Library

[18]

W. Willinger, R. Govindan, S. Jamin, V. Paxson, and S. Shenker, "Scaling phenomena in the Internet: Critically examining criticality," Proc. Natl. Acad. Sci USA 99 2573-2580, (2002).

[19]

A. Lakhina, J. W. Byers, M. Crovella and P. Xie, "Sampling Biases in IP Topology Measurements," Technical Report BUCS-TR-2002-021, Department of Computer Sciences, Boston University (2002).

[20]

A. Clauset and C. Moore, "Traceroute sampling makes random graphs appear to have power law degree distributions," arXiv:cond-mat/0312674 (2003).

[21]

T. Petermann and P. De Los Rios, "Exploration of scale-free networks - Do we measure the real exponents?", Eur. Phys. J B 38, 201 (2004).

[22]

L. C. Freeman, "A Set of Measures of Centrality Based on Betweenness," Sociometry 40, 35-41 (1977).

[23]

U. Brandes, "A Faster Algorithm for Betweenness Centrality," J. Math. Soc. 25(2), 163-177, (2001).

[24]

K.-I. Goh, B. Kahng, and D. Kim, "Universal Behavior of Load Distribution in Scale-Free Networks," Phys. Rev. Lett. 87, 278701 (2001).

[25]

P. Erdös and P. Rényi, "On random graphs I," Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960).

[26]

D. J. Watts and S. H. Strogatz, "Collective dynamics of small-world networks," Nature 393, 440-442 (1998).

[27]

A.-L. Barabási and R. Albert, "Emergence of scaling in random networks," Science 286, 509-512 (1999).

[28]

S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, "Size-dependent degree distribution of a scale-free growing network," Phys. Rev. E 63, 062101 (2001).

[29]

M. Barthélemy, "Betweenness Centrality in Large Complex Networks," Eur. Phys. J B 38, 163 (2004).

Cited By

Mérindol PDonnet BBonaventure OPansiot JAllman M(2010)On the impact of layer-2 on node degree distributionProceedings of the 10th ACM SIGCOMM conference on Internet measurement10.1145/1879141.1879164(179-191)Online publication date: 1-Nov-2010
https://dl.acm.org/doi/10.1145/1879141.1879164
Flaxman AVera J(2007)Bias reduction in traceroute sampling - towards a more accurate map of the internetProceedings of the 5th international conference on Algorithms and models for the web-graph10.5555/1777879.1777880(1-15)Online publication date: 11-Dec-2007
https://dl.acm.org/doi/10.5555/1777879.1777880

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Published In

cover image Guide Proceedings

CAAN'04: Proceedings of the First international conference on Combinatorial and Algorithmic Aspects of Networking

August 2004

205 pages

ISBN:3540278737

Editors:
Alejandro López-Ortiz
Cheriton School of Computer Science, University of Waterloo, Waterloo, Ont., Canada
,
Angèle M. Hamel
Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, Canada

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 05 August 2004

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Cited By

Mérindol PDonnet BBonaventure OPansiot JAllman M(2010)On the impact of layer-2 on node degree distributionProceedings of the 10th ACM SIGCOMM conference on Internet measurement10.1145/1879141.1879164(179-191)Online publication date: 1-Nov-2010
https://dl.acm.org/doi/10.1145/1879141.1879164
Flaxman AVera J(2007)Bias reduction in traceroute sampling - towards a more accurate map of the internetProceedings of the 5th international conference on Algorithms and models for the web-graph10.5555/1777879.1777880(1-15)Online publication date: 11-Dec-2007
https://dl.acm.org/doi/10.5555/1777879.1777880

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