article

Exploring networks with traceroute-like probes: theory and simulations

Authors:

Luca Dall'Asta,

Ignacio Alvarez-Hamelin,

Alexei Vázquez,

Alessandro VespignaniAuthors Info & Claims

Theoretical Computer Science, Volume 355, Issue 1

Pages 6 - 24

https://doi.org/10.1016/j.tcs.2005.12.009

Published: 06 April 2006 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, akin to the merging of different spanning trees to a set of destination, has been argued to introduce uncontrolled sampling biases that might produce statistical properties of the sampled graph which sharply differ from the original ones. In this paper, we explore these biases and provide a statistical analysis of their origin. We derive an analytical approximation for the probability of edge and vertex detection 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. In particular, we find that the edge and vertex detection probability depends on the betweenness centrality of each element. This allows us to show that shortest path routed sampling provides a better characterization of underlying graphs with broad distributions of connectivity. We complement the analytical discussion with a throughout numerical investigation of simulated mapping strategies in network models with different topologies. We show that sampled graphs provide a fair qualitative characterization of the statistical properties of the original networks in a fair range of different strategies and exploration parameters. Moreover, we characterize the level of redundancy and completeness of the exploration process as a function of the topological properties of the network. Finally, we study numerically how the fraction of vertices and edges discovered in the sampled graph depends on the particular deployements of probing sources. The results might hint the steps toward more efficient mapping strategies.

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Cited By

Yang GZhou JHe CMao Y(2024)Distance-edge-monitoring sets of networksActa Informatica10.1007/s00236-024-00453-z61:2(183-198)Online publication date: 1-Jun-2024
https://dl.acm.org/doi/10.1007/s00236-024-00453-z
Foucaud FMarcille PMyint ZSandeep RSen STaruni S(2024)Monitoring Edge-Geodetic Sets in Graphs: Extremal Graphs, Bounds, ComplexityAlgorithms and Discrete Applied Mathematics10.1007/978-3-031-52213-0_3(29-43)Online publication date: 15-Feb-2024
https://dl.acm.org/doi/10.1007/978-3-031-52213-0_3
Afshar RGoodrich MMatias POsegueda MAgrawal KAzar Y(2021)Parallel Network Mapping AlgorithmsProceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3409964.3461822(410-413)Online publication date: 6-Jul-2021
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Index Terms

Exploring networks with traceroute-like probes: theory and simulations
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Networks

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Published In

cover image Theoretical Computer Science

Theoretical Computer Science Volume 355, Issue 1

Complex networks

6 April 2006

103 pages

ISSN:0304-3975

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Publisher

Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 06 April 2006

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Cited By

Yang GZhou JHe CMao Y(2024)Distance-edge-monitoring sets of networksActa Informatica10.1007/s00236-024-00453-z61:2(183-198)Online publication date: 1-Jun-2024
https://dl.acm.org/doi/10.1007/s00236-024-00453-z
Foucaud FMarcille PMyint ZSandeep RSen STaruni S(2024)Monitoring Edge-Geodetic Sets in Graphs: Extremal Graphs, Bounds, ComplexityAlgorithms and Discrete Applied Mathematics10.1007/978-3-031-52213-0_3(29-43)Online publication date: 15-Feb-2024
https://dl.acm.org/doi/10.1007/978-3-031-52213-0_3
Afshar RGoodrich MMatias POsegueda MAgrawal KAzar Y(2021)Parallel Network Mapping AlgorithmsProceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3409964.3461822(410-413)Online publication date: 6-Jul-2021
https://dl.acm.org/doi/10.1145/3409964.3461822
Foucaud FKlasing RMiller MRyan J(2020)Monitoring the Edges of a Graph Using DistancesAlgorithms and Discrete Applied Mathematics10.1007/978-3-030-39219-2_3(28-40)Online publication date: 13-Feb-2020
https://dl.acm.org/doi/10.1007/978-3-030-39219-2_3
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Gera RJuliano NSchmitt K(2017)Optimizing Network Discovery with Clever WalksProceedings of the 2017 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining 201710.1145/3110025.3120961(1217-1224)Online publication date: 31-Jul-2017
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Gregori ELenzini LOrsini C(2013)k-Dense communities in the Internet AS-level topology graphComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2012.09.01157:1(213-227)Online publication date: 1-Jan-2013
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