### Abstract

Comparing graphs to determine the level of underlying structural similarity between them is a widely encountered problem in computer science. It is particularly relevant to the study of Internet topologies, such as the generation of synthetic topologies to represent the Internet's AS topology. We derive a new metric that enables exactly such a structural comparison: the weighted spectral distribution. We then apply this metric to three aspects of the study of the Internet's AS topology. i) We use it to quantify the effect of changing the mixing properties of a simple synthetic network generator. ii) We use this quantitative understanding to examine the evolution of the Internet's AS topology over approximately seven years, finding that the distinction between the Internet core and periphery has blurred over time. iii) We use the metric to derive optimal parameterizations of several widely used AS topology generators with respect to a large-scale measurement of the real AS topology.

Original language | English |
---|---|

Article number | 5233839 |

Pages (from-to) | 164-176 |

Number of pages | 13 |

Journal | IEEE/ACM Transactions on Networking |

Volume | 18 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Feb 2010 |

Externally published | Yes |

### Fingerprint

### Keywords

- Graph metrics
- Internet topology
- Spectral graph theory
- Topology generation

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Software
- Computer Science Applications
- Computer Networks and Communications

### Cite this

*IEEE/ACM Transactions on Networking*,

*18*(1), 164-176. [5233839]. https://doi.org/10.1109/TNET.2009.2022369

**Weighted spectral distribution for internet topology analysis : Theory and applications.** / Fay, Damien; Haddadi, Hamed; Thomason, Andrew; Moore, Andrew W.; Mortier, Richard; Jamakovic, Almerima; Uhlig, Steve; Rio, Miguel.

Research output: Contribution to journal › Article

*IEEE/ACM Transactions on Networking*, vol. 18, no. 1, 5233839, pp. 164-176. https://doi.org/10.1109/TNET.2009.2022369

}

TY - JOUR

T1 - Weighted spectral distribution for internet topology analysis

T2 - Theory and applications

AU - Fay, Damien

AU - Haddadi, Hamed

AU - Thomason, Andrew

AU - Moore, Andrew W.

AU - Mortier, Richard

AU - Jamakovic, Almerima

AU - Uhlig, Steve

AU - Rio, Miguel

PY - 2010/2/1

Y1 - 2010/2/1

N2 - Comparing graphs to determine the level of underlying structural similarity between them is a widely encountered problem in computer science. It is particularly relevant to the study of Internet topologies, such as the generation of synthetic topologies to represent the Internet's AS topology. We derive a new metric that enables exactly such a structural comparison: the weighted spectral distribution. We then apply this metric to three aspects of the study of the Internet's AS topology. i) We use it to quantify the effect of changing the mixing properties of a simple synthetic network generator. ii) We use this quantitative understanding to examine the evolution of the Internet's AS topology over approximately seven years, finding that the distinction between the Internet core and periphery has blurred over time. iii) We use the metric to derive optimal parameterizations of several widely used AS topology generators with respect to a large-scale measurement of the real AS topology.

AB - Comparing graphs to determine the level of underlying structural similarity between them is a widely encountered problem in computer science. It is particularly relevant to the study of Internet topologies, such as the generation of synthetic topologies to represent the Internet's AS topology. We derive a new metric that enables exactly such a structural comparison: the weighted spectral distribution. We then apply this metric to three aspects of the study of the Internet's AS topology. i) We use it to quantify the effect of changing the mixing properties of a simple synthetic network generator. ii) We use this quantitative understanding to examine the evolution of the Internet's AS topology over approximately seven years, finding that the distinction between the Internet core and periphery has blurred over time. iii) We use the metric to derive optimal parameterizations of several widely used AS topology generators with respect to a large-scale measurement of the real AS topology.

KW - Graph metrics

KW - Internet topology

KW - Spectral graph theory

KW - Topology generation

UR - http://www.scopus.com/inward/record.url?scp=77249117640&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77249117640&partnerID=8YFLogxK

U2 - 10.1109/TNET.2009.2022369

DO - 10.1109/TNET.2009.2022369

M3 - Article

VL - 18

SP - 164

EP - 176

JO - IEEE/ACM Transactions on Networking

JF - IEEE/ACM Transactions on Networking

SN - 1063-6692

IS - 1

M1 - 5233839

ER -