### Abstract

Comparison of graph structures is a frequently encountered problem across a number of problem domains. Comparing graphs requires a metric to discriminate which features of the graphs are considered important. The spectrum of a graph is often claimed to contain all the information within a graph, but the raw spectrum contains too much information to be directly used as a useful metric. In this paper we introduce a metric, the weighted spectral distribution, that improves on the raw spectrum by discounting those eigenvalues believed to be unimportant and emphasizing the contribution of those believed to be important. We use this metric to optimize the selection of parameter values for generating Internet topologies. Our metric leads to parameter choices that appear sensible given prior knowledge of the problem domain: the resulting choices are close to the default values of the topology generators and, in the case of some generators, fall within the expected region. This metric provides a means for meaningfully optimizing parameter selection when generating topologies intended to share structure with, but not match exactly, measured graphs.

Original language | English |
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Title of host publication | Performance Evaluation Review |

Pages | 67-72 |

Number of pages | 6 |

Volume | 37 |

Edition | 3 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

Event | 2nd Workshop on Hot Topics in Measurement and Modeling of Computer Systems, HotMetrics 2009 - Seattle, WA, United States Duration: 19 Jun 2009 → 19 Jun 2009 |

### Other

Other | 2nd Workshop on Hot Topics in Measurement and Modeling of Computer Systems, HotMetrics 2009 |
---|---|

Country | United States |

City | Seattle, WA |

Period | 19/6/09 → 19/6/09 |

### Fingerprint

### Keywords

- Degree-based generators
- Graph metrics
- Internet topology
- Topology generation

### ASJC Scopus subject areas

- Computer Networks and Communications
- Hardware and Architecture
- Software

### Cite this

*Performance Evaluation Review*(3 ed., Vol. 37, pp. 67-72) https://doi.org/10.1145/1710115.1710129

**A weighted spectrum metric for comparison of Internet topologies.** / Fay, Damien; Haddadi, Hamed; Moore, Andrew W.; Mortier, Richard; Uhlig, Steve; Jamakovic, Almerima.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Performance Evaluation Review.*3 edn, vol. 37, pp. 67-72, 2nd Workshop on Hot Topics in Measurement and Modeling of Computer Systems, HotMetrics 2009, Seattle, WA, United States, 19/6/09. https://doi.org/10.1145/1710115.1710129

}

TY - GEN

T1 - A weighted spectrum metric for comparison of Internet topologies

AU - Fay, Damien

AU - Haddadi, Hamed

AU - Moore, Andrew W.

AU - Mortier, Richard

AU - Uhlig, Steve

AU - Jamakovic, Almerima

PY - 2010

Y1 - 2010

N2 - Comparison of graph structures is a frequently encountered problem across a number of problem domains. Comparing graphs requires a metric to discriminate which features of the graphs are considered important. The spectrum of a graph is often claimed to contain all the information within a graph, but the raw spectrum contains too much information to be directly used as a useful metric. In this paper we introduce a metric, the weighted spectral distribution, that improves on the raw spectrum by discounting those eigenvalues believed to be unimportant and emphasizing the contribution of those believed to be important. We use this metric to optimize the selection of parameter values for generating Internet topologies. Our metric leads to parameter choices that appear sensible given prior knowledge of the problem domain: the resulting choices are close to the default values of the topology generators and, in the case of some generators, fall within the expected region. This metric provides a means for meaningfully optimizing parameter selection when generating topologies intended to share structure with, but not match exactly, measured graphs.

AB - Comparison of graph structures is a frequently encountered problem across a number of problem domains. Comparing graphs requires a metric to discriminate which features of the graphs are considered important. The spectrum of a graph is often claimed to contain all the information within a graph, but the raw spectrum contains too much information to be directly used as a useful metric. In this paper we introduce a metric, the weighted spectral distribution, that improves on the raw spectrum by discounting those eigenvalues believed to be unimportant and emphasizing the contribution of those believed to be important. We use this metric to optimize the selection of parameter values for generating Internet topologies. Our metric leads to parameter choices that appear sensible given prior knowledge of the problem domain: the resulting choices are close to the default values of the topology generators and, in the case of some generators, fall within the expected region. This metric provides a means for meaningfully optimizing parameter selection when generating topologies intended to share structure with, but not match exactly, measured graphs.

KW - Degree-based generators

KW - Graph metrics

KW - Internet topology

KW - Topology generation

UR - http://www.scopus.com/inward/record.url?scp=77955125160&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955125160&partnerID=8YFLogxK

U2 - 10.1145/1710115.1710129

DO - 10.1145/1710115.1710129

M3 - Conference contribution

VL - 37

SP - 67

EP - 72

BT - Performance Evaluation Review

ER -