Technical reports

# Weighted spectral distribution

**Damien Fay, Hamed Haddadi, Steve Uhlig, Andrew W. Moore, Richard Mortier, Almerima Jamakovic**

September 2008, 13 pages

## 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 the AB generator, 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.

## Full text

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## BibTeX record

@TechReport{UCAM-CL-TR-729, author = {Fay, Damien and Haddadi, Hamed and Uhlig, Steve and Moore, Andrew W. and Mortier, Richard and Jamakovic, Almerima}, title = {{Weighted spectral distribution}}, year = 2008, month = sep, url = {http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-729.pdf}, institution = {University of Cambridge, Computer Laboratory}, number = {UCAM-CL-TR-729} }