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.
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A weighted spectrum metric for comparison of internet topologies
Fay, Damien; Haddadi, Hamed; Moore, Andrew W.; Mortier, Richard; Uhlig, Steve; Jamakovic, Almerima
Follow ACM SIGMETRICS Performance Evaluation Review
, Volume 37 (3)
Association for Computing Machinery – Jan 21, 2010
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