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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.