Keywords: Goodness of fit Model selection Applications of spectral graph theory Models of network structure a b s t r a c t We introduce a new statistic, 'spectral goodness of fit' (SGOF) to measure how well a network model explains the structure of the pattern of ties in an observed network. SGOF provides a measure of fit analogous to the standard R 2 in linear regression. Additionally, as it takes advantage of the properties of the spectrum of the graph Laplacian, it is suitable for comparing

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... network models of diverse functional forms, including both fitted statistical models and algorithmic generative models of networks. After introducing, defining, and providing guidance for interpreting SGOF, we illustrate the properties of the statistic with a number of examples and comparisons to existing techniques. We show that such a spectral approach to assessing model fit fills gaps left by earlier methods and can be widely applied. (J. Shore). such, we provide a goodness of fit measure that can be applied across modeling techniques. http://dx.