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We introduce a new methodology for model selection in the context of modelingnetwork data. The statistical network analysis literature has developed manydifferent classes of network data models, with notable model classes includingstochastic block models, latent position models, and exponential families ofrandom graph models. A persistent question in the statistical network analysisliterature lies in understanding how to compare different models for thepurpose of model selection and evaluating goodness-of-fit, especially whenmodels have different mathematical foundations. In this work, we develop anovel non-parametric method for model selection in network data settings whichexploits the information contained in the spectrum of the graph Laplacian inorder to obtain a measure of goodness-of-fit for a defined set of network datamodels. We explore the performance of our proposed methodology to popularclasses of network data models through numerous simulation studies,demonstrating the practical utility of our method through two applications.

Model selection for network data based on spectral information