  We introduce a new methodology for model selection in the context of modeling
network data. The statistical network analysis literature has developed many
different classes of network data models, with notable model classes including
stochastic block models, latent position models, and exponential families of
random graph models. A persistent question in the statistical network analysis
literature lies in understanding how to compare different models for the
purpose of model selection and evaluating goodness-of-fit, especially when
models have different mathematical foundations. In this work, we develop a
novel non-parametric method for model selection in network data settings which
exploits the information contained in the spectrum of the graph Laplacian in
order to obtain a measure of goodness-of-fit for a defined set of network data
models. We explore the performance of our proposed methodology to popular
classes of network data models through numerous simulation studies,
demonstrating the practical utility of our method through two applications.
