  Networks describe the, often complex, relationships between individual
actors. In this work, we address the question of how to determine whether a
parametric model, such as a stochastic block model or latent space model, fits
a dataset well and will extrapolate to similar data. We use recent results in
random matrix theory to derive a general goodness-of-fit test for dyadic data.
We show that our method, when applied to a specific model of interest, provides
an straightforward, computationally fast way of selecting parameters in a
number of commonly used network models. For example, we show how to select the
dimension of the latent space in latent space models. Unlike other network
goodness-of-fit methods, our general approach does not require simulating from
a candidate parametric model, which can be cumbersome with large graphs, and
eliminates the need to choose a particular set of statistics on the graph for
comparison. It also allows us to perform goodness-of-fit tests on partial
network data, such as Aggregated Relational Data. We show with simulations that
our method performs well in many situations of interest. We analyze several
empirically relevant networks and show that our method leads to improved
community detection algorithms. R code to implement our method is available on
Github.
