  We introduce a novel cross-validation method that we call latinCV and we
compare this method to other model selection methods using data generated from
a stochastic block model. Comparing latinCV to other cross-validation methods,
we show that latinCV performs similarly to a method described in
\cite{hoff2008modeling} and that latinCV has a significantly larger true model
recovery accuracy than the NCV method of \cite{chen2014network}. We also show
that the reason for this discrepancy is related to the larger variance of the
NCV estimate. Comparing latinCV to alternative model selection methods, we show
that latinCV performs better than information criteria AIC and BIC, as well as
the community detection method infomap and a routine that attempts to maximize
modularity. The simulation study in this paper includes a range of network
sizes and generative parameters for the stochastic block model that allow us to
examine the relationship between model selection accuracy and the size and
complexity of the model. Overall, latinCV performs more accurate model
selection, and avoids overfitting better than any of the other model selection
methods considered.
