  Network models are applied across many domains where data can be represented
as a network. Two prominent paradigms for modeling networks are statistical
models (probabilistic models for the observed network) and mechanistic models
(models for network growth and/or evolution). Mechanistic models are better
suited for incorporating domain knowledge, to study effects of interventions
(such as changes to specific mechanisms) and to forward simulate, but they
typically have intractable likelihoods. As such, and in a stark contrast to
statistical models, there is a relative dearth of research on model selection
for such models despite the otherwise large body of extant work. In this paper,
we propose a simulator-based procedure for mechanistic network model selection
that borrows aspects from Approximate Bayesian Computation (ABC) along with a
means to quantify the uncertainty in the selected model. To select the most
suitable network model, we consider and assess the performance of several
learning algorithms, most notably the so-called Super Learner, which makes our
framework less sensitive to the choice of a particular learning algorithm. Our
approach takes advantage of the ease to forward simulate from mechanistic
network models to circumvent their intractable likelihoods. The overall process
is flexible and widely applicable. Our simulation results demonstrate the
approach's ability to accurately discriminate between competing mechanistic
models. Finally, we showcase our approach with a protein-protein interaction
network model from the literature for yeast (Saccharomyces cerevisiae).
