  From interacting cellular components to networks of neurons and neural
systems, interconnected units comprise a fundamental organizing principle of
the nervous system. Understanding how their patterns of connections and
interactions give rise to the many functions of the nervous system is a primary
goal of neuroscience. Recently, this pursuit has begun to benefit from the
development of new mathematical tools that can relate a system's architecture
to its dynamics and function. These tools, which are known collectively as
network science, have been used with increasing success to build models of
neural systems across spatial scales and species. Here we discuss the nature of
network models in neuroscience. We begin with a review of model theory from a
philosophical perspective to inform our view of networks as models of complex
systems in general, and of the brain in particular. We then summarize the types
of models that are frequently studied in network neuroscience along three
primary dimensions: from data representations to first-principles theory, from
biophysical realism to functional phenomenology, and from elementary
descriptions to coarse-grained approximations. We then consider ways to
validate these models, focusing on approaches that perturb a system to probe
its function. We close with a description of important frontiers in the
construction of network models and their relevance for understanding
increasingly complex functions of neural systems.
