  A fundamental understanding of the network architecture of the brain is
necessary for the further development of theories explicating circuit function.
Perhaps as a derivative of its initial application to abstract informational
systems, network science provides many methods and summary statistics that
address the network's topological characteristics with little or no thought to
its physical instantiation. Recent progress has capitalized on quantitative
tools from network science to parsimoniously describe and predict neural
activity and connectivity across multiple spatial and temporal scales. Yet, for
embedded systems, physical laws can directly constrain processes of network
growth, development, and function, and an appreciation of those physical laws
is therefore critical to an understanding of the system. Recent evidence
demonstrates that the constraints imposed by the physical shape of the brain,
and by the mechanical forces at play in its development, have marked effects on
the observed network topology and function. Here, we review the rules imposed
by space on the development of neural networks and show that these rules give
rise to a specific set of complex topologies. We present evidence that these
fundamental wiring rules affect the repertoire of neural dynamics that can
emerge from the system, and thereby inform our understanding of network
dysfunction in disease. We also discuss several computational tools,
mathematical models, and algorithms that have proven useful in delineating the
effects of spatial embedding on a given networked system and are important
considerations for addressing future problems in network neuroscience. Finally,
we outline several open questions regarding the network architectures that
support circuit function, the answers to which will require a thorough and
honest appraisal of the role of physical space in brain network anatomy and
physiology.
