  The central nervous system is composed of many individual units -- from cells
to areas -- that are connected with one another in a complex pattern of
functional interactions that supports perception, action, and cognition. One
natural and parsimonious representation of such a system is a graph in which
nodes (units) are connected by edges (interactions). While applicable across
spatiotemporal scales, species, and cohorts, the traditional graph approach is
unable to address the complexity of time-varying connectivity patterns that may
be critically important for an understanding of emotional and cognitive state,
task-switching, adaptation and development, or aging and disease progression.
Here we survey a set of tools from applied mathematics that offer measures to
characterize dynamic graphs. Along with this survey, we offer suggestions for
visualization and a publicly-available MATLAB toolbox to facilitate the
application of these metrics to existing or yet-to-be acquired neuroimaging
data. We illustrate the toolbox by applying it to a previously published data
set of time-varying functional graphs, but note that the tools can also be
applied to time-varying structural graphs or to other sorts of relational data
entirely. Our aim is to provide the neuroimaging community with a useful set of
tools, and an intuition regarding how to use them, for addressing emerging
questions that hinge on accurate and creative analyses of dynamic graphs.
