  Modern neuroimaging techniques provide us with unique views on brain
structure and function; i.e., how the brain is wired, and where and when
activity takes place. Data acquired using these techniques can be analyzed in
terms of its network structure to reveal organizing principles at the systems
level. Graph representations are versatile models where nodes are associated to
brain regions and edges to structural or functional connections. Structural
graphs model neural pathways in white matter that are the anatomical backbone
between regions. Functional graphs are built based on functional connectivity,
which is a pairwise measure of statistical interdependency between activity
traces of regions. Therefore, most research to date has focused on analyzing
these graphs reflecting structure or function.
  Graph signal processing (GSP) is an emerging area of research where signals
recorded at the nodes of the graph are studied atop the underlying graph
structure. An increasing number of fundamental operations have been generalized
to the graph setting, allowing to analyze the signals from a new viewpoint.
Here, we review GSP for brain imaging data and discuss their potential to
integrate brain structure, contained in the graph itself, with brain function,
residing in the graph signals. We review how brain activity can be meaningfully
filtered based on concepts of spectral modes derived from brain structure. We
also derive other operations such as surrogate data generation or
decompositions informed by cognitive systems. In sum, GSP offers a novel
framework for the analysis of brain imaging data.
