  This paper presents methods to analyze functional brain networks and signals
from graph spectral perspectives. The notion of frequency and filters
traditionally defined for signals supported on regular domains such as discrete
time and image grids has been recently generalized to irregular graph domains,
and defines brain graph frequencies associated with different levels of spatial
smoothness across the brain regions. Brain network frequency also enables the
decomposition of brain signals into pieces corresponding to smooth or rapid
variations. We relate graph frequency with principal component analysis when
the networks of interest denote functional connectivity. The methods are
utilized to analyze brain networks and signals as subjects master a simple
motor skill. We observe that brain signals corresponding to different graph
frequencies exhibit different levels of adaptability throughout learning.
Further, we notice a strong association between graph spectral properties of
brain networks and the level of exposure to tasks performed, and recognize the
most contributing and important frequency signatures at different task
familiarity.
