  The application of graph theory to model the complex structure and function
of the brain has shed new light on its organization and function, prompting the
emergence of network neuroscience. Despite the tremendous progress that has
been achieved in this field, still relatively few methods exploit the topology
of brain networks to analyze brain activity. Recent attempts in this direction
have leveraged on graph spectral analysis and graph signal processing to
decompose brain activity in connectivity eigenmodes or gradients. If results
are promising in terms of interpretability and functional relevance,
methodologies and terminology are sometimes confusing. The goals of this paper
are twofold. First, we summarize recent contributions related to connectivity
gradients and graph signal processing, and attempt a clarification of the
terminology and methods used in the field, while pointing out current
methodological limitations. Second, we discuss the perspective that the
functional relevance of connectivity gradients could be fruitfully exploited by
considering them as graph Fourier bases of brain activity.
