The application of graph theory to model the complex structure and function of the brain has shed new light on its organization, 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 the one hand graph spectral analysis (to decompose brain connectivity into eigenmodes or gradients) and the other graph signal processing (to decompose brain activity “coupled to” an underlying network in graph Fourier modes). These studies have used a variety of imaging techniques (e.g., fMRI, electroencephalography, diffusion-weighted and myelin-sensitive imaging) and connectivity estimators to model brain networks. Results are promising in terms of interpretability and functional relevance, but methodologies and terminology are variable. 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.

Human and animal brain studies bring converging evidence of a possible role for the cerebellum and the cerebro-cerebellar system in impulsivity. However, the precise nature of the relation between cerebro-cerebellar coupling and impulsivity is far from understood. Characterizing functional connectivity (FC) patterns between large-scale brain networks that mediate different forms of impulsivity, and the cerebellum may improve our understanding of this relation. Here, we analyzed static and dynamic features of cerebro-cerebellar FC using a highly sampled resting-state functional magnetic resonance imaging (rs-fMRI) dataset and tested their association with two widely used self-reports of impulsivity: the UPPS-P impulsive behavior scale and the behavioral inhibition/approach systems (BIS/BAS) in a large group of healthy subjects ( N = 134, ≈ 1 hr of rs-fMRI/subject). We employed robust data-driven techniques to identify cerebral and cerebellar resting-state networks and extract descriptive summary measures of static and dynamic cerebro-cerebellar FC. We observed evidence linking BIS, BAS, sensation seeking, and lack of premeditation to the total strength and temporal variability of FC within networks connecting regions of the prefrontal cortex, precuneus, posterior cingulate cortex, basal ganglia, and thalamus with the cerebellum. Overall, our findings improve the existing knowledge of the neural correlates of impulsivity and the behavioral correlates of the cerebro-cerebellar system. Author Summary Accumulating evidence from preclinical and neuroimaging studies proposes that the cerebellum regulates impulsive behavior through its interactions with brain regions that subserve control and reward processes. To further explore this proposal, we analyzed static and dynamic aspects of resting-state functional connectivity between the cerebellum and distinct large-scale brain networks using robust methods and evaluated them against a set of self-reported measures of impulsivity. We found compelling new evidence linking multiple forms of impulsivity to strength and temporal variability of FC between large-scale cerebral networks, involved in top-down control and reward, and the cerebellum. Our findings highlight the utility of combining static and dynamic FC approaches in furthering current understanding of cerebro-cerebellar coupling and the neurobiology of complex behaviors.