Brain networks can be defined and explored through their connectivity. Here, we analyzed the relationship between structural connectivity (SC) across 2,514 regions that cover the entire brain and brainstem, and their dynamic functional connectivity (DFC). To do so, we focused on a combination of two metrics: the first assesses the degree of SC-DFC similarity -i.e. the extent to which the dynamic functional correlations can be explained by structural pathways-; and the second is the intrinsic variability of the DFC networks over time. Overall, we found that cerebellar networks have a smaller DFC variability than other networks in the brain. Moreover, the internal structure of the cerebellum could be clearly divided in two distinct posterior and anterior parts, the latter also connected to the brainstem. The mechanism to maintain small variability of the DFC in the posterior part of the cerebellum is consistent with another of our findings, namely, that this structure exhibits the highest SC-DFC similarity relative to the other networks studied, i.e. structure constrains the variation in dynamics. By contrast, the anterior part of the cerebellum also exhibits small DFC variability but it has the lowest SC-DFC similarity, suggesting a different mechanism is at play. Because this structure connects to the brainstem, which regulates sleep cycles, cardiac and respiratory functioning, we suggest that such critical functionality drives the low variability in the DFC. Overall, the low variability detected in DFC expands our current knowledge of cerebellar networks, which are extremely rich and complex, participating in a wide range of cognitive functions, from movement control and coordination to executive function or emotional regulation. Moreover, the association between such low variability and structure suggests that differentiated computational principles can be applied in the cerebellum as opposed to other structures, such as the cerebral cortex.