Investigations of the human brain's connectomic architecture have produced two alternative models: one describes the brain's spatial structure in terms of localized networks, and the other describes the brain's temporal structure in terms of whole-brain states. Here, we used tools from connectivity dynamics to develop a synthesis that bridges these models. Using task-free fMRI data, we investigated the assumptions undergirding current models of the connectome. Consistent with state-based models, our results suggest that localized networks are superordinate approximations of underlying dynamic states. Furthermore, each of these localized, moment-to-moment connectivity states is associated with global changes in the whole-brain functional connectome. By nesting localized connectivity states within their whole-brain contexts, we demonstrate the relative temporal independence of brain networks. Our assay for functional autonomy of coordinated neural systems is broadly applicable across populations, and our findings provide evidence of structure in temporal dynamics that complements the well-described spatial organization of the brain.