Unbiased and efficient sampling of timeseries reveals redundancy of brain network and gradient structure.

Many studies in human neuroscience seek to understand the structure of brain networks and gradients. Few studies, however, have tested the redundancy between these outwardly distinct features. Here, we developed methods to directly enable such tests. We built on insights from linear algebra to develop methods for unbiased and efficient sampling of timeseries with network or gradient constraints. We used these methods to show considerable redundancy between popular definitions of network and gradient structure in functional MRI data. On the one hand, we found that network constraints largely accounted for the structure of three major gradients. On the other hand, we found that gradient constraints largely accounted for the structure of seven major networks. Our results imply that some networks and gradients may denote discrete and continuous representations of the same aspects of functional MRI data. We suggest that integrated explanations can reduce redundancy by avoiding the attribution of independent existence or function to these features.