The significance of negative correlations in brain connectivity.

Understanding the modularity of functional magnetic resonance imaging (fMRI)-derived brain networks or "connectomes" can inform the study of brain function organization. However, fMRI connectomes additionally involve negative edges, which may not be optimally accounted for by existing approaches to modularity that variably threshold, binarize, or arbitrarily weight these connections. Consequently, many existing Q maximization-based modularity algorithms yield variable modular structures. Here, we present an alternative complementary approach that exploits how frequent the blood-oxygen-level-dependent (BOLD) signal correlation between two nodes is negative. We validated this novel probability-based modularity approach on two independent publicly-available resting-state connectome data sets (the Human Connectome Project [HCP] and the 1,000 functional connectomes) and demonstrated that negative correlations alone are sufficient in understanding resting-state modularity. In fact, this approach (a) permits a dual formulation, leading to equivalent solutions regardless of whether one considers positive or negative edges; (b) is theoretically linked to the Ising model defined on the connectome, thus yielding modularity result that maximizes data likelihood. Additionally, we were able to detect novel and consistent sex differences in modularity in both data sets. As data sets like HCP become widely available for analysis by the neuroscience community at large, alternative and perhaps more advantageous computational tools to understand the neurobiological information of negative edges in fMRI connectomes are increasingly important.