Co-existence of Modularity and Anti-modularity in the Functional brain connectomes

The brain requires coordination among different regions to execute cognitive tasks, which may involve both positive- and negative-correlations. The topology of these correlations may indicate the mechanism underlying brain functioning in a given state. Here, we study changes in the functional connectomes (FCs) of both the positive and negative-correlations across various cognitive task states relative to the resting state, using publicly available electroencephalographic (EEG) data. Considering the EEG-specific topographical cortical regions as topographical modules (TMs), we find that the FC comprising positive correlations (G+) is modular. In contrast, networks of negative-correlations (G-) are anti-modular, with more connections between TMs than within them, and are associated with improved overall topological efficiency. These functional networks also show variability across frequency bands and brain states. In the low-frequency delta band, resting states exhibit higher modularity and anti-modularity than task states; in contrast, in the high-frequency Gamma band, modularity and anti-modularity are much higher during task states than in the resting state. The k-core analysis of all networks further reveals differences: G+ is more hierarchical and robust than G- across all states. Moreover, the task-state networks are always more hierarchical than the resting-state networks across all frequency bands. In the high-frequency gamma band, they are also significantly more robust than the resting-state networks. These networks also differ in the topology of their innermost core constituents: the innermost core regions of G+ are randomly connected and spatially localized, mostly in posterior brain regions across subjects, in the high-frequency gamma band. Whereas those in G- are spatially de-localized, cover the extreme anterior and extreme posterior brain regions, and remain anti-modular in all the frequency bands. Overall, our analysis reveals the presence of an anti-modular organization of functionally specialized TMs alongside their modular organization and points to task- and resting-state differences in their topologies.