Overlapping communities reveal rich structure in large-scale brain networks during rest and task conditions.

Large-scale analysis of functional MRI data has revealed that brain regions can be grouped into stable "networks" or communities. In many instances, the communities are characterized as relatively disjoint. Although recent work indicates that brain regions may participate in multiple communities (for example, hub regions), the extent of community overlap is poorly understood. To address these issues, here we investigated large-scale brain networks based on "rest" and task human functional MRI data by employing a mixed-membership Bayesian model that allows each brain region to belong to all communities simultaneously with varying membership strengths. The approach allowed us to 1) compare the structure of disjoint and overlapping communities; 2) determine the relationship between functional diversity (how diverse is a region's functional activation repertoire) and membership diversity (how diverse is a region's affiliation to communities); 3) characterize overlapping community structure; 4) characterize the degree of non-modularity in brain networks; 5) study the distribution of "bridges", including bottleneck and hub bridges. Our findings revealed the existence of dense community overlap that was not limited to "special" hubs. Furthermore, the findings revealed important differences between community organization during rest and during specific task states. Overall, we suggest that dense overlapping communities are well suited to capture the flexible and task dependent mapping between brain regions and their functions.