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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 …