The human brain is the most fascinating and complex organ. It directs all our actions and thoughts. Despite the large body of brain studies, little is known about the neural basis of its large-scale structure. In this dissertation, I take advantage of several network-based and statistical techniques to investigate the spatial and temporal aspects of large-scale functional networks of the human brain during "rest" and "task" conditions using functional MRI data.

Large-scale analysis of human brain function has revealed that brain regions can be grouped into networks or communities. Most studies adopt a framework in which brain regions belong to only one community. Yet studies in general fields of knowledge suggest that in most cases complex networks consist of interwoven sets of overlapping communities. A mixed-membership framework can better characterize the complex networks. In this dissertation, I employed a mixed-membership Bayesian model to characterize overlapping community structure of the brain at both "rest" and "task" conditions. The approach allowed us to quantify how task performance reconfigures brain communities at rest, and 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). Furthermore, I could study the distribution of key regions, named "bridges", in transferring information across the brain communities. Our findings revealed that the overlapping framework described the brain in ways that were not captured by disjoint clustering, and thus provided a richer landscape of large-scale brain networks. Overall, I suggest that overlapping networks are better suited to capture the flexible and task-dependent mapping between brain regions and their functions.

Finally, I developed a dynamic intersubject network analysis technique to study the temporal changes of the emotional brain at the level of large-scale brain networks by formulating a manipulation in which threat levels varied continuously during the experiment. Our results illustrate that cohesion within and between networks changed dynamically with threat level. Together, our findings reveal that characterizing emotional processing should be done at the level of distributed networks, and not simply at the level of evoked responses in specific brain regions.