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Brain anatomy and physiology support the human ability to navigate a complex space of perceptions and actions. To maneuver across an ever-changing landscape of mental states, the brain invokes cognitive control – a set of dynamic processes that engage and disengage different sets of brain regions to modulate attention, switch between tasks, and inhibit prepotent responses. Current theory suggests that cooperative and competitive interactions between brain areas may mediate processes of network reorganization that support transitions between dynamical states. In this study, we used a quantitative approach to identify distinct topological states of functional interactions and examine how their expression relates to cognitive control processes and behavior. In particular, we acquired fMRI BOLD signal in twenty–eight healthy subjects as they performed two cognitive control tasks – a local-global perception switching task using Navon figures and a Stroop interference task – each with low cognitive control demand and high cognitive control demand conditions. Based on these data, we constructed dynamic functional brain networks and used a parts-based network decomposition technique called non-negative matrix factorization to identify putative cognitive control subgraphs whose temporal expression captured key dynamical states involved in control processes. Our results demonstrate that the temporal expression of these functional subgraphs reflect cognitive demands and are associated with individual differences in task-based performance. These findings offer insight into how coordinated changes in the cooperative and competitive roles of distributed brain networks map trajectories between cognitively demanding brain states.