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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 groups of brain regions to modulate attention, switch between tasks, and inhibit prepotent responses. Current theory posits that correlated and anticorrelated brain activity may signify cooperative and competitive interactions between brain areas that subserve adaptive behavior. In this study, we use a quantitative approach to identify distinct topological motifs of functional interactions and examine how their expression relates to cognitive control processes and behavior. In particular, we acquire fMRI BOLD signal in twenty-eight healthy subjects as they perform two cognitive control tasks—a Stroop interference task and a local-global perception switching task using Navon figures—each with low and high cognitive control demand conditions. Based on these data, we construct dynamic functional brain networks and use a parts-based, network decomposition technique called non-negative matrix factorization to identify putative cognitive control subgraphs whose temporal expression captures distributed network structures involved in different phases of cooperative and competitive control processes. Our results demonstrate that temporal expression of the subgraphs fluctuate alongside changes in cognitive demand and are associated with individual differences in task performance. These findings offer insight into how coordinated changes in the cooperative and competitive roles of cognitive systems map trajectories between cognitively demanding brain states., Author summary Brain networks support the human ability to navigate a complex space of perceptions and actions through cognitive control. Here we ask, “How do brain networks coordinate task-relevant information as individuals adapt to cognitive demands imposed by a task?” We study the fMRI BOLD signal of twenty-eight healthy subjects as they perform two cognitive control tasks—a Stroop interference task and a local-global perception switching task using Navon figures—with low and high cognitive load conditions. We construct functional networks and use a machine learning technique called non-negative matrix factorization to identify topological motifs whose expression fluctuates across different phases of cognitive control processes. We find that motifs stratify the brain network into a hierarchy of distributed functional processes that adapt to changes in cognitive demand and predict individual differences in task performance. These data offer insight into how network interactions linking cognitive systems coordinate transitions between cognitively demanding brain states.