Growing evidence suggests that coordinated activity within specific functional brain networks supports cognitive ability, and that abnormalities in brain connectivity may underlie cognitive deficits observed in neuropsychiatric diseases, such as schizophrenia. Two functional networks, the fronto-parietal network (FPN) and cingulo-opercular network (CON), are hypothesized to support top-down control of executive functioning, and have therefore emerged as potential drivers of cognitive impairment in disease-states. Graph theoretic analyses of functional connectivity data can characterize network topology, allowing the relationships between cognitive ability and network integrity to be examined. In the current study we applied graph analysis to pseudo-resting state data in 54 healthy subjects and 46 schizophrenia patients, and measured overall cognitive ability as the shared variance in performance from tasks of episodic memory, verbal memory, processing speed, goal maintenance, and visual integration. We found that, across all participants, cognitive ability was significantly positively associated with the local and global efficiency of the whole brain, FPN, and CON, but not with the efficiency of a comparison network, the auditory network. Additionally, the participation coefficient of the right anterior insula, a major hub within the CON, significantly predicted cognition, and this relationship was independent of CON global efficiency. Surprisingly, we did not observe strong evidence for group differences in any of our network metrics. These data suggest that functionally efficient task control networks support better cognitive ability in both health and schizophrenia, and that the right anterior insula may be a particularly important hub for successful cognitive performance across both health and disease