Studying functional connectivity in the human brain has brought about significant insight into cognitive dysfunction and compensation in individuals with epilepsy. The utilization of graph-theory in these analyses offers a novel and powerful method to understand the impact of epilepsy on cognition. Among the normal population and over 50% of patients with drug drug-resistant temporal lobe (TLE) the left hemisphere is dominant for language. However, during evaluation for epilepsy surgery about 20-40% of TLE patients are found who are able to speak while their left hemisphere is under temporary anesthesia. We chose to study epilepsy-related language dysfunction by using two fMRI language tasks (verbal fluency, verb generation) in six such patients. By comparing their fMRI activation and connectivity to that of six TLE patients with typical language representation and nine control participants we found that atypical language representation is associated with bilateral brain activation and higher connectivity in the right superior temporal gyrus and right insula. Network analysis also indicated that TLE patients had less efficient language networks than control participants. Poorer neuropsychological scores (Boston Naming Test and verbal IQ) were associated with this gre ater network inefficiency and inability to inhibit task-irrelevant brain regions. Earlier age of seizure onset was found to be associated with atypical language activation and connectivity. Our results show that graph-theory-based analyses can help better understand how epilepsy impacts cognition. In TLE patients, they indicate that an inability to disengage task non-relevant brain regions may be a vital factor in cognitive dysfunction.