Stroke is a medical condition that affects the brain and represents a leading cause of death and disability. Associated with drug therapy, rehabilitative treatment is essential for promoting recovery. In the present work, we report an EEG-based study concerning a left ischemic stroke patient affected by conduction aphasia. Specifically, the objective is to compare the brain functional connectivity before and after an intensive rehabilitative treatment. The analysis was performed by means of local and global efficiency measures related to the execution of three tasks: naming, repetition and reading. As expected, the results showed that the treatment led to a balancing of the values of both parameters between the two hemispheres since the rehabilitation contributed to the creation of new neural patterns to compensate for the disrupted ones. Moreover, we observed that for both name and repetition tasks, shortly after the stroke, the global and local connectivity are lower in the affected lobe (left hemisphere) than in the unaffected one (right hemisphere). Conversely, for the reading task, global and local connectivity are higher in the impaired lobe. This apparently contrasting trend can be due to the effects of stroke, which affect not only the site of structural damage but also brain regions belonging to a functional network. Moreover, changes in network connectivity can be task-dependent. This work can be considered a first step for future EEG-based studies to establish the most suitable connectivity measures for supporting the treatment of stroke and monitoring the recovery process.