Chronic stroke patients with heterogeneous lesions, but no direct damage to the primary sensorimotor cortex, are capable of longitudinally acquiring the ability to modulate sensorimotor rhythms using grasping imagery of the affected hand. Volitional modulation of neural activity can be used to drive grasping functions of the paralyzed hand through a brain–computer interface. The neural substrates underlying this skill are not known. Here, we investigated the impact of individual patient's lesion pathology on functional and structural network integrity related to this volitional skill. Magnetoencephalography data acquired throughout training was used to derive functional networks. Structural network models and local estimates of extralesional white matter microstructure were constructed using T1-weighted and diffusion-weighted magnetic resonance imaging data. We employed a graph theoretical approach to characterize emergent properties of distributed interactions between nodal brain regions of these networks. We report that interindividual variability in patients’ lesions led to differential impairment of functional and structural network characteristics related to successful post-training sensorimotor rhythm modulation skill. Patients displaying greater magnetoencephalography global cost-efficiency, a measure of information integration within the distributed functional network, achieved greater levels of skill. Analysis of lesion damage to structural network connectivity revealed that the impact on nodal betweenness centrality of the ipsilesional primary motor cortex, a measure that characterizes the importance of a brain region for integrating visuomotor information between frontal and parietal cortical regions and related thalamic nuclei, correlated with skill. Edge betweenness centrality, an analogous measure, which assesses the role of specific white matter fibre pathways in network integration, showed a similar relationship between skill and a portion of the ipsilesional superior longitudinal fascicle connecting premotor and posterior parietal visuomotor regions known to be crucially involved in normal grasping behaviour. Finally, estimated white matter microstructure integrity in regions of the contralesional superior longitudinal fascicle adjacent to primary sensorimotor and posterior parietal cortex, as well as grey matter volume co-localized to these specific regions, positively correlated with sensorimotor rhythm modulation leading to successful brain–computer interface control. Thus, volitional modulation of ipsilesional neural activity leading to control of paralyzed hand grasping function through a brain–computer interface after longitudinal training relies on structural and functional connectivity in both ipsilesional and contralesional parietofrontal pathways involved in visuomotor information processing. Extant integrity of this structural network may serve as a future predictor of response to longitudinal therapeutic interventions geared towards training sensorimotor rhythms in the lesioned brain, secondarily improving grasping function through brain–computer interface applications.