We aimed to determine whether structural brain connectivity is significantly associated with the response to sumatriptan in patients with migraine. We retrospectively enrolled patients with newly diagnosed migraine who underwent brain diffusion-tensor imaging (DTI) at the time of diagnosis, with regular follow-up for at least 6 months after the initial diagnosis. Patients were classified into good- and poor-responder groups according to their response to sumatriptan. We analyzed the structural connectivity using DTI by applying graph theory using DSI Studio software. We enrolled 59 patients (35 good responders and 24 poor responders) and 30 healthy controls. Global structural connectivity differed significantly between patients with migraine and healthy controls, while local structural connectivity differed significantly between good and poor responders. The betweenness centrality was lower in good responders than in poor responders in the left lateral geniculate thalamic nucleus (26.078 vs. 41.371, p=0.039) and right medial mediodorsal magnocellular thalamic nucleus (60.856 vs. 90.378, p=0.021), whereas was higher in good responders in the left lateral pulvinar thalamic nucleus (98.365 vs. 50.347, p=0.003) and right medial pulvinar thalamic nucleus (216.047 vs. 156.651, p=0.036). We found that structural connectivity in patients with migraine differed from that in healthy controls. Moreover, the local structural connectivity varied with the response to sumatriptan, which suggests that structural connectivity is a useful factor for predicting how a patient will respond to sumatriptan.