INTRODUCTION: Apathy is a common yet under-recognised feature of cerebral small vessel disease (SVD), but its underlying neurobiological basis is not yet understood. We hypothesized that damage to the reward network is associated with an increase of apathy in patients with SVD. METHODS: In 114 participants with symptomatic SVD, defined as a magnetic resonance imaging confirmed lacunar stroke and confluent white matter hyperintensities, we used diffusion tensor imaging tractography to derive structural brain networks and graph theory to determine network efficiency. We determined which parts of the network correlated with apathy symptoms. We tested whether apathy was selectively associated with involvement of the reward network, compared with two "control networks" (visual and motor). RESULTS: Apathy symptoms negatively correlated with connectivity in network clusters encompassing numerous areas of the brain. Network efficiencies within the reward network correlated negatively with apathy scores; (r = - 0.344, p < 0.001), and remained significantly correlated after co-varying for the two control networks. Of the three networks tested, only variability in the reward network independently explained variance in apathetic symptoms, whereas this was not observed for the motor or visual networks. LIMITATIONS: The analysis refers only to cerebrum and not cerebellum. The apathy measure is derivative of depression measure. DISCUSSION: Our results suggest that reduced neural efficiency, particularly in the reward network, is associated with increased apathy in patients with SVD. Treatments which improve connectivity in this network may improve apathy in SVD, which in turn may improve psychiatric outcome after stroke.