Predicting functional outcomes after surgery and early adjuvant treatment is difficult due to the complex, extended, interlocking brain networks that underpin cognition. The aim of this study was to test glioma functional interactions with the rest of the brain, thereby identifying the risk factors of cognitive recovery or deterioration. Seventeen patients with diffuse non-enhancing glioma (aged 22-56 years) were longitudinally MRI scanned and cognitively assessed before and after surgery and during a 12-month recovery period (55 MRI scans in total after exclusions). We initially found, and then replicated in an independent dataset, that the spatial correlation pattern between regional and global BOLD signals (also known as global signal topography) was associated with tumour occurrence. We then estimated the coupling between the BOLD signal from within the tumour and the signal extracted from different brain tissues. We observed that the normative global signal topography is reorganised in glioma patients during the recovery period. Moreover, we found that the BOLD signal within the tumour and lesioned brain was coupled with the global signal and that this coupling was associated with cognitive recovery. Nevertheless, patients did not show any apparent disruption of functional connectivity within canonical functional networks. Understanding how tumour infiltration and coupling are related to patients' recovery represents a major step forward in prognostic development.