Compensation has been proposed as a mechanism to explain how individuals in very old age remain able to maintain normal cognitive functioning. Previous studies have provided evidence on the role of increasing functional connectivity as a compensatory mechanism for age-related white matter damage. However, we lack direct investigation into how these mechanisms contribute to the preservation of cognition in the very old population. We examined a cohort of near-centenarians and centenarians without dementia (aged 95-103 years, n=44). We constructed a structural disconnection matrix based on the disruption of white matter pathways caused by white matter hyperintensities (WMHs), aiming to explore the relationship between functional connections, cognitive preservation and white matter damage. Our results revealed that structural damage can reliably explain the variations of functional connections or cognitive maintenance. Notably, we found significant correlations between the weights in the functional connectivity model and the weights in the cognition model. We observed positive correlations between models for brain disconnections and cognitive function in near-centenarians and centenarians. The strongest effects were found between attention and somatomotor network (SMN) (r=0.397, p<
0.001), memory and SMN (r=0.333 p<
0.001), fluency and visual network (VIS) - control network (CN) (r=0.406, p<
0.001), language and VIS (r=0.309, p<
0.001), visuospatial ability and VIS-default mode network (DMN) (r=0.464, p<
0.001), as well as global cognition and VIS-DMN (r=0.335, p<
0.001). These findings suggest that enhancement of functional connectivity may serve as a compensatory mechanism, such that it mitigates the effects of white matter damage and contributes to preserved cognitive performance in very old age.