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Examining individuals with Leber’s hereditary optic neuropathy (LHON) provides a rare opportunity to understand how changes in mitochondrial DNA and loss of vision can be related to changes in organization of the whole-brain structural network architecture. In comparison with the previous neuroimaging studies with LHON participants, which were focused mainly on analyzing changes which occur in different areas of the patient’s brain, network analysis not only makes it possible to observe single white matter fibers’ aberrations but also the whole-brain nature of these changes. The purpose of our study was to better understand whole-brain neural network changes in LHON participants and see the correlation between the clinical data and the changes. To achieve this, we examined fifteen LHON patients and seventeen age-matched healthy subjects with the usage of ultra-high filed 7T magnetic resonance imaging (MRI). Basing on the analysis on MRI diffusion tensor imaging (DTI) data, whole-brain structural neural networks were reconstructed with the use of the minimum spanning tree algorithm (MST) for every participant. Our results revealed that the structural network in LHON participants was altered at both the local and the global level. The global network structures of LHON subjects were less centralized with path-like organization and there was an imbalance in the main hub centrality. Moreover, the inspection of nodes and hubs in terms of their anatomical placement revealed that in the LHON participants the prominent hubs were located within the basal ganglia (i.e. bilateral caudate, left pallidum), which differed them from healthy controls. An analysis of the relationships between the global MST metrics and LHON participants’ clinical characteristics revealed significant correlations between the global network metrics and the duration of illness. Furthermore, the nodal parameters of the optic chiasm were significantly correlated with the duration of illness and the averaged thickness of the right retinal nerve fiber layer (RNFL). These findings clearly showed that the progression of the disease is accompanied by alterations within the brain network structure and its efficiency.