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Neuroimaging studies have shown topological disruptions of both functional and structural whole-brain networks in major depressive disorder (MDD). This study examined common and specific alterations between these two types of networks and whether the alterations were differentially involved in the two hemispheres. Multimodal MRI data were collected from 35 MDD patients and 35 healthy controls, whose functional and structural hemispheric networks were constructed, characterized, and compared. We found that functional brain networks were profoundly altered at multiple levels, while structural brain networks were largely intact in patients with MDD. Specifically, the functional alterations included decreases in intra-hemispheric (left and right) and inter-hemispheric (heterotopic) functional connectivity; decreases in local, global and normalized global efficiency for both hemispheric networks; increases in normalized local efficiency for the left hemispheric networks; and decreases in intra-hemispheric integration and inter-hemispheric communication in the dorsolateral superior frontal gyrus, anterior cingulate gyrus and hippocampus. Regarding hemispheric asymmetry, largely similar patterns were observed between the functional and structural networks: the right hemisphere was over-connected and more efficient than the left hemisphere globally; the occipital and partial regions exhibited leftward asymmetry, and the frontal and temporal sites showed rightward lateralization with regard to regional connectivity profiles locally. Finally, the functional–structural coupling of intra-hemispheric connections was significantly decreased and correlated with the disease severity in the patients. Overall, this study demonstrates modality- and hemisphere-dependent and invariant network alterations in MDD, which are helpful for understanding elaborate and characteristic patterns of integrative dysfunction in this disease.