Background: Recurrent complex visual hallucinations (VHs) are common in dementia with Lewy bodies (DLB). Previous investigations suggest that VHs are associated with connectivity changes within and between large scale networks involved in visual processing and attention. Aim: To examine more directly whether VH in DLB reflects direct changes in neuronal activity between cortical regions assessing metabolic connectivity with 18 F-fluorodeoxyglucose (FDG)-positron emission tomography (PET)/magnetic resonance and graph theory. Methods: Twenty-six patients with probable DLB (13 VHs and 13 no-VHs; mean age: 72.9 ± 6.87 years vs. 70.2 ± 7.96 years) were enrolled. T1-weighted 3T-MR images and FDG-PET data were coacquired using an integrated PET/MR scanner. MR images defined cortical parcels of the Shaefer-Yeo atlas for multiple functional networks. We computed in each parcel the regional standardized-uptake-values (SUV) corrected for partial volume and normalized to the cerebellar cortex. Strength degree, clustering coefficient, characteristic path length, and hubs were analyzed with graph analysis. Results: The mean 18 F-FDG-PET SUVr of parcels belonging to the visual and dorsal attention networks (DANs) were significantly lower in the VH group ( p = 0.01). Metabolism in the right temporoparietal cortex correlated with VH severity ( R = -0.58; p < 0.01). VH patients showed weaker metabolic connectivity in the parietal, temporal, and occipital cortex of the default mode network, DAN, and visual networks, but more robust connectivity in the right insula and orbitofrontal cortex. A lower global efficiency characterized the VH group, except for ventral attention network and limbic network. Conclusions: VHs in DLB correlate with lower glucose metabolism and weaker metabolic connectivity in the parietal-occipital cortex, but stronger connectivity in the limbic system. Impact statement This study shows that application of the graph theory to 18 F-fluorodeoxyglucose-positron emission tomography data, commonly acquired during the diagnostic workflow in neurodegenerative diseases, could be used to obtain information of functional connectivity at a group level, with results that are consistent with other data commonly used in brain functional investigation (e.g., electroencephalography or functional magnetic resonance). New network-based methods of metabolic image analyses, such as graph analysis, are a recent area of research with a potential capacity to extract information on alterations of metabolic connectivity that may become pharmacological and neuromodulation targets of the physiopathology of recurrent complex visual hallucinations.