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Recently, some studies have applied the graph theory in brain network analysis in Alzheimer's disease (AD) and Mild Cognitive Impairment (MCI). However, relatively little research has specifically explored the properties of the metabolic network in apolipoprotein E (APOE) ε4 allele carriers. In our study, all the subjects, including ADs, MCIs and NCs (normal controls) were divided into 165 APOE ε4 carriers and 165 APOE ε4 noncarriers. To establish the metabolic network for all brain regions except the cerebellum, cerebral glucose metabolism data obtained from FDG-PET (¹⁸F-fluorodeoxyglu-cose positron emission tomography) were segmented into 90 areas with automated anatomical labeling (AAL) template. Then, the properties of the networks were computed to explore the between-group differences. Our results suggested that both APOE ε4 carriers and noncarriers showed the small-world properties. Besides, compared with APOE ε4 noncarriers, the carriers showed a lower clustering coefficient. In addition, significant changes in 6 hub brain regions were found in between-group nodal centrality. Namely, compared with APOE ε4 noncarriers, significant decreases of the nodal centrality were found in left insula, right insula, right anterior cingulate, right paracingulate gyri, left cuneus, as well as significant increases in left paracentral lobule and left heschl gyrus in APOE ε4 carriers. Increased local short distance interregional correlations and disrupted long distance interregional correlations were found, which may support the point that the APOE ε4 carriers were more similar with AD or MCI in FDG uptake. In summary, the organization of …