The conceptual significance of understanding functional brain alterations and cognitive deficits associated with Alzheimer's disease (AD) process has been widely established. However, the whole-brain functional networks of AD and its prodromal stage, mild cognitive impairment (MCI), are not well clarified yet. In this study, we compared the characteristics of the whole-brain functional networks among cognitively normal (CN), MCI, and AD individuals by applying graph theoretical analyses to [(18)F] fluorodeoxyglucose positron emission tomography (FDG-PET) data. Ninety-four CN elderly, 183 with MCI, and 216 with AD underwent clinical evaluation and FDG-PET scan. The overall small-world property as seen in the CN whole-brain network was preserved in MCI and AD. In contrast, individual parameters of the network were altered with the following patterns of changes: local clustering of networks was lower in both MCI and AD compared to CN, while path length was not different among the three groups. Then, MCI had a lower level of local clustering than AD. Subgroup analyses for AD also revealed that very mild AD had lower local clustering and shorter path length compared to mild AD. Regarding the local properties of the whole-brain networks, MCI and AD had significantly decreased normalized betweenness centrality in several hubs regionally associated with the default mode network compared to CN. Our results suggest that the functional integration in whole-brain network progressively declines due to the AD process. On the other hand, functional relatedness between neighboring brain regions may not gradually decrease, but be the most severely altered in MCI stage and gradually re-increase in clinical AD stages.