One medical challenge in studying the amyloid-β (Aβ) peptide mechanism for Alzheimer's disease (AD) is exploring the law of beta toxic oligomers' diffusion in human brains in vivo. One beneficial means of solving this problem is brain network analysis based on graph theory. In this study, the characteristics of Aβ functional brain networks of Healthy Control (HC), Mild Cognitive Impairment (MCI), and AD groups were compared by applying graph theoretical analyses to Carbon 11-labeled Pittsburgh compound B positron emission tomography (11C PiB-PET) data. 120 groups of PiB-PET images from the ADNI database were analyzed. The results showed that the small-world property of MCI and AD were lost as compared to HC. Furthermore, the local clustering of networks was higher in both MCI and AD as compared to HC, whereas the path length was similar among the three groups. The results also showed that there could be four potential Aβ toxic oligomer seeds: Frontal_Sup_Medial_L, Parietal_Inf_L, Frontal_Med_Orb_R, and Parietal_Inf_R. These four seeds are corresponding to Regions of Interests referred by physicians to clinically diagnose AD.