The disease roots of Alzheimer's disease (AD) are unknown. Functional connection (FC) methodology based on functional MRI data is an effective lever to investigate macroscopic neural activity patterns. However, regional properties of brain architecture have been less investigated by special markers of graph indexes in general mental disorders. In terms of the set of the abnormal edges in the FCs matrix, this paper introduces the strength index (S-scores) of region centrality on the principle of holism. Then, the important process is to investigate the S-scores of regions and subsystems in 36 healthy controls, 38 mild cognitive impairment (MCI) patients and 34 AD patients. At the edge level, abnormal FCs is numerically increasing progressively from MCI to AD brains. At the region level, the CUN.L, PAL.R, THA.L, and TPOsup.R regions are highlighted with abnormal S-scores in MCI patients. By comparison, more regions are abnormal in AD patients, which are PreCG.L, INS.R, DCG.L, AMYG.R, IOG.R, FFG.L, PoCG.L, PCUN.R, TPOsup.L, MTG.L, and TPOmid.L. Importantly, the regions in DMN have abnormal S-scores in AD groups. At the module level, the S-scores of frontal, parietal, occipital lobe, and cerebellum are found in MCI and AD patients. Meanwhile, the abnormal lateralization is inferred because of the S-scores of left and top hemisphere in the AD group. Though this is strictly a contrastive study, the S-score may be a meaningful imaging marker for excavating AD psychopathology.