The change in hypometabolism affects the regional links in the brain network. Here, to understand the underlying brain metabolic network deficits during the early stage and disease evolution of AD (Alzheimer disease), we applied correlation analysis to identify the metabolic connectivity patterns using 18F-FDG PET data for NC (normal control), sMCI (stable MCI), pMCI (progressive MCI) and AD, and explore the inter- and intra-hemispheric connectivity between anatomically-defined brain regions. Regions extracted from 90 anatomical structures were used to construct the matrix for measuring the inter- and intra-hemispheric connectivity. The brain connectivity patterns from the metabolic network show a decreasing trend of inter- and intra-hemispheric connections for NC, sMCI, pMCI and AD. Connection of temporal to the frontal or occipital regions is a characteristic pattern for conversion of NC to MCI, and the density of links in the parietal-occipital network is a differential pattern between sMCI and pMCI. The reduction pattern of inter and intra-hemispheric brain connectivity in the metabolic network depends on the disease stages, and is with a decreasing trend with respect to disease severity. Both frontal-occipital and parietal-occipital connectivity patterns in the metabolic network using 18F-FDG PET are the key feature for differentiating disease groups in AD.