Recently, many researchers have used graph theory to study the aberrant brain structures in Alzheimer's disease (AD) and have made great progress. However, the characteristics of the cortical network in Mild Cognitive Impairment (MCI) are still largely unexplored. In this study, the gray matter volumes obtained from magnetic resonance imaging (MRI) for all brain regions except the cerebellum were parcellated into 90 areas using the automated anatomical labeling (AAL) template to construct cortical networks for 98 normal controls (NCs), 113 MCIs and 91 ADs. The measurements of the network properties were calculated for each of the three groups respectively. We found that all three cortical networks exhibited small-world properties and those strong interhemispheric correlations existed between bilaterally homologous regions. Among the three cortical networks, we found the greatest clustering coefficient and the longest absolute path length in AD, which might indicate that the organization of the cortical network was the least optimal in AD. The small-world measures of the MCI network exhibited intermediate values. This finding is logical given that MCI is considered to be the transitional stage between normal aging and AD. Out of all the between-group differences in the clustering coefficient and absolute path length, only the differences between the AD and normal control groups were statistically significant. Compared with the normal controls, the MCI and AD groups retained their hub regions in the frontal lobe but showed a loss of hub regions in the temporal lobe. In addition, altered interregional correlations were detected in the parahippocampus gyrus, medial temporal lobe, cingulum, fusiform, medial frontal lobe, and orbital frontal gyrus in groups with MCI and AD. Similar to previous studies of functional connectivity, we also revealed increased interregional correlations within the local brain lobes and disrupted long distance interregional correlations in groups with MCI and AD.