Brain network alterations in patients with Alzheimer's disease (AD) has been the subject of much investigation, but the biological mechanisms underlying these alterations remain poorly understood. Here, we aim to identify the changes in brain networks in patients with AD and mild cognitive impairment (MCI), and provide an accurate algorithm for classification of these patients from healthy control subjects (HC) by using a graph theoretical approach and advanced machine learning methods. Multivariate Granger causality analysis was performed on resting-state functional magnetic resonance imaging (rs-fMRI) data of 34 AD, 89 MCI, and 45 HC to calculate various directed graph measures. The graph measures were used as the original feature set for the machine learning algorithm. Filter and wrapper feature selection methods were applied to the original feature set to select an optimal subset of features. An accuracy of 93.3% was achieved for classification of AD, MCI, and HC using the optimal features and the naïve Bayes classifier. We also performed a hub node analysis and found that the number of hubs in HC, MCI, and AD were 12, 10, and 9, respectively, suggesting that patients with AD experience disturbance of critical communication areas in their brain network as AD progresses. The findings of this study provide insight into the neurophysiological mechanisms underlying MCI and AD. The proposed classification method highlights the potential of directed graph measures of rs-fMRI data for identification of the early stage of AD.