Amnestic mild cognitive impairment (MCI) is a degenerative neurological disorder at the early stage of Alzheimer's disease (AD). This work is a pilot study aimed at developing a simple scalp-EEG-based method for screening and monitoring MCI and AD. Specifically, the use of graphical analysis of inter-channel coherence of resting EEG for the detection of MCI and AD at early stages is explored. Resting EEG records from 48 age-matched subjects (mean age 75.7 years)--15 normal controls (NC), 16 with early-stage MCI, and 17 with early-stage AD--are examined. Network graphs are constructed using pairwise inter-channel coherence measures for delta-theta, alpha, beta, and gamma band frequencies. Network features are computed and used in a support vector machine model to discriminate among the three groups. Leave-one-out cross-validation discrimination accuracies of 93.6% for MCI vs. NC (p < 0.0003), 93.8% for AD vs. NC (p < 0.0003), and 97.0% for MCI vs. AD (p < 0.0003) are achieved. These results suggest the potential for graphical analysis of resting EEG inter-channel coherence as an efficacious method for noninvasive screening for MCI and early AD.