In this paper, we investigate the abnormalities of electroencephalograph (EEG) signals in the Alzheimer's disease (AD) by analyzing 16-scalp electrodes EEG signals and make a comparison with the normal controls. Coherence is introduced to measure the pair-wise normalized linear synchrony and functional correlations between two EEG signals in different frequency domains, and graph analysis is further used to investigate the influence of AD on the functional connectivity of human brain. Data analysis results show that, compared with the control group, the pair-wise coherence of AD group is significantly decreased, especially for the theta and alpha frequency bands in the frontal and parieto-occipital regions. Furthermore, functional connectivity among different brain regions is reconstructed based on EEG, which exhibit obvious small-world properties. Graph analysis demonstrates that the local functional connections between regions for AD decrease. In addition, it is found that small-world properties of AD networks are largely weakened, by calculating its average path lengths, clustering coefficients, global efficiency, local efficiency, and small-worldness. The obtained results show that both pair-wise coherence and functional network can be taken as effective measures to distinguish AD patients from the normal, which may benefit our understanding of the disease.