Alzheimer's disease (AD) is the most common type of dementia and a neurodegenerative disease with progressive cognitive dysfunction as the main feature. How to identify the early changes of cognitive dysfunction and give appropriate treatments is of great significance to delay the onset of dementia. Some other researches have shown that AD is associated with abnormal changes of brain networks. To study human brain functional connectivity characteristics in AD, 16 channels electroencephalogram (EEG) were recorded under resting and eyes-closed condition in 15 AD patients and 15 subjects in the control group. The synchronization likelihood of the full-band and alpha-band (8-13 Hz) data were evaluated, which resulted in the synchronization likelihood coefficient matrices. Considering a threshold T, the matrices were converted into binary graphs. Then the graphs of two groups were measured by topological parameters including the clustering coefficient and global efficiency. The results showed that the global efficiency of the network in full-band EEG was significantly smaller in AD group for the values of T=0.06 and T=0.07, but there was no statistically significant difference in the clustering coefficients between the two groups for the values of T (0.05-0.07). However, the clustering coefficient and global efficiency were significantly lower in AD patients at alpha-band for the same threshold range than those of subjects in the control group. It suggests that there may be decreases of the brain connectivity strength in AD patients at alpha-band of the resting-state EEG. This study provides a support for quantifying functional brain state of AD from the brain network perspective.