Electroencephalogram data is used to extract functional networks connecting correlated human brain sites. Analysis of the resulting network shows statistical characteristic of complex network: the clustering coefficient is orders of magnitude larger than those of equivalent random networks, which is typical of small-world network and the distribution of degree is close to the scale-free network. All these properties reflect important functional information about brain states. To the alcoholic, the characteristic index of their brain is obviously different from the control group. Brain neural network information entropy and brain neural network normal information entropy are also defined to measure the complex network characteristic. A criterion in diagnosis and therapy of clinical encephalopathy is given. Calculation results illustrate that the brain neural network information entropy of alcoholic is quite distinct from the control.