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This paper presents an analysis of the severity of alcohol use disorder (AUD) based on electroencephalogram (EEG) signals and alcohol drinking experiments by utilizing power spectral density (PSD) and the transitions that occur as individuals drink alcohol in increasing amounts. We use data from brain-computer interface (BCI) experiments using alcohol stimulus recorded from a group of seventeen alcohol-drinking male participants and the assessment scores of the alcohol use disorders identification test (AUDIT). This method investigates the mild, moderate, and severe symptoms of AUD using the three key domains of AUDIT, which are hazardous alcohol use, dependence symptoms, and severe alcohol use. We utilize the EEG spectral power of the theta, alpha, and beta frequency bands by observing the transitions from the initial to the final phase of alcohol consumption. Our results are compared for people with low-risk alcohol consumption, harmful or hazardous alcohol consumption, and lastly, the likelihood of AUD based on the individual assessment scores of the AUDIT. We use Balanced Iterative Reducing and Clustering using Hierarchies (BIRCH) to cluster the results of the transitions in EEG signals and the overall brain activity of all the participants for the entire duration of the alcohol-drinking experiments. This study can be useful in creating an automatic AUD severity level detection tool for alcoholics to aid in early intervention and supplement evaluations by mental health professionals.