With recent advancements in the processing of brain signals, the classification of psychological disorders has gained increasing importance. While previous studies were mostly limited to the classification of one or two disorders, this study addresses the classification of five distinct conditions, including a healthy control group and four types of psychological disorders (depression, schizophrenia, mild cognitive impairment, and Alzheimer’s disease) using the analysis of electroencephalogram signals. This research presents various combinations of functional connectivity measures including Pearson correlation coefficient, phase locking value, and mutual information to generate connectivity matrices without redundant data. The features were extracted from the matrices using local graph structures and through Shannon entropy, logarithmic energy entropy, and singular value decomposition. For final classification, machine learning algorithms including K-nearest neighbors and Naïve Bayes were used. Moreover, the capability of different electroencephalogram frequency bands in classifying psychological states was investigated. This study achieved an accuracy of 90.29% in diagnosing mild cognitive impairment by combining Pearson correlation and mutual information in the beta frequency band using the largest singular value feature and the K-nearest neighbors’ classifier. Additionally, by combining phase locking value and mutual information in the gamma frequency band using the largest singular value and the Naïve Bayes algorithm, an accuracy of 89.53% was achieved. Furthermore, by combining three features (Shannon entropy, logarithmic energy entropy, and singular value decomposition) in the combination of Pearson correlation and phase locking value in the beta frequency band using the K-nearest neighbors’ algorithm, an accuracy of 90.63% was obtained. In the diagnosis of depression, by combining Pearson correlation and phase locking value in the gamma frequency band using the Naïve Bayes algorithm, an accuracy of 88.52% was achieved.