Medical informatics is one of the most promising areas of computer science. One of the goals of medical informatics is to develop software to search for disease markers and predictors. The activity of the brain default-mode network is seen as an index to predict the degree of risk of a wide range of mental pathologies, including depression. Usually, the default-mode network activity is measured using functional magnetic resonance imaging. However, to date, there are no reliable tools to effectively assess the functional state of the default-mode network based on electroencephalography analysis. For investigation of brain activity markers of default-mode network activity, an electroencephalography data processing algorithm has been developed in the presented study. Based on the channel correlation of electrodes, specific to the default-mode network, the algorithm obtains connectivity metrics in brain regions and of the network in total. This metric was used for making machine learning models. Models can classify network connectivity metrics to experimental conditions with high precision. Training data was taken from ICBrainDB - an open-access dataset of electroencephalography, psychometry and genetics. In the future, the method we have developed can be applied as a tool for the early diagnosis of depression and other socially significant mental disorders.