Stroke is the main cause of disability among neurological diseases. There are questions of the accuracy of topical diagnosis and rehabilitation prognosis in clinical practice. Answers to these questions may be given by an approach to the study of the nervous system as a dynamic network consisting of a set of brain regions with anatomical and functional connections between them. Active study of the connectome in neurological patients in recent years became possible due to the availability of noninvasive neuroimaging methods. This review covers types of connectome and most accessible methods of obtaining research data for their construction in a neurological hospital. The review also describes resting-state networks that reflect basic brain activity in the absence of tasks. Resting-state connectivity can be used for the diagnosis of patients with severe neurological deficits. Also, changes in resting-state connectivity may indicate recovery after a stroke. The connectome analysis uses graph theory, representing the nervous system as a set of nodes and connections between them, and providing a mathematical framework allowing to study it, and methods of algebraic topology that expand the possibilities of analyzing neuroimaging data beyond graph theory. Attention is paid to the concept of self-organized criticality, which describes the brain as a system located near the critical point, where the transmission of information is most optimized. Also presented are data from studies of self-organized criticality in relation to the dynamics of recovery of patients after stroke.