Need of new reading of sociological concepts of society of risk, network society, complex society and different scientific views on modern society in relation to process of an institutionalization of digital sociology as special sociological theory, subject matter and special methodology of knowledge of digital reality has been substantiated. Methodological approaches to use of the principles, the ideas and categories of various schools of sciences, groups of erudite and certain representatives of sociological science to development of the conceptual and categorial device, methodical potential and tools of digital sociology have been adduced. Special attention has been paid to the consideration of the concept of social network of the American sociologist Richard Mark Emerson in the context of digitalization. From positions of the concept of Richard Mark Emerson emergence of new dependences of users of Internet network on special category of subjects socially of interaction – moderators, administrators, owners of resources, the controlling public authorities and also manipulators of people’s attention has been explained; the specific motivation, which reveals itself in such phenomena as hypertrophied aspiration to the self-presentation (“selfie”, etc.); representation of the distorted virtual image for communications, hyperactivity in the appeal to various resources (“Internet surfing”) and also prevalence of motivators and estimated means – anonymous comments, “likes”, posts, reposts, symbolical encouragement and awards. Besides that, the behavior of Internet users has been considered in the context of the theory of the rational choice of the American sociologist James S. Coleman: at all risks of virtual interaction, the choice for integration of social communications into digital space, use of Internet resources for satisfaction of  personal and group needs brings more vital benefits for people, than folding of social activity in the Internet network.