This article is devoted to the theoretical understanding of the social network phenomenon and the methodology of its research. A social network is considered as an abstract, ideal-typical construct which makes it possible to get to the level of extreme generalization of already-existing knowledge concerning networks, and to develop the universal tools of conducting analytical operations with the objects exhibiting network characteristics. The methodology of social topology can be referred to with these tools. The criteria of demarcating the systematic and network approach from the systematic and topological approach have been defined. The application of the topological tools of social network analysis, relational sociology, and actor-network theory in studying the main branches of network approach was analyzed from the authors’ positions concerning the conditional division of social topology into the topology of space and the topology of form based on the works of Rene Thom, Kurt Levin, and Pierre Bourdieu. It has been discovered that the research of social network analysis and relational sociology makes use of spatial topology at different rates. The topology of form, in its turn, is developed only in the context of the actor-network theory, first of all, in the works of John Law and his followers. The conclusions made on the basis of analytical operations prove that there is an urgent need to develop the complex synthetic topology involving all quantitative and qualitative achievements made by those separate researchers who deal with topology. Eventually, the use of this theoretical and methodological framework can reveal new facets of understanding social networks.