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The subject matter of the article is the process of modeling social networks. The goal is to develop a computer model of a social network with a recommendation system. The tasks to be solved are to research the methods of generating social networks, to realize the computer model of a social network with a recommender system. The methods used are graph theory, theory of algorithms, statistics theory, probability theory, object-oriented programming. The following results: the research of existing methods for modeling social networks was conducted, in particular, such social network models as the Barabasi-Albert model, the Erdős-Renyi model and the Bollobаs-Riordan model were considered. The concept of complex networks was considered. The research of the basic properties of graphs of social networks was considered. The social network computer model with a recommender system based on the modified Barabasi-Albert model with using graph database Neo4j and programming language Python was developed. The developed model allows to model a network with users and text posts and may contain following connections "friends", "follower", "published", "viewed", "like", "similar", "recommended", and also allows testing of algorithms of recommender systems and conduct research to changes in a social network after creating and proposing recommendations. The testing of the developed computer model of virtual social network with a recommender system was conducted. Conclusions. The research of various methods of modeling social networks was conducted. The concept of complex networks was investigated. The main properties of social network graphs are considered. The computer model of a social network with a recommendation system that contains various types of nodes and connections that allow testing a recommender system algorithm has been developed. The developed model of a social network with a recommender system was tested to check its similarity with real social networks. The developed computer model of a social network has the values of network graph parameters corresponding to the values characteristic of real social networks, which allows using the developed model to research the processes that can occur in real social networks.