This article studies the use of social networks as new forms of virtual social space, which allows realizing different types of fraud. The issue is especially urgent due to the actions of users and organizations on social networks and their insufficient level of information literacy about computer security. This research aims to provide a social analysis of computer criminality before devising any effective actions for increasing security level of interactions in social networks and preventing Internet crime. This article depicts some general principles, including negative and positive features of user interactions on social networks, accounting for real public relations and government regulations in Internet security and computer crime. The results of the research have revealed the contemporary distinctive conditions for implementing, increasing, and developing computer crime on social networks, its specifics, aims, and technological components. The authors describe different kinds of criminal acts on social networks, their typology, and the fraudulent methods. This research emphasizes the deficiency of knowledge on information security, demonstrated by the Internet users. Based on the data acquired during social analysis, the authors recommend a number of personal, legal, and public actions for protecting user personal data and preventing computer crime on the Internet and social networks.