In recent decades, social network anonymization has become a crucial research field due to its pivotal role in preserving users' privacy. However, the high diversity of approaches introduced in relevant studies poses a challenge to gaining a profound understanding of the field. In response to this, the current study presents an exhaustive and well-structured bibliometric analysis of the social network anonymization field. To begin our research, related studies from the period of 2007-2022 were collected from the Scopus Database then pre-processed. Following this, the VOSviewer was used to visualize the network of authors' keywords. Subsequently, extensive statistical and network analyses were performed to identify the most prominent keywords and trending topics. Additionally, the application of co-word analysis through SciMAT and the Alluvial diagram allowed us to explore the themes of social network anonymization and scrutinize their evolution over time. These analyses culminated in an innovative taxonomy of the existing approaches and anticipation of potential trends in this domain. To the best of our knowledge, this is the first bibliometric analysis in the social network anonymization field, which offers a deeper understanding of the current state and an insightful roadmap for future research in this domain.