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Anonymization is a practical solution for preserving user’s privacy in data publishing. Data owners such as hospitals, banks, social network (SN) service providers, and insurance companies anonymize their user’s data before publishing it to protect the privacy of users whereas anonymous data remains useful for legitimate information consumers. Many anonymization models, algorithms, frameworks, and prototypes have been proposed/developed for privacy preserving data publishing (PPDP). These models/algorithms anonymize users’ data which is mainly in the form of tables or graphs depending upon the data owners. It is of paramount importance to provide good perspectives of the whole information privacy area involving both tabular and SN data, and recent anonymization researches. In this paper, we presents a comprehensive survey about SN (i.e., graphs) and relational (i.e., tabular) data anonymization techniques used in the PPDP. We systematically categorize the existing anonymization techniques into relational and structural anonymization, and present an up to date thorough review on existing anonymization techniques and metrics used for their evaluation. Our aim is to provide deeper insights about the PPDP problem involving both graphs and tabular data, possible attacks that can be launched on the sanitized published data, different actors involved in the anonymization scenario, and major differences in amount of private information contained in graphs and relational data, respectively. We present various representative anonymization methods that have been proposed to solve privacy problems in application-specific scenarios of the SNs. Furthermore, we highlight the user’s re-identification methods used by malevolent adversaries to re-identify people uniquely from the privacy preserved published data. Additionally, we discuss the challenges of anonymizing both graphs and tabular data, and elaborate promising research directions. To the best of our knowledge, this is the first work to systematically cover recent PPDP techniques involving both SN and relational data, and it provides a solid foundation for future studies in the PPDP field.