In this paper, we study the quantification, practice, and implications of structural data de-Anonymization, including social data, mobility traces, and so on. First, we answer several open questions in structural data de-Anonymization by quantifying perfect and (1-epsilon )-perfect structural data de-Anonymization, where epsilon is the error tolerated by a de-Anonymization scheme. To the best of our knowledge, this is the first work on quantifying structural data de-Anonymization under a general data model, which closes the gap between the structural data de-Anonymization practice and theory. Second, we conduct the first large-scale study on the de-Anonymizability of 26 real world structural data sets, including social networks, collaborations networks, communication networks, autonomous systems, peer-To-peer networks, and so on. We also quantitatively show the perfect and (1-epsilon )-perfect de-Anonymization conditions of the 26 data sets. Third, following our quantification, we present a practical attack [a novel single-phase cold start optimization-based de-Anonymization (ODA) algorithm]. An experimental analysis of ODA shows that ∼ 77.7 %-83.3% of the users in Gowalla (196 591 users and 950 327 edges) and 86.9%-95.5% of the users in Google+ (4 692 671 users and 90 751 480 edges) are de-Anonymizable in different scenarios, which implies that the structure-based de-Anonymization is powerful in practice. Finally, we discuss the implications of our de-Anonymization quantification and our ODA attack and provide some general suggestions for future secure data publishing.