On Your Social Network De-anonymizablity: Quantification and Large Scale Evaluation with Seed Knowledge

In this paper, we conduct the first comprehensive quantification on the perfect de-anonymizability and partial deanonymizability of real world social networks with seed information in general scenarios, where a social network can follow an arbitrary distribution model. This quantification provides the theoretical foundation for existing structure based de-anonymization attacks (e.g., [1][2][3]) and closes the gap between de-anonymization practice and theory. Besides that, our quantification can serve as a testing-stone for the effectiveness of anonymization techniques, i.e., researchers can employ our quantified structural conditions to evaluate the potential deanonymizability of the anonymized social networks. Based on our quantification, we conduct a large scale evaluation on the de-anonymizability of 24 various real world social networks by quantitatively showing: 1) the conditions for perfect and (1 - epsilon) de-anonymization of a social network, where. specifies the tolerated de-anonymization error, and 2) the number of users of a social network that can be successfully de-anonymized. Furthermore, we show that, both theoretically and experimentally, the overall structural information based de-anonymization attack is much more powerful than the seed knowledge-only based de-anonymization attack, and even without any seed information, a social network can be perfectly or partially de-anonymized. Finally, we discuss the implications of this work. Our findings are expected to shed light on the future research in the structural data anonymization and de-anonymization area, and to help data owners evaluate their structural data vulnerability before data sharing and publishing.