document: On the privacy of anonymized networks The proliferation of online social networks , and the concomitant accumulation of user data , give rise to hotly debated issues of privacy , security , and control . One specific challenge is the sharing or public release of anonymized data without accidentally leaking personally identifiable information ( PII ) . Unfortunately , it is often difficult to ascertain that sophisticated statistical techniques , potentially employing additional external data sources , are unable to break anonymity . In this paper , we consider an instance of this problem , where the object of interest is the structure of a social network , i.e. , a graph describing users and their links . Recent work demonstrates that anonymizing node identities may not be sufficient to keep the network private : the availability of node and link data from another domain , which is correlated with the anonymized network , has been used to re-identify the anonymized nodes . This paper is about conditions under which such a de-anonymization process is possible . We attempt to shed light on the following question : can we assume that a sufficiently sparse network is inherently anonymous , in the sense that even with unlimited computational power , de-anonymization is impossible ? Our approach is to introduce a random graph model for a version of the de-anonymization problem , which is parameterized by the expected node degree and a similarity parameter that controls the correlation between two graphs over the same vertex set . We find simple conditions on these parameters delineating the boundary of privacy , and show that the mean node degree need only grow slightly faster than log n with network size n for nodes to be identifiable . Our results have policy implications for sharing of anonymized network information .
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