Optimal de-anonymization in random graphs with community structure

Anonymized social network graphs published for academic or advertisement purposes are subject to de-anonymization attacks by leveraging side information in the form of a second, public social network graph correlated with the anonymized graph. This is because the two are from the same underlying graph of true social relationships. In this paper, the maximum a posteriori (MAP) estimates of user identities for the anonymized graph are characterized and sufficient conditions for successful de-anonymization for underlying graphs with community structure are provided. The results generalize prior work that assumed underlying graphs of Erdíís-Renyi type, and prove the optimality of the attack strategy adopted in the literature.