De-anonymizing clustered social networks by percolation graph matching

On-line social networks offer the opportunity to collect a huge amount of valuable information about billions of users. The analysis of this data by service providers and unintended third parties are posing serious treats to user privacy. In particular, recent work has shown that users participating in more than one on-line social network can be identified based only on the structure of their links to other users. An effective tool to de-anonymize social network users is represented by graph matching algorithms. Indeed, by exploiting a sufficiently large set of seed nodes, a percolation process can correctly match almost all nodes across the different social networks. In this paper, we show the crucial role of clustering, which is a relevant feature of social network graphs (and many other systems). Clustering has both the effect of making matching algorithms more prone to errors, and the potential to greatly reduce the number of seeds needed to trigger percolation. We show these facts by considering a fairly general class of random geometric graphs with variable clustering level. We assume that seeds can be identified in particular sub-regions of the network graph, while no a-priori knowledge about the location of the other nodes is required. Under these conditions, we show how clever algorithms can achieve surprisingly good performance while limiting the number of matching errors.