De-anonymizing scale-free social networks by percolation graph matching

We address the problem of social network de-anonymization when relationships between people are described by scale-free graphs. In particular, we propose a rigorous, asymptotic mathematical analysis of the network de-anonymization problem while capturing the impact of power-law node degree distribution, which is a fundamental and quite ubiquitous feature of many complex systems such as social networks. By applying bootstrap percolation and a novel graph slicing technique, we prove that large inhomogeneities in the node degree lead to a dramatic reduction of the initial set of nodes that must be known a priori (the seeds) in order to successfully identify all other users. We characterize the size of this set when seeds are selected using different criteria, and we show that their number can be as small as n% for any small ε > 0. Our results are validated through simulation experiments on real social network graphs

De-anonymyzing scale-free social networks by using spectrum partitioning method

Social network data is widely shared, forwarded and published to third parties, which led to the risks of privacy disclosure. Even thought the network provider always perturbs the data before publishing it, attackers can still recover anonymous data according to the collected auxiliary information. In this paper, we transform the problem of de-anonymization into node matching problem in graph, and the de-anonymization method can reduce the number of nodes to be matched at each time. In addition, we use spectrum partitioning method to divide the social graph into disjoint subgraphs, and it can effectively be applied to large-scale social networks and executed in parallel by using multiple processors. Through the analysis of the influence of power-law distribution on de-anonymization, we synthetically consider the structural and personal information of users which made the feature information of the user more practical

Social Network De-anonymization Under Scale-free User Relations

We tackle the problem of user de-anonymization in social networks characterized by scale-free relationships between users. The network is modeled as a graph capturing the impact of power-law node degree distribution, which is a fundamental and quite common feature of social networks. Using this model, we present a de-anonymization algorithm that exploits an initial set of users, called seeds, that are known a priori. By employing bootstrap percolation theory and a novel graph slicing technique, we develop a rigorous analysis of the proposed algorithm under asymptotic conditions. Our analysis shows that large inhomogeneities in the node degree lead to a dramatic reduction of the size of the seed set that is necessary to successfully identify all other users. We characterize this set size when seeds are properly selected based on the node degree as well as when seeds are uniformly distributed. We prove that, given n nodes, the number of seeds required for network de-anonymization can be as small as n^epsilon, for any small epsilon>0. Additionally, we discuss the complexity of our de-anonymization algorithm and validate our results through numerical experiments on a real social network graph