On the k-Anonymization of Time-varying and Multi-layer Social Graphs

The popularity of online social media platforms pro-vides an unprecedented opportunity to study real-world complex networks of interactions. However, releasing this data to researchers and the public comes at the cost of potentially exposing private and sensitive user in-formation. It has been shown that a naive anonymiza-tion of a network by removing the identity of the nodes is not sufficient to preserve users ’ privacy. In order to deal with malicious attacks, k-anonymity solutions have been proposed to partially obfuscate topological infor-mation that can be used to infer nodes ’ identity. In this paper, we study the problem of ensuring k-anonymity in time-varying graphs, i.e., graphs with a structure that changes over time, and multi-layer graphs, i.e., graphs with multiple types of links. More specif-ically, we examine the case in which the attacker has access to the degree of the nodes. The goal is to gen-erate a new graph where, given the degree of a node in each (temporal) layer of the graph, such a node remains indistinguishable from other k − 1 nodes in the graph. In order to achieve this, we find the optimal partitioning of the graph nodes such that the cost of anonymizing the degree information within each group is minimum. We show that this reduces to a special case of a Gen-eralized Assignment Problem, and we propose a simple yet effective algorithm to solve it. Finally, we introduce an iterated linear programming approach to enforce the realizability of the anonymized degree sequences. The efficacy of the method is assessed through an extensive set of experiments on synthetic and real-world graphs