k-Anonymity on Graphs using the Szemerédi Regularity Lemma

Graph anonymisation aims at reducing the ability of an attacker to identify the nodes of a graph by obfuscating its structural information. In k-anonymity, this means making each node indistinguishable from at least other k-1 nodes. Simply stripping the nodes of a graph of their identifying label is insufficient, as with enough structural knowledge an attacker can still recover the nodes identities. We propose an algorithm to enforce k-anonymity based on the Szemerédi regularity lemma. Given a graph, we start by computing a regular partition of its nodes. The Szemerédi regularity lemma ensures that such a partition exists and that the edges between the sets of nodes behave quasi-randomly. With this partition to hand, we anonymize the graph by randomizing the edges within each set, obtaining a graph that is structurally similar to the original one yet the nodes within each set are structurally indistinguishable. Unlike other k-anonymisation methods, our approach does not consider a single type of attack, but instead it aims to prevent any structure-based de-anonymisation attempt. We test our framework on a wide range of real-world networks and we compare it against another simple yet widely used k-anonymisation technique demonstrating the effectiveness of our approach.