Conditional adjacency anonymity in social graphs under active attacks

Social network data is typically made available in a graph format, where users and their relations are represented by vertices and edges, respectively. In doing so, social graphs need to be anonymised to resist various privacy attacks. Among these, the so-called active attacks, where an adversary has the ability to enrol sybil accounts in the social network, have proven difficult to counteract. In this article, we provide an anonymisation technique that successfully thwarts active attacks while causing low structural perturbation. We achieve this goal by introducing (k, Γ G,ℓ) -adjacency anonymity: a privacy property based on (k, ℓ) -anonymity that alleviates the computational burden suffered by anonymisation algorithms based on (k, ℓ) -anonymity and relaxes some of its assumptions on the adversary capabilities. We show that the proposed method is efficient and establish tight bounds on the number of modifications that it performs on the original graph. Experimental results on real-life and randomly generated graphs show that when compared to methods based on (k, ℓ) -anonymity, the new method continues to provide protection from equally capable active attackers while introducing a much smaller number of changes in the graph structure

Distance-based vertex identification in graphs: The outer multiset dimension

Given a graph $G$ and a subset of vertices $S = \{w_1, \ldots, w_t\} \subseteq V(G)$, the multiset representation of a vertex $u\in V(G)$ with respect to $S$ is the multiset $m(u|S) = \{| d_G(u, w_1), \ldots, d_G(u, w_t) |\}$. A subset of vertices $S$ such that $m(u|S) = m(v|S) \iff u = v$ for every $u, v \in V(G) \setminus S$ is said to be a multiset resolving set, and the cardinality of the smallest such set is the outer multiset dimension. We study the general behaviour of the outer multiset dimension, and determine its exact value for several graph families. We also show that computing the outer multiset dimension of arbitrary graphs is NP-hard, and provide methods for efficiently handling particular cases