Algorithms for Efficiently Computing Structural Anonymity in Complex Networks

This paper proposes methods for efficiently computing the anonymity of entities in networks. We do so by partitioning nodes into equivalence classes where a node is k-anonymous if it is equivalent to k − 1 other nodes. This assessment of anonymity is crucial when one wants to share data and must ensure the anonymity of entities represented is compliant with privacy laws. Additionally, in such an assessment, it is necessary to account for a realistic amount of information in the hands of a possible attacker that attempts to de-anonymize entities in the network. However, measures introduced in earlier work often assume a fixed amount of attacker knowledge. Therefore, in this work, we use a new parameterized measure for anonymity called d-k-anonymity. This measure can be used to model the scenario where an attacker has perfect knowledge of a node’s surroundings up to a given distance d. This poses nontrivial computational challenges, as naive approaches would employ large numbers of possibly computationally expensive graph isomorphism checks. This paper proposes novel algorithms that severely reduce this computational burden. In particular, we present an iterative approach, assisted by techniques for preprocessing nodes that are trivially automorphic and heuristics that exploit graph invariants. We evaluate our algorithms on three well-known graph models and a wide range of empirical network datasets. Results show that our approaches significantly speed up the computation by multiple orders of magnitude, which allows one to compute d-k-anonymity for a range of meaningful values of d on large empirical networks with tens of thousands of nodes and over a million edges.