On the [Formula: see text] -anonymity of networks via their k-metric antidimension

This work focuses on the [Formula: see text] -anonymity of some networks as a measure of their privacy against active attacks. Two different types of networks are considered. The first one consists of graphs with a predetermined structure, namely cylinders, toruses, and 2-dimensional Hamming graphs, whereas the second one is formed by randomly generated graphs. In order to evaluate the [Formula: see text] -anonymity of the considered graphs, we have computed their k-metric antidimension. To this end, we have taken a combinatorial approach for the graphs with a predetermined structure, whereas for randomly generated graphs we have developed an integer programming formulation and computationally tested its implementation. The results of the combinatorial approach, as well as those from the implementations indicate that, according to the [Formula: see text] -anonymity measure, only the 2-dimensional Hamming graphs and some general random dense graphs are achieving some higher privacy properties.