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This work focuses on the (k,l)-anonymity of some networks as a measure oftheir privacy against active attacks.  Two different types of networks are considered. The first one consists ofgraphs with a predetermined structure, namely cylinders, toruses, and$2$-dimensional Hamming graphs, whereas the second one is formed by randomlygenerated graphs. In order to evaluate the (k,l)-anonymity of the consideredgraphs, we have computed their k-metric antidimension. To this end, we havetaken a combinatorial approach for the graphs with a predetermined structure,whereas for randomly generated graphs we have developed an integer programmingformulation and computationally tested its implementation. The results of thecombinatorial approach, as well as those from the implementations indicatethat, according to the (k,l)-anonymity measure, only the 2-dimensional Hamminggraphs and some general random dense graphs are achieving some higher privacyproperties.

On the (k,l)-anonymity of networks via their $k$-metric antidimension