  Network complexity, network information content analysis, and lossless
compressibility of graph representations have been played an important role in
network analysis and network modeling. As multidimensional networks, such as
time-varying, multilayer, or dynamic multilayer networks, gain more relevancy
in network science, it becomes crucial to investigate in which situations
universal algorithmic methods based on algorithmic information theory applied
to graphs cannot be straightforwardly imported into the multidimensional case.
In this direction, as a worst-case scenario of lossless compressibility
distortion that increases linearly with the number of distinct dimensions, this
article presents a counter-intuitive phenomenon that occurs when dealing with
networks within non-uniform and sufficiently large multidimensional spaces. In
particular, we demonstrate that the algorithmic information necessary to encode
multidimensional networks that are isomorphic to logarithmically compressible
monoplex networks may display exponentially larger distortions in the general
case.
