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.

中文翻译：

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多维网络中的算法信息失真

网络复杂性、网络信息内容分析和图表示的无损压缩性在网络分析和网络建模中发挥了重要作用。随着多维网络，如时变、多层或动态多层网络，在网络科学中获得更多的相关性，研究在哪些情况下基于算法信息理论的通用算法方法不能直接导入到多维网络中变得至关重要。案件。在这个方向上，作为随不同维度数量线性增加的无损压缩失真的最坏情况，本文提出了在处理非均匀和足够大的多维空间内的网络时发生的反直觉现象。特别是，