An Algorithmic Information Distortion in Multidimensional Networks

TL;DR

This paper investigates how the complexity and compressibility of multidimensional networks can significantly differ from simpler networks, revealing exponential distortions in algorithmic information content in certain cases.

Contribution

It introduces a counter-intuitive phenomenon showing that encoding multidimensional networks can require exponentially more information than expected, especially in large, non-uniform spaces.

Findings

Algorithmic information necessary can grow exponentially in multidimensional networks.

Lossless compressibility distortion increases linearly with the number of dimensions.

Multidimensional networks may exhibit greater complexity than their monoplex counterparts.

Abstract

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.