Article
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Preserved in Portico This version is not peer-reviewed
Algorithmic Information Distortions in Node-Aligned and Node-Unaligned Multidimensional Networks
Version 1
: Received: 27 February 2021 / Approved: 2 March 2021 / Online: 2 March 2021 (09:31:09 CET)
Version 2 : Received: 11 May 2021 / Approved: 12 May 2021 / Online: 12 May 2021 (13:44:32 CEST)
Version 2 : Received: 11 May 2021 / Approved: 12 May 2021 / Online: 12 May 2021 (13:44:32 CEST)
A peer-reviewed article of this Preprint also exists.
Abrahão, F.S.; Wehmuth, K.; Zenil, H.; Ziviani, A. Algorithmic Information Distortions in Node-Aligned and Node-Unaligned Multidimensional Networks. Entropy 2021, 23, 835. Abrahão, F.S.; Wehmuth, K.; Zenil, H.; Ziviani, A. Algorithmic Information Distortions in Node-Aligned and Node-Unaligned Multidimensional Networks. Entropy 2021, 23, 835.
Abstract
In this article, we investigate limitations of importing methods based on algorithmic information theory from monoplex networks into multidimensional networks (such as multilayer networks) that have a large number of extra dimensions (i.e., aspects). In the worst-case scenario, it has been previously shown that node-aligned multidimensional networks with non-uniform multidimensional spaces can display exponentially larger algorithmic information (or lossless compressibility) distortions with respect to their isomorphic monoplex networks, so that these distortions grow at least linearly with the number of extra dimensions. In the present article, we demonstrate that node-unaligned multidimensional networks, either with uniform or non-uniform multidimensional spaces, can also display exponentially larger algorithmic information distortions with respect to their isomorphic monoplex networks. However, unlike the node-aligned non-uniform case studied in previous work, these distortions in the node-unaligned case grow at least exponentially with the number of extra dimensions. On the other hand, for node-aligned multidimensional networks with uniform multidimensional spaces, we demonstrate that any distortion can only grow up to a logarithmic order of the number of extra dimensions. Thus, these results establish that isomorphisms between finite multidimensional networks and finite monoplex networks do not preserve algorithmic information in general and highlight that the algorithmic information of the multidimensional space itself needs to be taken into account in multidimensional network complexity analysis.
Keywords
multidimensional networks; network complexity; lossless compression; information distortion; graph isomorphism; multiaspect graphs; multilayer networks; information content analysis; algorithmic complexity
Subject
Computer Science and Mathematics, Computer Science
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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