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This article presents a theoretical investigation of generalized encodedforms of networks in a uniform multidimensional space. First, we study encodednetworks with (finite) arbitrary node dimensions (or aspects), such as timeinstants or layers. In particular, we study these networks that are formalizedin the form of multiaspect graphs. In the context of node-aligned non-uniform(or node-unaligned non-uniform and uniform) multidimensional spaces, previousresults has shown that, unlike classical graphs, the algorithmic information ofa multidimensional network is not in general dominated by the algorithmicinformation of the binary sequence that determines the presence or absence ofedges. In the present work, first we demonstrate the existence of suchalgorithmic information distortions for node-aligned uniform multidimensionalnetworks. Secondly, we show that there are particular cases of infinite nestingfamilies of finite uniform multidimensional networks such that each member ofthese families is incompressible. From these results, we also recover thenetwork topological properties and equivalences in irreducible informationcontent of multidimensional networks in comparison to their isomorphicclassical graph counterpart in the previous literature. These results togetherestablish a universal algorithmic approach and set limitations and conditionsfor irreducible information content analysis in comparing arbitrary networkswith a large number of dimensions, such as multilayer networks.

Algorithmic information distortions and incompressibility in uniform multidimensional networks