On Sequential Structures in Incompressible Multidimensional Networks

Author(s)

Abrahao, Felipe S. ; Wehmuth, Klaus ; Zenil, Hector ; Ziviani, Artur

• Document type: Journal article
• Source: PARALLEL PROCESSING LETTERS; v. 34, n. 03N04, p. 35-pg., 2024-11-20.

Abstract

In order to deal with multidimensional structure representations of real-world networks, as well as with their worst-case irreducible information content analysis, the demand for new graph abstractions increases. This article investigates incompressible multidimensional networks defined by generalized graph representations. In particular, we mathematically study the lossless incompressibility of snapshot-dynamic networks and multiplex networks in comparison to the lossless incompressibility of more general forms of dynamic networks and multilayer networks, from which snapshot-dynamic networks or multiplex networks are particular cases. Our theoretical investigation first explores fundamental and basic conditions for connecting the sequential growth of information with sequential interdimensional structures such as time in dynamic networks, and secondly it presents open problems demanding future investigation. Although there may be a dissonance between sequential information dynamics and sequential topology in the general case, we demonstrate that incompressibility (or algorithmic randomness) dissolves it, preventing both the algorithmic dynamics and the interdimensional structure of multidimensional networks from displaying a snapshot-like behavior (as characterized by any arbitrary mathematical theory). Thus, beyond methods based on statistics or probability as traditionally seen in random graphs and complex networks models, representational incompressibility implies a necessary underlying constraint in the multidimensional network topology. We argue that the study of how isomorphic transformations and their respective algorithmic information distortions can characterize sequential interdimensional structures in (multidimensional) networks helps the analysis of network topological properties while being agnostic to the chosen theory, algorithm, computation model, and programming language. (AU)

• FAPESP's process: 23/05593-1 - Algorithmic information dynamics of formal theories
• Grantee: Felipe Sobreira Abrahão
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 21/14501-8 - Algorithmic-informational systemics: toward a formal theory from mutually self-organizing partial structures
• Grantee: Felipe Sobreira Abrahão
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 15/24493-1 - INECiD: internet and the new age of data science
• Grantee: Artur Ziviani
• Support Opportunities: Regular Research Grants