Multi-Dimensional Network Analysis: Tensor-Based Betweenness Centrality Revolutionizes 5G Networks

Michael Mann,
RGM Global Ventures, NY, USA
Michaelmann390@gmail.com

DOI: 10.36724/2664-066X-2024-10-6-2-7

SYNCHROINFO JOURNAL. Volume 10, Number 6 (2024). P. 2-7.

Abstract

The analysis of 5G networks presents unique challenges that consistently push the boundaries of traditional network theory. While investigating resource allocation problems in telecommunications networks, it became evident that conventional graph-theoretic approaches fall short when dealing with multi-dimensional relationships and dynamic topologies. This observation motivated the development of a more robust analytical framework. This paper presents a theoretical framework for analyzing multi-dimensional networks through the integration of tensor-based betweenness centrality and cooperative game theory. The work establishes mathematical foundations for network analysis, proves optimality conditions, and provides complexity bounds. The framework extends to 5G networks while maintaining mathematical rigor. The main contribution is the development of Tensor-Based Betweenness Centrality (TBBC), with complete mathematical proofs of its properties and convergence characteristics.

Keywords:  5G Networks, Tensor-Based Betweenness Centrality

References

[1] L. C. Freeman, “A set of measures of centrality based on betweenness,” Sociometry, vol. 40, no. 1, pp. 35-41, 1977.

[2] U. Brandes, “A faster algorithm for betweenness centrality,” Journal of Mathematical Sociology, vol. 25, no. 2, pp. 163-177, 2001.

[3] M. Mann, “Theoretical Analysis of an Adaptive Closeness Centrality-Based Algorithm for Dynamic Optimization of Transportation Networks,” in 2024 International Conference on Engineering Management of Communication and Technology (EMCTECH), IEEE, 2024, pp. 1-5.

[4] G. Kossinets, and D. J. Watts, “Empirical analysis of an evolving social network,” Science, vol. 311, no. 5757, pp. 88-90, 2006.

[5] M. G. Rodriguez and B. Schölkopf, “Submodular inference of diffusion networks from multiple trees,” in Proc. ICML, pp. 489-496, 2012.

[6] Y. Zhang et al., “Tensor-based network analysis,” IEEE Trans. Network Science, vol. 5, no. 2, pp. 82-96, 2023.

[7] H. Wang et al., “Game-theoretic approaches to network centrality,” Network Science, vol. 12, no. 1, pp. 45-67, 2024.

[8] T. Kolda and B. Bader, “Tensor decompositions and applications,” SIAM Review, vol. 51, no. 3, pp. 455-500, 2009.

[9] M. Newman, “Networks: An Introduction,” Oxford University Press, 2010.

[10] P. Erdős and A. Rényi, “On random graphs,” Publicationes Mathematicae, vol. 6, pp. 290-297, 1959.

[11] D. Easley and J. Kleinberg, “Networks, Crowds, and Markets: Reasoning about a Highly Connected World,” Cambridge University Press, 2010.

[12] A. L. Barabási and R. Albert, “Emergence of scaling in random networks,” Science, vol. 286, no. 5439, pp. 509-512, 1999.

[13] J. Nash, “Non-cooperative games,” Annals of Mathematics, vol. 54, no. 2, pp. 286-295, 1951.

[14] R. Albert and A. L. Barabási, “Statistical mechanics of complex networks,” Reviews of Modern Physics, vol. 74, no. 1, pp. 47-97, 2002.

[15] S. Brin and L. Page, “The anatomy of a large-scale hypertextual Web search engine,” Computer Networks and ISDN Systems, vol. 30, pp. 107-117, 1998.

[16] M. E. J. Newman, “The structure and function of complex networks,” SIAM Review, vol. 45, no. 2, pp. 167-256, 2003.