ON HYPER G-MATRICES AND NETWORK MODELS IN COMMUNICATION SYSTEMS

Keleş H.

Journal of Applied and Pure Mathematics, cilt.8, sa.1-2, ss.45-58, 2026 (Hakemli Dergi)

Özet

This paper explores the relationship between computer networks, communication systems, and a novel framework called Hyper G-matrices. We first describe how networks can be represented using adjacency, degree, and Laplacian matrices. We then generalize these representations to include networks with positive, negative, or absent interactions, which are relevant to communication and social systems. The connection between these structures and the framework of Hyper G-matrices, which capture matrix pairs related by diagonal transformations, provides new insights into how different representations of networks can be unified under a generalized algebraic framework. Furthermore, we discuss potential applications in network robustness, flow optimization, distributed computation, and quantum networks, and we analyze the spectral properties of these network matrices.