SPECTRAL STABILITY OF DYNAMIC WEIGHTED HYPERGRAPHS UNDER NONLINEAR EDGE PERTURBATIONS - Basma Abdhadi Ibrahim (Antis-Publisher, 2026)
Objective: Traditional graph models are inherently limited to pairwise dyadic relationships, rendering them insufficient for capturing the complex, higher-order group interactions pervasive in modern network systems. Method: In this paper, we establish a rigorous mathematical framework to analytically bound and evaluate the spectral stability of the hypergraph Laplacian under nonlinear edge dynamics. Diverging from conventional linear matrix approximations, we leverage multilinear algebra to model the dynamic network as a time-evolving tensor field. We present a generalized, higher-order multilinear extension of Weyl’s inequality, proving that the shift in the Z-eigenvalue spectrum is rigorously bounded by the fractional (m-1)-th root of the perturbation tensor's spectral norm. Results: This theoretical breakthrough mathematically formalizes the inherent