Gaussian behavior of eigenvectors in sparse random graphs

Sparse random graphs are widely viewed as discrete models of chaotic physical systems. Heuristically, this suggests that eigenvectors of the adjacency operator should exhibit Gaussian statistics. We prove that a broad class of random graphs, including both random regular graphs and irregular configuration-type models, display local Gaussian behavior. Notably, our approach does not rely on local law universality; instead, it is based on combinatorial and entropy-based arguments intrinsic to the graph structure.