Central limit theorem for the principal eigenvalue and eigenvector of Chung-Lu random graphs
Probability
2024-09-20 v1 Disordered Systems and Neural Networks
Statistical Mechanics
Mathematical Physics
math.MP
Abstract
A Chung-Lu random graph is an inhomogeneous Erd\H{o}s-R\'enyi random graph in which vertices are assigned average degrees, and pairs of vertices are connected by an edge with a probability that is proportional to the product of their average degrees, independently for different edges. We derive a central limit theorem for the principal eigenvalue and the components of the principal eigenvector of the adjacency matrix of a Chung-Lu random graph. Our derivation requires certain assumptions on the average degrees that guarantee connectivity, sparsity and bounded inhomogeneity of the graph.
Cite
@article{arxiv.2207.03531,
title = {Central limit theorem for the principal eigenvalue and eigenvector of Chung-Lu random graphs},
author = {Pierfrancesco Dionigi and Diego Garlaschelli and Rajat Subhra Hazra and Frank den Hollander and Michel Mandjes},
journal= {arXiv preprint arXiv:2207.03531},
year = {2024}
}