Central limit theorem for the principal eigenvalue and eigenvector of Chung-Lu random graphs

Pierfrancesco Dionigi; Diego Garlaschelli; Rajat Subhra Hazra; Frank den Hollander; Michel Mandjes

doi:10.1088/2632-072x/acb8f7

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arXiv · 2207.03531

Central limit theorem for the principal eigenvalue and eigenvector of Chung-Lu random graphs

Pierfrancesco Dionigi·Diego Garlaschelli·Rajat Subhra Hazra·Frank den Hollander·Michel Mandjes

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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.

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Pierfrancesco Dionigi, Diego Garlaschelli, Rajat Subhra Hazra, Frank den Hollander, Michel Mandjes. 2022-07-07. Central limit theorem for the principal eigenvalue and eigenvector of Chung-Lu random graphs. https://doi.org/10.1088/2632-072x%2Facb8f7

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