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

A Chung–Lu random graph is an inhomogeneous Erdős–Rényi 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...

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Bibliographic Details
Published in:Journal of physic, complexity complexity, 2023-03, Vol.4 (1), p.15008
Main Authors: Dionigi, Pierfrancesco, Garlaschelli, Diego, Subhra Hazra, Rajat, den Hollander, Frank, Mandjes, Michel
Format: Article
Language:English
Subjects:
adjacency matrix
central limit theorem
Chung–Lu random graph
principal eigenvalue and eigenvector
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Summary:A Chung–Lu random graph is an inhomogeneous Erdős–Rényi 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.
ISSN:2632-072X
2632-072X
DOI:10.1088/2632-072X/acb8f7