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...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2023-01-01
|
| Series: | Journal of Physics: Complexity |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-072X/acb8f7 |
| _version_ | 1827916148394426368 |
|---|---|
| author | Pierfrancesco Dionigi Diego Garlaschelli Rajat Subhra Hazra Frank den Hollander Michel Mandjes |
| author_facet | Pierfrancesco Dionigi Diego Garlaschelli Rajat Subhra Hazra Frank den Hollander Michel Mandjes |
| author_sort | Pierfrancesco Dionigi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-13T03:09:53Z |
| format | Article |
| id | doaj.art-6ae9826b83984ea58e9704605bf3b859 |
| institution | Directory Open Access Journal |
| issn | 2632-072X |
| language | English |
| last_indexed | 2024-03-13T03:09:53Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Journal of Physics: Complexity |
| spelling | doaj.art-6ae9826b83984ea58e9704605bf3b8592023-06-26T15:09:25ZengIOP PublishingJournal of Physics: Complexity2632-072X2023-01-014101500810.1088/2632-072X/acb8f7Central limit theorem for the principal eigenvalue and eigenvector of Chung–Lu random graphsPierfrancesco Dionigi0https://orcid.org/0000-0003-2180-8669Diego Garlaschelli1https://orcid.org/0000-0001-6035-1783Rajat Subhra Hazra2https://orcid.org/0000-0002-9254-4763Frank den Hollander3https://orcid.org/0000-0003-2866-9470Michel Mandjes4https://orcid.org/0000-0001-6783-4833Mathematical Institute, Leiden University , PO Box 9512, 2300 RA Leiden, The NetherlandsLorentz Institute for Theoretical Physics, Leiden University , PO Box 9504, 2300 RA Leiden, The Netherlands; IMT School for Advanced Studies , Piazza S. Francesco 19, 55100 Lucca, Italy; INDAM-GNAMPA Istituto Nazionale di Alta Matematica ‘Francesco Severi’ , Piazzale Aldo Moro 5, 00185 Roma, ItalyMathematical Institute, Leiden University , PO Box 9512, 2300 RA Leiden, The NetherlandsMathematical Institute, Leiden University , PO Box 9512, 2300 RA Leiden, The NetherlandsKorteweg–de Vries Institute, University of Amsterdam , PO Box 94248, 1090 GE Amsterdam, The NetherlandsA 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.https://doi.org/10.1088/2632-072X/acb8f7Chung–Lu random graphadjacency matrixprincipal eigenvalue and eigenvectorcentral limit theorem |
| spellingShingle | Pierfrancesco Dionigi Diego Garlaschelli Rajat Subhra Hazra Frank den Hollander Michel Mandjes Central limit theorem for the principal eigenvalue and eigenvector of Chung–Lu random graphs Journal of Physics: Complexity Chung–Lu random graph adjacency matrix principal eigenvalue and eigenvector central limit theorem |
| title | Central limit theorem for the principal eigenvalue and eigenvector of Chung–Lu random graphs |
| title_full | Central limit theorem for the principal eigenvalue and eigenvector of Chung–Lu random graphs |
| title_fullStr | Central limit theorem for the principal eigenvalue and eigenvector of Chung–Lu random graphs |
| title_full_unstemmed | Central limit theorem for the principal eigenvalue and eigenvector of Chung–Lu random graphs |
| title_short | Central limit theorem for the principal eigenvalue and eigenvector of Chung–Lu random graphs |
| title_sort | central limit theorem for the principal eigenvalue and eigenvector of chung lu random graphs |
| topic | Chung–Lu random graph adjacency matrix principal eigenvalue and eigenvector central limit theorem |
| url | https://doi.org/10.1088/2632-072X/acb8f7 |
| work_keys_str_mv | AT pierfrancescodionigi centrallimittheoremfortheprincipaleigenvalueandeigenvectorofchunglurandomgraphs AT diegogarlaschelli centrallimittheoremfortheprincipaleigenvalueandeigenvectorofchunglurandomgraphs AT rajatsubhrahazra centrallimittheoremfortheprincipaleigenvalueandeigenvectorofchunglurandomgraphs AT frankdenhollander centrallimittheoremfortheprincipaleigenvalueandeigenvectorofchunglurandomgraphs AT michelmandjes centrallimittheoremfortheprincipaleigenvalueandeigenvectorofchunglurandomgraphs |