Central limit theorem for the principal eigenvalue and eigenvector of Chung-Lu random graphs
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910610673893376 |
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| author | Dionigi, Pierfrancesco Garlaschelli, Diego Hazra, Rajat Subhra Hollander, Frank den Mandjes, Michel |
| author_facet | Dionigi, Pierfrancesco Garlaschelli, Diego Hazra, Rajat Subhra Hollander, Frank den Mandjes, Michel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03531 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Central limit theorem for the principal eigenvalue and eigenvector of Chung-Lu random graphs Dionigi, Pierfrancesco Garlaschelli, Diego Hazra, Rajat Subhra Hollander, Frank den Mandjes, Michel Probability Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics 60B20, 60C05, 60K35 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. |
| title | Central limit theorem for the principal eigenvalue and eigenvector of Chung-Lu random graphs |
| topic | Probability Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics 60B20, 60C05, 60K35 |
| url | https://arxiv.org/abs/2207.03531 |