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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.18259 |
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| _version_ | 1866914773773320192 |
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| author | Mendez-Bermudez, J. A. Aguilar-Sanchez, R. |
| author_facet | Mendez-Bermudez, J. A. Aguilar-Sanchez, R. |
| contents | Singular-value statistics (SVS) has been recently presented as a random matrix theory tool able to properly characterize non-Hermitian random matrix ensembles [PRX Quantum {\bf 4}, 040312 (2023)]. Here, we perform a numerical study of the SVS of the non-Hermitian adjacency matrices $\mathbf{A}$ of directed random graphs, where $\mathbf{A}$ are members of diluted real Ginibre ensembles. We consider two models of directed random graphs: Erdös-Rényi graphs and random regular graphs. Specifically, we focus on the ratio $r$ between nearest neighbor singular values and the minimum singular value $λ_{min}$. We show that $\langle r \rangle$ (where $\langle \cdot \rangle$ represents ensemble average) can effectively characterize the transition between mostly isolated vertices to almost complete graphs, while the probability density function of $λ_{min}$ can clearly distinguish between different graph models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18259 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singular-value statistics of directed random graphs Mendez-Bermudez, J. A. Aguilar-Sanchez, R. Applications Singular-value statistics (SVS) has been recently presented as a random matrix theory tool able to properly characterize non-Hermitian random matrix ensembles [PRX Quantum {\bf 4}, 040312 (2023)]. Here, we perform a numerical study of the SVS of the non-Hermitian adjacency matrices $\mathbf{A}$ of directed random graphs, where $\mathbf{A}$ are members of diluted real Ginibre ensembles. We consider two models of directed random graphs: Erdös-Rényi graphs and random regular graphs. Specifically, we focus on the ratio $r$ between nearest neighbor singular values and the minimum singular value $λ_{min}$. We show that $\langle r \rangle$ (where $\langle \cdot \rangle$ represents ensemble average) can effectively characterize the transition between mostly isolated vertices to almost complete graphs, while the probability density function of $λ_{min}$ can clearly distinguish between different graph models. |
| title | Singular-value statistics of directed random graphs |
| topic | Applications |
| url | https://arxiv.org/abs/2404.18259 |