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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2506.04426 |
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| _version_ | 1866908773711347712 |
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| author | Grebík, Jan Král', Daniel Liu, Xizhi Pikhurko, Oleg Slipantschuk, Julia |
| author_facet | Grebík, Jan Král', Daniel Liu, Xizhi Pikhurko, Oleg Slipantschuk, Julia |
| contents | The relation between densities of cycles and the spectrum of a graphon, which implies that the spectra of convergent graphons converge, fundamentally relies on the self-adjointness of the linear operator associated with a graphon. In this short paper, we consider the setting of digraphons, which are limits of directed graphs, and prove that the spectra of convergent digraphons converge. Using this result, we establish the relation between densities of directed cycles and the spectrum of a digraphon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of spectra of digraph limits Grebík, Jan Král', Daniel Liu, Xizhi Pikhurko, Oleg Slipantschuk, Julia Combinatorics The relation between densities of cycles and the spectrum of a graphon, which implies that the spectra of convergent graphons converge, fundamentally relies on the self-adjointness of the linear operator associated with a graphon. In this short paper, we consider the setting of digraphons, which are limits of directed graphs, and prove that the spectra of convergent digraphons converge. Using this result, we establish the relation between densities of directed cycles and the spectrum of a digraphon. |
| title | Convergence of spectra of digraph limits |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.04426 |