A Cheeger Inequality for Size-Specific Conductance
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910005076164608 |
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| author | Huang, Yufan Gleich, David F. |
| author_facet | Huang, Yufan Gleich, David F. |
| contents | The $μ$-conductance measure proposed by Lovász and Simonovits is a size-specific conductance score that identifies the set with smallest conductance while disregarding those sets with volume smaller than a $μ$ fraction of the whole graph. Using $μ$-conductance enables us to study the network structures in new ways. In this manuscript we study a modified spectral cut for $μ$-conductance that is a natural relaxation of the integer program of $μ$-conductance and show that the optimum of this program has a two-sided Cheeger inequality with $μ$-conductance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11452 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Cheeger Inequality for Size-Specific Conductance Huang, Yufan Gleich, David F. Discrete Mathematics Social and Information Networks The $μ$-conductance measure proposed by Lovász and Simonovits is a size-specific conductance score that identifies the set with smallest conductance while disregarding those sets with volume smaller than a $μ$ fraction of the whole graph. Using $μ$-conductance enables us to study the network structures in new ways. In this manuscript we study a modified spectral cut for $μ$-conductance that is a natural relaxation of the integer program of $μ$-conductance and show that the optimum of this program has a two-sided Cheeger inequality with $μ$-conductance. |
| title | A Cheeger Inequality for Size-Specific Conductance |
| topic | Discrete Mathematics Social and Information Networks |
| url | https://arxiv.org/abs/2303.11452 |