Detectability of hierarchical communities in networks
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866911007766478848 |
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| author | Peel, Leto Schaub, Michael T. |
| author_facet | Peel, Leto Schaub, Michael T. |
| contents | We study the problem of recovering a planted hierarchy of partitions in a network. The detectability of a single planted partition has previously been analysed in detail and a phase transition has been identified below which the partition cannot be detected. Here we show that, in the hierarchical setting, there exist additional phases in which the presence of multiple consistent partitions can either help or hinder detection. Accordingly, the detectability limit for non-hierarchical partitions typically provides insufficient information about the detectability of the complete hierarchical structure, as we highlight with several constructive examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_07525 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Detectability of hierarchical communities in networks Peel, Leto Schaub, Michael T. Social and Information Networks Machine Learning Physics and Society We study the problem of recovering a planted hierarchy of partitions in a network. The detectability of a single planted partition has previously been analysed in detail and a phase transition has been identified below which the partition cannot be detected. Here we show that, in the hierarchical setting, there exist additional phases in which the presence of multiple consistent partitions can either help or hinder detection. Accordingly, the detectability limit for non-hierarchical partitions typically provides insufficient information about the detectability of the complete hierarchical structure, as we highlight with several constructive examples. |
| title | Detectability of hierarchical communities in networks |
| topic | Social and Information Networks Machine Learning Physics and Society |
| url | https://arxiv.org/abs/2009.07525 |