Average Jaccard Index of Random Graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910704827629568 |
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| author | Feng, Qunqiang Guo, Shuai Hu, Zhishui |
| author_facet | Feng, Qunqiang Guo, Shuai Hu, Zhishui |
| contents | The asymptotic behavior of the Jaccard index in $G(n,p)$, the classical Erdös-Rényi random graphs model, is studied in this paper, as $n$ goes to infinity. We first derive the asymptotic distribution of the Jaccard index of any pair of distinct vertices, as well as the first two moments of this index. Then the average of the Jaccard indices over all vertex pairs in $G(n,p)$ is shown to be asymptotically normal under an additional mild condition that $np\to\infty$ and $n^2(1-p)\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09804 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Average Jaccard Index of Random Graphs Feng, Qunqiang Guo, Shuai Hu, Zhishui Probability Combinatorics The asymptotic behavior of the Jaccard index in $G(n,p)$, the classical Erdös-Rényi random graphs model, is studied in this paper, as $n$ goes to infinity. We first derive the asymptotic distribution of the Jaccard index of any pair of distinct vertices, as well as the first two moments of this index. Then the average of the Jaccard indices over all vertex pairs in $G(n,p)$ is shown to be asymptotically normal under an additional mild condition that $np\to\infty$ and $n^2(1-p)\to\infty$. |
| title | Average Jaccard Index of Random Graphs |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2311.09804 |