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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.02717 |
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| _version_ | 1866908299558912000 |
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| author | Pachon, Angelica Stephenson, Robin |
| author_facet | Pachon, Angelica Stephenson, Robin |
| contents | We study a generalization of the affine preferential attachment model where triangles are randomly added to the graph. We show that the model exhibits an asymptotically power-law degree distribution with adjustable parameter $γ\in (1,\infty)$, and positive clustering. However, the clustering behaviour depends on how it is measured. With high probability, the average local clustering coefficient remains positive, independently of $γ$, whereas the expectation of the global clustering coefficient does not vanish only when $γ>3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Clustering in a preferential attachment network with triangles Pachon, Angelica Stephenson, Robin Probability We study a generalization of the affine preferential attachment model where triangles are randomly added to the graph. We show that the model exhibits an asymptotically power-law degree distribution with adjustable parameter $γ\in (1,\infty)$, and positive clustering. However, the clustering behaviour depends on how it is measured. With high probability, the average local clustering coefficient remains positive, independently of $γ$, whereas the expectation of the global clustering coefficient does not vanish only when $γ>3$. |
| title | Clustering in a preferential attachment network with triangles |
| topic | Probability |
| url | https://arxiv.org/abs/2504.02717 |