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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.19035 |
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| _version_ | 1866909328408051712 |
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| author | Nakayama, Kazuaki Hisakado, Masato Mori, Shintaro |
| author_facet | Nakayama, Kazuaki Hisakado, Masato Mori, Shintaro |
| contents | The Asymmetric BA model extends the Barabási-Albert scale-free network model by introducing a parameter $ω$. As $ω$ varies, the model transitions through different network structures: an extended lattice at $ω= -1$, a random graph at $ω= 0$, and the original scale-free network at $ω= 1$. We derive the exact degree distribution for $ω= -r/(r+k)$, where $k \in \{0,1,\cdots\}$, and develop a perturbative expansion around these values of $ω$. Additionally, we show that for $ω= -1 + \varepsilon$, the clustering coefficient scales as $\ln t / \sqrt{\varepsilon} t$ and approaches zero as $t \to \infty$, confirming the absence of small-world properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19035 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Structural Properties of the Asymmetric Barabási-Albert Model in the Lattice Limit Nakayama, Kazuaki Hisakado, Masato Mori, Shintaro Statistical Mechanics The Asymmetric BA model extends the Barabási-Albert scale-free network model by introducing a parameter $ω$. As $ω$ varies, the model transitions through different network structures: an extended lattice at $ω= -1$, a random graph at $ω= 0$, and the original scale-free network at $ω= 1$. We derive the exact degree distribution for $ω= -r/(r+k)$, where $k \in \{0,1,\cdots\}$, and develop a perturbative expansion around these values of $ω$. Additionally, we show that for $ω= -1 + \varepsilon$, the clustering coefficient scales as $\ln t / \sqrt{\varepsilon} t$ and approaches zero as $t \to \infty$, confirming the absence of small-world properties. |
| title | Structural Properties of the Asymmetric Barabási-Albert Model in the Lattice Limit |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2409.19035 |