Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.19035 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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.