2024/09/27 by Kazuaki Nakayama, Nakayama, Kazuaki, Masato Hisakado +3
Physics and Astronomy · #FOS: Physical sciences #Quantum chaos and dynamical systems #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2409.19035
openalex publication_date 2024/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ∈ \0,1,⋯\, and develop a perturbative expansion around these values of ω. Additionally, we show that for ω= -1 + ε, the clustering coefficient scales as ln t / √(ε) t and approaches zero as t → ∞, confirming the absence of small-world properties.