2025/05/28 by Kazuki Wataya, Wataya, Kazuki, Takehisa Hasegawa +1
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Graph theory and applications #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2505.22166
openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate bond percolation on the Song-Havlin-Makse (SHM) network, a scale-free tree with a tunable degree exponent and dimensionality. Using a generating function approach, we analytically derive the average size and the fractal exponent of the root cluster for deterministic cases. Our analysis reveals that bond percolation on the SHM network remains in a nonpercolating phase for all p < 1 when the network is fractal (i.e., finite-dimensional), whereas it exhibits a critical phase, where the cluster size distribution follows a power-law with a p-dependent exponent, throughout the entire range of p when the network is small-world (i.e., infinite-dimensional), regardless of the specific dimensionality or degree exponent. The analytical results are in excellent agreement with Monte Carlo simulations.