2007/01/08 by Haijun Zhou, Reinhard Lipowsky · 1 citation
Mathematics · Physics and Astronomy · #Asynchronous communication #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Degree (music) #Exponent #Mathematics #Opinion Dynamics and Social Influence #Physics #Random field #Relaxation (psychology) #Scale (ratio) #Scale-free network #Scaling #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2007/01/p01009
20 pages, 8 figures
openalex publication_date 2007/01/08 · arxiv created 2007/01/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Activity or spin patterns on random scale-free network are studied by mean field analysis and computer simulations. These activity patterns evolve in time according to local majority-rule dynamics which is implemented using (i) parallel or synchronous updating and (ii) random sequential or asynchronous updating. Our mean-field calculations predict that the relaxation processes of disordered activity patterns become much more efficient as the scaling exponent γ of the scale-free degree distribution changes from γ >5/2 to γ < 5/2. For γ > 5/2, the corresponding decay times increase as ln(N) with increasing network size N whereas they are independent of N for γ < 5/2. In order to check these mean field predictions, extensive simulations of the pattern dynamics have been performed using two different ensembles of random scale-free networks: (A) multi-networks as generated by the configuration method, which typically leads to many self-connections and multiple edges, and (B) simple-networks without self-connections and multiple edges.