2008/03/11 by Federico Vázquez, F. Vazquez, Victor M. Eguı́luz +1
Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/1367-2630/10/6/063011
published as New Journal of Physics 10, 063011 (2008) · 20 pages, 8 figures
arxiv created 2008/03/11 · openalex publication_date 2008/06/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract. We present a mathematical description of the voter model dynamics on uncorrelated networks. When the average degree of the graph is µ ≤ 2 the system reaches complete order exponentially fast. For µ> 2, a finite system falls, before it fully orders, in a quasistationary state in which the average density of active links (links between opposite-state nodes) in surviving runs is constant and equal to (µ−2)3(µ−1) , while an infinite large system stays ad infinitum in a partially ordered stationary active state. The mean life time of the quasistationary state is proportional to the mean time to reach the fully ordered state T, which scales as T ∼ (µ−1)µ2N(µ−2)µ2, where N is the number of nodes of the network, and µ2 is the second moment of the degree distribution. We find good agreement between these analytical results and numerical simulations on random networks with various degree distributions.