Incomplete ordering of the voter model on small-world networks

2002/10/31 by Claudio Castellano, Daniele Vilone, Alessandro Vespignani · 5 citations
Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Quantum many-body systems #cond-mat.stat-mech

paper · pdf · doi:10.1209/epl/i2003-00490-0

published as Europhys. Lett. 63, 153 (2003) · 6 pages, 3 figures, published version

openalex publication_date 2003/07/01 · arxiv created 2003/07/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We investigate how the topology of small-world networks affects the dynamics of the voter model for opinion formation. We show that, contrary to what occurs on regular topologies with local interactions, the voter model on small-world networks does not display the emergence of complete order in the thermodynamic limit. The system settles in a stationary state with coexisting opinions whose lifetime diverges with the system size. Hence the nontrivial connectivity pattern leads to the counterintuitive conclusion that long-range connections inhibit the ordering process. However, for networks of finite size, for which full uniformity is reached, the ordering process takes a time shorter than on a regular lattice of the same size.

Citations

• Statistical mechanics of complex networks
• The Dissemination of Culture

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