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Incomplete ordering of the voter model on small-world networks

Claudio Castellano·Daniele Vilone·Alessandro Vespignani
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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.

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Claudio Castellano, Daniele Vilone, Alessandro Vespignani. 2003-07-29. Incomplete ordering of the voter model on small-world networks. https://doi.org/10.1209/epl%2Fi2003-00490-0

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