How does degree heterogeneity affect an order-disorder transition?

2007/02/28 by Renaud Lambiotte, R. Lambiotte · 3 citations
Physics and Astronomy · Social Sciences · #Language and cultural evolution #Opinion Dynamics and Social Influence #Statistical Mechanics and Entropy #physics.soc-ph

paper · pdf · doi:10.1209/0295-5075/78/68002

published as EPL, 78 (2007) 68002 · 5 pages, 3 figures

arxiv created 2007/04/17 · openalex publication_date 2007/05/25 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28

Abstract

We focus on the role played by the node degree distribution on the way collective phenomena emerge on complex networks. To address this question, we focus analytically on a typical model for cooperative behaviour, the Majority Rule, applied to dichotomous networks. The latter are composed of two kinds of nodes, each kind i being characterized by a degree k_i. Dichotomous networks are therefore a simple instance of heterogeneous networks, especially adapted in order to reveal the effect of degree heterogeneity. Our main result are that degree heterogeneity affects the location of the order-disorder transition and that the system exhibits non-equipartition of the average opinion between the two kinds of nodes. This effect is observed in the ordered phase and in the disordered phase.

Citations

• Voter model dynamics in complex networks: Role of dimensionality, disorder, and degree distribution
• Emergence of scaling in random networks
• Multiscaling in inelastic collisions
• Majority model on a network with communities

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• Opinion formation in laggard societies
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