Eur. Phys. J. B (2012) 85: 88
https://doi.org/10.1140/epjb/e2012-20501-1

Regular Article

Heterogenous mean-field analysis of a generalized voter-like model on networks

¹ Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain
² Departamento de Electromagnetismo y Física de la Materia, Facultad de Ciencias, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
³ State Key Lab. of Industrial Control Technology, Institute of Cyber-systems and Control, Zhejiang University, Hangzhou 310027, P.R. China
⁴ Department of Physics, College of Computer and Information Sciences, Bouvé College of Health Sciences, Northeastern University, MA02115 Boston, USA

^a e-mail: moretti.paolo@gmail.com

Received: 21 June 2011
Received in final form: 9 January 2012
Published online: 5 March 2012

Abstract

We propose a generalized framework for the study of voter models in complex networks at the heterogeneous mean-field (HMF) level that (i) yields a unified picture for existing copy/invasion processes and (ii) allows for the introduction of further heterogeneity through degree-selectivity rules. In the context of the HMF approximation, our model is capable of providing straightforward estimates for central quantities such as the exit probability and the consensus/fixation time, based on the statistical properties of the complex network alone. The HMF approach has the advantage of being readily applicable also in those cases in which exact solutions are difficult to work out. Finally, the unified formalism allows one to understand previously proposed voter-like processes as simple limits of the generalized model.