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Generalized Voter-Like Models on Heterogeneous Networks

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Dynamics On and Of Complex Networks, Volume 2

Abstract

This Chapter presents a generalized model of consensus formation, which is able to encompass all previous formulations of copy/invasion processes inspired by variations on the voter model and the Moran process. It considered the implementation of such generalized dynamics on a heterogeneous contact pattern, represented by a complex network, and derived the theoretical predictions for the relevant dynamical quantities, within the assumptions of the heterogeneous mean-field theory. The chapter provides a brief review of previous results that can be recovered by this generalized formalism, and considers a novel application to the case of opinion formation in a social network. In particular, it addressed the case in which the opinion strength of an individual is related to his/her degree centrality in the network. It has been that in scale-free networks strong selectivity rules (which make less connected individuals much more prone to change their opinions than more-connected ones or vice versa) lead to a steeper growth of consensus time with the system size, making the ordering process slower in general. Numerical simulations on quenched networks show that the HMF theory is able to predict such behavior with reasonable accuracy. Slight deviations from the theoretical predictions are encountered in certain regions of the phase diagram, but they are due to quenched-network effects that the HMF theory is not be able to capture.

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Acknowledgements

We acknowledge financial support from the Spanish MEC (FEDER) under Projects No. FIS2010-21781-C02-01 and FIS2009-08451, and the Junta de Andalucía, under Project No. P09-FQM4682. R.P.-S. acknowledges additional support through ICREA Academia, funded by the Generalitat de Catalunya.

Author information

Authors and Affiliations

  1. Departamento de Electromagnetismo y Física de la Materia and Instituto “Carlos I” de Física Teórica y Computacional, Universidad de Granada, Facultad de Ciencias, Fuentenueva s/n, E-18071, Granada, Spain

    Paolo Moretti

  2. Department of Physics, College of Computer and Information Sciences, Bouvé College of Health Sciences, Northeastern University, Boston, MA, 02120, USA

    Andrea Baronchelli

  3. Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034, Barcelona, Spain

    Michele Starnini & Romualdo Pastor-Satorras

Authors
  1. Paolo Moretti
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  2. Andrea Baronchelli
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  3. Michele Starnini
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  4. Romualdo Pastor-Satorras
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Corresponding author

Correspondence to Paolo Moretti .

Editor information

Editors and Affiliations

  1. Dept. Computer Science & Engineering, Indian Institute of Technology Kharagpur, Kharagpur, 721302, West Bengal, India

    Animesh Mukherjee

  2. Microsoft Research Lab India, 9 Lavelle Road, Bangalore, 560001, India

    Monojit Choudhury

  3. , Laboratoire J.A. Dieudonné, Université de Nice - Sophie Antipolis, Parc Valrose, Nice 02, 06108, France

    Fernando Peruani

  4. Dept. Computer Science & Engineering, Indian Institute of Technology Kharagpur, Kharagpur, 721302, West Bengal, India

    Niloy Ganguly

  5. Department of Mathematical Engineering, Université Catholique de Louvain, 4, Avenue George Lemaître, Louvain-la-Neuve, B-1348, Belgium

    Bivas Mitra

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Moretti, P., Baronchelli, A., Starnini, M., Pastor-Satorras, R. (2013). Generalized Voter-Like Models on Heterogeneous Networks. In: Mukherjee, A., Choudhury, M., Peruani, F., Ganguly, N., Mitra, B. (eds) Dynamics On and Of Complex Networks, Volume 2. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-6729-8_14

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