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Graph fission in an evolving voter model.

Publication ,  Journal Article
Durrett, R; Gleeson, JP; Lloyd, AL; Mucha, PJ; Shi, F; Sivakoff, D; Socolar, JES; Varghese, C
Published in: Proceedings of the National Academy of Sciences of the United States of America
March 2012

We consider a simplified model of a social network in which individuals have one of two opinions (called 0 and 1) and their opinions and the network connections coevolve. Edges are picked at random. If the two connected individuals hold different opinions then, with probability 1 - α, one imitates the opinion of the other; otherwise (i.e., with probability α), the link between them is broken and one of them makes a new connection to an individual chosen at random (i) from those with the same opinion or (ii) from the network as a whole. The evolution of the system stops when there are no longer any discordant edges connecting individuals with different opinions. Letting ρ be the fraction of voters holding the minority opinion after the evolution stops, we are interested in how ρ depends on α and the initial fraction u of voters with opinion 1. In case (i), there is a critical value α(c) which does not depend on u, with ρ ≈ u for α > α(c) and ρ ≈ 0 for α < α(c). In case (ii), the transition point α(c)(u) depends on the initial density u. For α > α(c)(u), ρ ≈ u, but for α < α(c)(u), we have ρ(α,u) = ρ(α,1/2). Using simulations and approximate calculations, we explain why these two nearly identical models have such dramatically different phase transitions.

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Published In

Proceedings of the National Academy of Sciences of the United States of America

DOI

EISSN

1091-6490

ISSN

0027-8424

Publication Date

March 2012

Volume

109

Issue

10

Start / End Page

3682 / 3687

Related Subject Headings

  • Social Support
  • Public Opinion
  • Probability
  • Politics
  • Models, Theoretical
  • Models, Statistical
  • Humans
  • Diffusion
  • Computer Simulation
  • Algorithms
 

Citation

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Durrett, R., Gleeson, J. P., Lloyd, A. L., Mucha, P. J., Shi, F., Sivakoff, D., … Varghese, C. (2012). Graph fission in an evolving voter model. Proceedings of the National Academy of Sciences of the United States of America, 109(10), 3682–3687. https://doi.org/10.1073/pnas.1200709109
Durrett, Richard, James P. Gleeson, Alun L. Lloyd, Peter J. Mucha, Feng Shi, David Sivakoff, Joshua E. S. Socolar, and Chris Varghese. “Graph fission in an evolving voter model.Proceedings of the National Academy of Sciences of the United States of America 109, no. 10 (March 2012): 3682–87. https://doi.org/10.1073/pnas.1200709109.
Durrett R, Gleeson JP, Lloyd AL, Mucha PJ, Shi F, Sivakoff D, et al. Graph fission in an evolving voter model. Proceedings of the National Academy of Sciences of the United States of America. 2012 Mar;109(10):3682–7.
Durrett, Richard, et al. “Graph fission in an evolving voter model.Proceedings of the National Academy of Sciences of the United States of America, vol. 109, no. 10, Mar. 2012, pp. 3682–87. Epmc, doi:10.1073/pnas.1200709109.
Durrett R, Gleeson JP, Lloyd AL, Mucha PJ, Shi F, Sivakoff D, Socolar JES, Varghese C. Graph fission in an evolving voter model. Proceedings of the National Academy of Sciences of the United States of America. 2012 Mar;109(10):3682–3687.
Journal cover image

Published In

Proceedings of the National Academy of Sciences of the United States of America

DOI

EISSN

1091-6490

ISSN

0027-8424

Publication Date

March 2012

Volume

109

Issue

10

Start / End Page

3682 / 3687

Related Subject Headings

  • Social Support
  • Public Opinion
  • Probability
  • Politics
  • Models, Theoretical
  • Models, Statistical
  • Humans
  • Diffusion
  • Computer Simulation
  • Algorithms