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The European Physical Journal B

, Volume 57, Issue 3, pp 331–335 | Cite as

Order-disorder phase transition in a cliquey social network

  • M. WołoszynEmail author
  • D. Stauffer
  • K. Kułakowski
Interdisciplinary Physics

Abstract.

We investigate the network model of community by Watts, Dodds and Newman (D.J. Watts et al., Science 296, 1302 (2002)) as a hierarchy of groups, each of 5 individuals. A homophily parameter α controls the probability proportional to exp (-αx) of selection of neighbours against distance x. The network nodes are endowed with spin-like variables si = ± 1, with Ising interaction J > 0. The Glauber dynamics is used to investigate the order-disorder transition. The transition temperature Tc is close to 3.8 for α < 0.0 and it falls down to zero above this value. The result provides a mathematical illustration of the social ability to a collective action via weak ties, as discussed by Granovetter in 1973.

PACS.

89.65.-s Social and economic systems 61.43.-j Disordered solids 

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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Faculty of Physics and Applied Computer Science, AGH University of Science and TechnologyKrakówPoland
  2. 2.Institute of Theoretical Physics, Cologne UniversityKölnGermany

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