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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 10: Social-, Information-, and Production Networks

AKSOE 10.1: Vortrag

Mittwoch, 28. März 2007, 13:30–14:00, H8

Collective behaviour in clustered social networks. — •Maciej Wołoszyn¹, Dietrich Stauffer², and Krzysztof Kułakowski¹ — ¹Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland — ²Institute of Theoretical Physics, University of Köln, Zülpicher Str. 77, D-50937 Köln, Germany

A hierarchy of groups forming the network model of community (D.J. Watts et al., Science 296 (2002) 1302) is investigated in search for the order-disorder phase transition. Each group consists of 5 individuals endowed with a spin-like variables s_i = ± 1 with Ising interaction J>0. Links between individuals are created with probability proportional to exp(−α x), where x is the distance in the hierarchy and α is a clustering parameter. The Metropolis algorithm is used to calculate the ordering temperature T_c from the relaxation time of the average value of spins. As a result, T_c was found to be close to 3.3 for α < 1.0 and falling down to zero above this value, which provides a mathematical illustration of the social ability to a collective action via weak ties, as discussed by M. Granovetter (Am. J. of Sociology 78 (1973) 1360).