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Reciprocity And The Emergence Of Power Laws In Social Networks

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  • MICHAEL SCHNEGG

    (Institute of Social Anthropology, University of Cologne, D-50923, Cologne, Germany)

Abstract

Research in network science has shown that many naturally occurring and technologically constructed networks arescale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (= degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponentsγ ~ 1than have been assumed in the past. Apparently humans do not only look for the most prominent players to play with. Moreover cooperation in humans is characterized through reciprocity, the tendency to give to those from whom one has received in the past. Both variables — reciprocity and the scaling exponent — are negatively correlated (r = -0.767,sig= 0.075). If we include this effect in simulations of growing networks, degree distributions emerge that are much closer to those empirically observed. While the proportion of nodes with small degrees decreases drastically as we introduce reciprocity, the scaling exponent is more robust and changes only when a relatively large proportion of attachment decisions follow this rule. If social networks are lessscale freethan previously assumed this has far reaching implications for policy makers, public health programs and marketing alike.

Suggested Citation

  • Michael Schnegg, 2006. "Reciprocity And The Emergence Of Power Laws In Social Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1067-1076.
  • Handle: RePEc:wsi:ijmpcx:v:17:y:2006:i:07:n:s0129183106009473
    DOI: 10.1142/S0129183106009473
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    References listed on IDEAS

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    1. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
    2. Henrich, Joseph & Boyd, Robert & Bowles, Samuel & Camerer, Colin & Fehr, Ernst & Gintis, Herbert (ed.), 2004. "Foundations of Human Sociality: Economic Experiments and Ethnographic Evidence from Fifteen Small-Scale Societies," OUP Catalogue, Oxford University Press, number 9780199262052.
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    Cited by:

    1. Kenji Itao & Kunihiko Kaneko, 2023. "Transition of social organisations driven by gift relationships," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-10, December.
    2. Schnegg, Michael & Linke, Theresa, 2015. "Living Institutions: Sharing and Sanctioning Water among Pastoralists in Namibia," World Development, Elsevier, vol. 68(C), pages 205-214.
    3. WALTHER Olivier, 2012. "Regional trade and economic networks in West Africa," LISER Working Paper Series 2012-07, Luxembourg Institute of Socio-Economic Research (LISER).
    4. Hohnisch, Martin & Pittnauer, Sabine & Stauffer, Dietrich, 2006. "A Percolation-Based Model Explaining Delayed Take-Off in New-Product Diffusion," Bonn Econ Discussion Papers 9/2006, University of Bonn, Bonn Graduate School of Economics (BGSE).

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