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Effect of Homophily on Network Evolution

Listed author(s):
  • Kibae Kim

    ()

    (Technology Management, Economics, and Policy Program; College of Engineering; Seoul National University)

  • Jörn Altmann

    ()

    (Technology Management, Economics, and Policy Program; College of Engineering; Seoul National University)

Although there is much research on network formation based on the preferential attach- ment rule, the research did not come up with a formula that, on the one hand, can re- produce shapes of cumulative degree distributions of empirical complex networks and, on the other hand, can represent intuitively theories on individual behavior. In this paper, we propose a formula that closes this gap by integrating into the formula for the preferential attachment rule (i.e., a node with higher degree is more likely to gain a new link) a repre- sentation of the theory of individual behavior with respect to nodes preferring to connect to other nodes with similar attributes (i.e., homophily). Based on this formula, we simulate the shapes of cumulative degree distributions for different levels of homophily and five different seed networks. Our simulation results suggest that homophily and the preferential attachment rule interact for all five types of seed networks. Surprisingly, the resulting cumulative degree distribution in log-log scale always shifts from a concave shape to a convex shape, as the level of homophily gets larger. Therefore, our formula can explain intuitively why some of the empirical complex networks show a linear cumulative degree distribution in log-log scale while others show either a concave or convex shape. Furthermore, another major finding indicates that homophily makes people of a group richer than people outside this group, which is a surprising and significant finding.

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File URL: ftp://147.46.237.98/DP-121.pdf
File Function: Second Version, 2017
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Paper provided by Seoul National University; Technology Management, Economics, and Policy Program (TEMEP) in its series TEMEP Discussion Papers with number 2015121.

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Length: 22 pages
Date of creation: Jan 2015
Date of revision: Mar 2017
Publication status: Published in Elsevier Journal on Communications in Nonlinear Science and Numerical Simulation.
Handle: RePEc:snv:dp2009:2015121
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  1. Bramoullé, Yann & Currarini, Sergio & Jackson, Matthew O. & Pin, Paolo & Rogers, Brian W., 2012. "Homophily and long-run integration in social networks," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1754-1786.
  2. B. J. Kim & A. Trusina & P. Minnhagen & K. Sneppen, 2005. "Self organized scale-free networks from merging and regeneration," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 43(3), pages 369-372, February.
  3. Wu, Fang & Huberman, Bernardo A. & Adamic, Lada A. & Tyler, Joshua R., 2004. "Information flow in social groups," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(1), pages 327-335.
  4. Kibae Kim & Jorn Altmann & Junseok Hwang, 2010. "The Impact of the Subgroup Structure on the Evolution of Networks: An Economic Model of Network Evolution," TEMEP Discussion Papers 201056, Seoul National University; Technology Management, Economics, and Policy Program (TEMEP), revised Feb 2010.
  5. Dangalchev, Chavdar, 2004. "Generation models for scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 659-671.
  6. Kibae Kim & Jorn Altmann & Junseok Hwang, 2010. "An Analysis of the Openness of the Web2.0 Service Network Based on Two Sets of Indices for Measuring the Impact of Service Ownership," TEMEP Discussion Papers 201067, Seoul National University; Technology Management, Economics, and Policy Program (TEMEP), revised Oct 2010.
  7. Barabási, A.L & Jeong, H & Néda, Z & Ravasz, E & Schubert, A & Vicsek, T, 2002. "Evolution of the social network of scientific collaborations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 590-614.
  8. Junseok Hwang & Jorn Altmann & Kibae Kim, 2009. "The Structural Evolution of the Web2.0 Service Network," TEMEP Discussion Papers 200914, Seoul National University; Technology Management, Economics, and Policy Program (TEMEP), revised Sep 2009.
  9. Wagner, Caroline S. & Leydesdorff, Loet, 2005. "Network structure, self-organization, and the growth of international collaboration in science," Research Policy, Elsevier, vol. 34(10), pages 1608-1618, December.
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