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Effect of Homophily on Network Evolution

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Kibae Kim & Jörn Altmann, 2015. "Effect of Homophily on Network Evolution," TEMEP Discussion Papers 2015121, Seoul National University; Technology Management, Economics, and Policy Program (TEMEP), revised Mar 2017.
  • Handle: RePEc:snv:dp2009:2015121
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    File URL: ftp://147.46.237.98/DP-121.pdf
    File Function: Second Version, 2017
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    References listed on IDEAS

    as
    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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    More about this item

    Keywords

    Complex Social Network Evolution; Cumulative Degree Distribution; Preferential Attachment Rule and Homophily; Empirical Data and Simulation.;

    JEL classification:

    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification

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