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Random–Walk–Based Segregation Measures

Author

Listed:
  • Marc Vorsatz
  • Pablo Coralio Ballester

Abstract

In this paper, we propose an intuitive way of how to measure residential segregation. Individuals are located in different nodes on a network that are interconnected through links. Each period, an individual either advances to an adjacent node or she stops moving. In this setting, the segregation index is then defined as the probability that a randomly chosen individual meets an individual of the same social group in the neighborhood where her random-walk terminates. It is shown in a dual theorem that the segregation index is as a natural generalization of the isolation index to networks and that it is proportional to the PageRank index applied by Google in order to determine the importance of web-pages. Finally, the segregation index is applied to the Spanish 2009 census tract data and compared with other prominent measures.

Suggested Citation

  • Marc Vorsatz & Pablo Coralio Ballester, 2010. "Random–Walk–Based Segregation Measures," Working Papers 2010-30, FEDEA.
    • Handle: RePEc:fda:fdaddt:2010-30
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    References listed on IDEAS

    as
    1. Federico Echenique & Roland G. Fryer, 2007. "A Measure of Segregation Based on Social Interactions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(2), pages 441-485.
    2. David M. Cutler & Edward L. Glaeser, 1997. "Are Ghettos Good or Bad?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(3), pages 827-872.
    3. George J. Borjas, 2021. "Ethnicity, Neighborhoods, and Human-Capital Externalities," World Scientific Book Chapters, in: Foundational Essays in Immigration Economics, chapter 7, pages 135-160, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Sandro Sousa & Vincenzo Nicosia, 2022. "Quantifying ethnic segregation in cities through random walks," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    2. Casilda Vega & Oscar Volij, 2014. "Segregation, informativeness and Lorenz dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 547-564, October.
    3. Hannu Salonen, 2016. "Equilibria and centrality in link formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1133-1151, November.
    4. Laetitia Gauvin & Annick Vignes & Jean-Pierre Nadal, 2013. "Modeling urban housing market dynamics: Can the socio-spatial segregation preserve some social diversity?," Post-Print hal-05494206, HAL.
    5. Gordon Anderson, 2018. "Measuring Aspects of Mobility, Polarization and Convergence in the Absence of Cardinality: Indices Based Upon Transitional Typology," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 139(3), pages 887-907, October.
    6. Oscar Volij, 2018. "Segregation: theoretical approaches," Chapters, in: Conchita D’Ambrosio (ed.), Handbook of Research on Economic and Social Well-Being, chapter 21, pages 480-503, Edward Elgar Publishing.
    7. Herings, P. Jean-Jacques & Peeters, Ronald & Tenev, Anastas P. & Thuijsman, Frank, 2021. "Naïve imitation and partial cooperation in a local public goods model," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 162-185.
    8. Abhimanyu Khan & Ronald Peeters & Frank Thuijsman & Philippe Uyttendaele, 2016. "Network Characteristics Enabling Efficient Coordination: A Simulation Study," Dynamic Games and Applications, Springer, vol. 6(4), pages 495-519, December.
    9. José M. Casado-Díaz & Raquel Simón-Albert & Hipólito Simón, 2022. "Reassessing the commuting penalty for immigrants: new evidence from Spain," Transportation, Springer, vol. 49(4), pages 1099-1132, August.
    10. Matthew Gentzkow & Jesse M. Shapiro & Matt Taddy, 2019. "Measuring Group Differences in High‐Dimensional Choices: Method and Application to Congressional Speech," Econometrica, Econometric Society, vol. 87(4), pages 1307-1340, July.
    11. Mariano Bosch & M. Carnero & Lídia Farré, 2015. "Rental housing discrimination and the persistence of ethnic enclaves," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 6(2), pages 129-152, June.
    12. repec:hic:wpaper:195 is not listed on IDEAS
    13. Gordon Anderson & Oliver Linton & Jasmin Thomas, 2017. "Similarity, dissimilarity and exceptionality: generalizing Gini’s transvariation to measure “differentness” in many distributions," METRON, Springer;Sapienza Università di Roma, vol. 75(2), pages 161-180, August.
    14. Fernández-Huertas Moraga, Jesús & Ferrer-i-Carbonell, Ada & Saiz, Albert, 2019. "Immigrant locations and native residential preferences: Emerging ghettos or new communities?," Journal of Urban Economics, Elsevier, vol. 112(C), pages 133-151.
    15. Sergio Currarini, & Elena Fumagalli & Fabrizio Panebianco, 2012. "Games on Networks: Direct Complements and Indirect Substitutes," Discussion Papers in Economics 13/04, Division of Economics, School of Business, University of Leicester.
    16. Arcón, Victoria & Caridi, Inés, 2025. "Homogenization scales in residential segregation through random walkers," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).
    17. Gauvin, Laetitia & Vignes, Annick & Nadal, Jean-Pierre, 2013. "Modeling urban housing market dynamics: Can the socio-spatial segregation preserve some social diversity?," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1300-1321.
    18. Michael D. König & Dominic Rohner & Mathias Thoenig & Fabrizio Zilibotti, 2017. "Networks in Conflict: Theory and Evidence From the Great War of Africa," Econometrica, Econometric Society, vol. 85, pages 1093-1132, July.

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    More about this item

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • 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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