Measuring geographic segregation: a graph-based approach

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Residential segregation is a multidimensional phenomenon that encompasses several conceptually distinct aspects of geographical separation between populations. While various indices have been developed as a response to different definitions of segregation, the reliance on such single-figure indices could oversimplify the complex, multidimensional phenomena. In this regard, this paper suggests an alternative graph-based approach that provides more detailed information than simple indices: The concentration profile graphically conveys information about how evenly a population group is distributed over the study region, and the spatial proximity profile depicts the degree of clustering across different threshold levels. These graphs can also be summarized into single numbers for comparative purposes, but the interpretation can be more accurate by inspecting the additional information. To demonstrate the use of these methods, the residential patterns of three major ethnic groups in Auckland, namely Māori, Pacific peoples, and Asians, are examined using the 2006 census data.

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  1. 1.

    In the segregation literature, the Lorenz curve is often constructed by plotting the cumulative proportion of one population group against that of the other group. The concentration profile is different from the Lorenz curve in the sense that it plots the cumulative proportion of the population group against their relative demographic share in geographic units.

  2. 2.

    In the 2006 census, Samoan was the largest population group in this broad ethnic category (49.3 %), followed by Cook Islands Māori (21.8 %), Tongan (19.0 %), Niuean (8.4 %), Fijian (3.7 %), Tokelauan (2.5 %), and Tuvaluan (1.0 %). Although each of these groups has distinct cultural, linguistic, and historical backgrounds, we analyze the “Pacific peoples” data as a whole to demonstrate the use of the proposed approach. Note that the census respondents were able to choose more than one ethnic group to describe their ethnicity. The sum of the individual proportions in this data set therefore exceeds 100 %.

  3. 3.

    While it may be beyond the scope of this paper to explain why Pacific peoples (and the Māori population) are clustered in the southern Auckland, previous studies suggest that the presence of state housing in this locality has attracted low-income Pacific peoples (Johnston et al. 2008).


  1. Allen R, Burgess S, Windmeijer F (2009) More reliable inference for segregation indices. CMPO Working Paper Series, vol 216. University of Bristol, Centre for Market and Public Organisation, Bristol

  2. Dorfman R (1979) A formula for the Gini coefficient. Rev Econ Stat 61(1):146–149

  3. Duncan OD, Duncan B (1955) A methodological analysis of segregation indexes. Am Sociol Rev 20(2):210–217

  4. Falk RF, Cortese CF, Cohen J (1978) Utilizing standardized indices of residential segregation: comment on Winship. Soc Forces 57(2):713–716. doi:10.2307/2577693

  5. Friesen W, Murphy L, Kearns R (2005) Spiced-up Sandringham: Indian transnationalism and new suburban spaces in Auckland, New Zealand. J Ethn Migr Stud 31(2):385–401

  6. Grbic D, Ishizawa H, Crothers C (2010) Ethnic residential segregation in New Zealand, 1991–2006. Soc Sci Res 39(1):25–38

  7. Hong S-Y, Yoon H-K (2013) Ethno-economic satellite: the case of Korean residential clusters in Auckland. Popul Space Place. doi:10.1002/psp.1764

  8. Hutchens RM (1991) Segregation curves, Lorenz curves, and inequality in the distribution of people across occupations. Math Soc Sci 21(1):31–51. doi:10.1016/0165-4896(91)90038-S

  9. Johnston R, Poulsen M, Forrest J (2005) Ethnic residential segregation across an urban system: the Maori in New Zealand, 1991–2001. Prof Geogr 57(1):115–129. doi:10.1111/j.0033-0124.2005.00464.x

  10. Johnston R, Poulsen M, Forrest J (2008) Asians, Pacific Islanders, and ethnoburbs in Auckland, New Zealand. Geogr Rev 98(2):214(228)

  11. Johnston R, Poulsen M, Forrest J (2010) Moving on from indices, refocusing on mix: on measuring and understanding ethnic patterns of residential segregation. J Ethn Migr Stud 36(4):697–706. doi:10.1080/13691830903505045

  12. Johnston R, Poulsen M, Forrest J (2011) Evaluating changing residential segregation in Auckland, New Zealand, using spatial statistics. Tijdschr Econ Soc Geogr 102(1):1–23. doi:10.1111/j.1467-9663.2009.00577.x

  13. Massey DS, Denton NA (1988) The dimensions of residential segregation. Soc Forces 67(2):281–315

  14. Morgan BS (1983) An alternate approach to the development of a distance-based measure of racial segregation. Am J Sociol 88(6):1237–1249

  15. Morrill RL (1991) On the measure of geographic segregation. Geogr Res Forum 11:25–36

  16. Openshaw S (1984) The modifiable areal unit problem. Geo, Norwich

  17. O’Sullivan D, Wong DWS (2007) A surface-based approach to measuring spatial segregation. Geogr Anal 39(2):147(122)

  18. Poulsen M, Johnston R, Forrest J (2002) Plural cities and ethnic enclaves: introducing a measurement procedure for comparative study. Int J Urban Reg Res 26(2):229–243

  19. Reardon SF, O’Sullivan D (2004) Measures of spatial segregation. Sociol Methodol 34(1):121–162

  20. Reardon S, Matthews S, O’Sullivan D, Lee B, Firebaugh G, Farrell C, Bischoff K (2008) The geographic scale of Metropolitan racial segregation. Demography 45(3):489–514. doi:10.1353/dem.0.0019

  21. Reardon SF, Farrell CR, Matthews SA, O’Sullivan D, Bischoff K, Firebaugh G (2009) Race and space in the 1990s: changes in the geographic scale of racial residential segregation, 1990–2000. Soc Sci Res 38(1):55–70

  22. White MJ (1983) The measurement of spatial segregation. Am J Sociol 88(5):1008–1018

  23. Winship C (1977) A revaluation of indexes of residential segregation. Soc Forces 55(4):1058–1066. doi:10.2307/2577572

  24. Wong DWS (1993) Spatial indices of segregation. Urban Stud 30(3):559–572

  25. Wong DWS (1997) Spatial dependency of segregation indices. Can Geogr 41(2):128–136

  26. Wong DWS, Reibel M, Dawkins C (2007) Introduction—segregation and neighborhood change: where are we after more than a half-century of formal analysis. Urban Geogr 28(4):305–311

  27. Wright R, Holloway S, Ellis M (2011) Reconsidering both diversity and segregation: a reply to Poulsen, Johnston and Forrest, and to Peach. J Ethn Migr Stud 37(1):167–176. doi:10.1080/1369183x.2011.523865

  28. Xue J, Friesen W, O’Sullivan D (2012) Diversity in Chinese Auckland: hypothesising multiple ethnoburbs. Popul Space Place 18:579–595. doi:10.1002/psp.688

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This work was supported by JSPS KAKENHI Grant Number 24-02309. We are thankful to the anonymous referees for their constructive comments.

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Correspondence to Seong-Yun Hong.

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Hong, S., Sadahiro, Y. Measuring geographic segregation: a graph-based approach. J Geogr Syst 16, 211–231 (2014).

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  • Segregation measures
  • Residential segregation
  • Segregation profiles
  • Concentration profile
  • Spatial proximity profile

JEL Classification

  • C4
  • C43
  • J15