Today, segregation indices are well-known and increasingly used in urban studies. This is hardly surprising, since segregation indices make it possible: "1) to qualify and compare the distribution in the metropolitan area of population groups that differ in ethnic origin, birth country or region, mother
tongue, visible minority status, and income, 2) to compare cities, and 3) to complete diachronic analyses" (Apparicio *et al.*, 2008: 2).

In a seminal paper on residential segregation indices, Massey and Denton (1988) classify them into five distinct dimensions: **evenness**, **exposure**, **concentration**, **clustering** and **centralization** (see Table below).

Dimension |
Description |

Adapted from Martori and Apparicio (2011). | |

Evenness | Evenness refers to the distribution of one or more population groups across the spatial units of the metropolitan area (e.g., census tracts). Evenness indices measure a group’s over- or under-representation in the spatial units of a metropolitan area: The more unevenly a population group is distributed across these spatial units, the more segregated it is. |

Exposure | Exposure is the degree of potential contact between members of the same group (one group) or between members of two groups (intergroup) inside spatial units. It measures the probability that members of one group will encounter members of their own group (isolation) or another group (interaction) in their spatial unit. |

Concentration | Concentration refers to the physical space occupied by a group. The less of the metropolitan area a group occupies, the more concentrated it is. According to Massey and Denton (1988), segregated minorities generally occupy a small portion of metropolitan areas. |

Clustering | Other indices measure clustering. The more contiguous spatial units a group occupies—thereby forming an enclave within the city—the more clustered and therefore segregated it is, according to this dimension. |

Centralization | Finally, centralization indices measure the degree to which a group is located near and in the center of the metropolitan area, which is usually defined as the central business district. The closer a group is to the city center, the more centralized and thus segregated it is according to this dimension. |

For each dimension, three distinct types of indices are usually identified:

- One-group indices that measure the distribution of a population group compared to the total population;
- Two-group indices that compare the distribution of a population group to another;
- Multigroup indices that analyze the distribution of several population groups simultaneously.

In addition, it is possible to map other indices, in particular:

- The location quotient which is useful for identifying spatial units in a metropolitan area where a population group is under-represented (LQ > 1) or conversely, over-represented (LQ < 1);
- The entropy or diversity index which is useful for identifying spatial units that are completely homogenous (inhabited by only one population group, H2 = 0) or maximally diversified (all population groups are equal in size, H2 = 1);
- The typology proposed by Poulsen
*et al.*

Dimension | Name | Abbreviation | Values | Authors | |

Adapted from Massey and Denton (1988), Apparicio (2000) and Apparicio et al. (2008). |
|||||

Evenness | 1. | Segregation index | IS | [0,1] | Duncan and Duncan (1955a, 1955b) |

2. | Segregation index adjusted for tract contiguity | IS(adj) | [0,1] | Morrill (1991) | |

3. | Segregation index adjusted for contiguous tract boundary lengths | IS(w) | [0,1] | Wong (1993) | |

4. | Segregation index adjusted for contiguous tract boundary lengths and perimeter/area ratio | IS(s) | [0,1] | Wong (1993) | |

5. | Entropy index | H | [0,1] | Theil (1972), Theil and Finezza (1971) | |

6. | Gini index | G | [0,1] | Duncan and Duncan (1955a) | |

7. | Atkinson index with b =0.1 | A(0.1) | [0,1] | Atkinson (1970) | |

8. | Atkinson index with b =0.5 | A(0.5) | [0,1] | Atkinson (1970) | |

9. | Atkinson index with b =0.9 | A(0.9) | [0,1] | Atkinson (1970) | |

Exposure | 10. | Isolation index | xPx | [0,1] | Bell (1954) |

11. | Correlation ratio | Eta^{2} |
[0,1] | Bell (1954), White (1986) | |

Concentration | 12. | Delta index | DEL | [0,1] | Hoover (1941), Duncan et al. (1961) |

13. | Absolute concentration index | ACO | [0,1] | Massey and Denton (1988) | |

Clustering | 14. | Absolute clustering index | ACL | [0,1] | Massey and Denton (1988) adapted from Geary (1954) and Dacey (1968) |

15. | Mean proximity between members of group X | Pxx | [0,∞] | Massey and Denton (1988) | |

16. | Mean proximity between members of group X (exp d)_{ij} |
Pxx Exp(d_{ij}) |
[0,∞] | Massey and Denton (1988) | |

17. | The distance-decay isolation index | DPxx | [0,1] | Morgan (1983) | |

Centralization | 18. | Proportion in Central City | PCC | [0,1] | Massey and Denton (1988) |

19. | Absolute centralization index | ACE | [-1,1] | Massey and Denton (1988) |

Dimension | Name | Abbreviation | Values | Authors | |

Adapted from Massey and Denton (1988), Apparicio (2000) and Apparicio et al. (2008). |
|||||

Evenness | 20. | Index of dissimilarity | ID | [0,1] | Duncan and Duncan (1955a, 1955b) |

21. | Dssimilarity index adjusted for tract contiguity | Id(adj) | [0,1] | Wong (1993) | |

22. | Dssimilarity index adjusted for contiguous tract boundary lengths | Id(w) | [0,1] | Wong (1993) | |

23. | Dssimilarity index adjusted for contiguous tract boundary lengths and perimeter/area ratio | Id(s) | [0,1] | Wong (1993) | |

24. | Deviational ellipse index | S | [0,1] | Wong (1999) | |

Exposure | 25. | Interaction index | xPy | [0,1] | Bell (1954) |

Concentration | 26. | Relative concentration index | RCO | [-1,1] | Massey and Denton (1988) |

Clustering |
27. | Mean proximity between members of group X and members of group Y | Pxy | [0,∞] | White (1986) |

28. | Mean proximity between members of group X and members of group Y
(exp d)_{ij} |
Pxy Exp(d_{ij}) |
[0,∞] | White (1986) | |

29. | Spatial proximity index | SP | [0,1] | White (1986) | |

30. | Relative clustering index | RCL | [-,∞,∞] | White (1986) | |

31. | The distance-decay isolation index | DPxy | [0,1] | Morgan (1983) | |

Centralization | 32. | Relative centralization index | RCE | [-1,1] | Duncan and Duncan (1955b) |

Dimension | Name | Abbreviation | Values | Authors | |

Adapted from Reardon and Firebaugh (2002) and Apparicio et al. (2008). |
|||||

Evenness | 33. | Multigroup dissimilarity index | D | [0,1] | Morgan (1975), Sakoda (1981) |

34. | Multigroup Gini index | G | [0,1] | Reardon (1998) | |

35. | Information theory index (entropy index) | H | [0,1] | Theil (1972), Theil and Finezza (1971) | |

36. | Squared coefficient of variation | C | [0,1] | Reardon and Firebaugh (2002) | |

37. | Deviational ellipse index | S | [0,1] | Wong (1999) | |

38. | Spatial version of multigroup dissimilarity index | SD | [0,1] | Wong (1999) | |

Exposure | 39. | Normalized exposure | P | [0,1] | James (1986) |

40. | Relative diversity | R | [0,1] | Carlson (1992), Goodman and Kruskal (1954), Reardon (1998) |

Name | Abbreviation | Values | Authors | ||

Adapted from Apparicio et al. (2008). |
|||||

41. | Location Quotient | QL | [0,∞] | Isard (1960) | |

42. | Entropy (diversity) measure | H2 | [0,1] | Theil (1972), Theil and Finezza (1971) | |

43. | Poulsen et al. typology |
Poulsen | [1,6] | Poulsen et al. (2001, 2002) |