Multiscalar Segregation Profiles¶

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Author: eli knaap

Last updated: 2026-09-04

Python implementation: CPython
Python version       : 3.14.7
IPython version      : 9.17.1

segregation: 2.5.6.dev83+g2e095ced1
geopandas  : 1.1.4
libpysal   : 4.15.0

For measuring spatial segregation dynamics, the segregation package provides a function for measuring multiscalar segregation profiles, as introduced by Reardon et al. The multiscalar profile is a tool for measuring spatial segregation dynamics–the way that a segregation index changes values as the concept of a neighborhood changes, and what that tells us about macro versus micro patterns of segregation.

The basic idea is to calculate a segregation statistic, then expand the spatial scope of a neighborhood, recalculate the statistic, and repeat. A multiscalar profile can be computed for any generalized spatial segregation index, which in the case of the segregation package, means a total of 23 indices, including single and multigroup varieties

from segregation.batch import implicit_multi_indices, implicit_single_indices

len(implicit_single_indices) + len(implicit_multi_indices)

Computing a Single Group Profile¶

import geopandas as gpd
import matplotlib.pyplot as plt

from libpysal.examples import load_example
from segregation.singlegroup import Dissim, Gini
from segregation.dynamics import compute_multiscalar_profile

sacramento = gpd.read_file(load_example("Sacramento1").get_path("sacramentot2.shp"))
sacramento = sacramento.to_crs(sacramento.estimate_utm_crs())

sac_gini_profile =  compute_multiscalar_profile(sacramento, segregation_index=Gini, 
                                                group_pop_var="BLACK", total_pop_var="TOT_POP", 
                                                distances= range(500,5500,500))

The function returns a pandas Series whose index is the neighborhood distance threshold, and the value is the segregation statistic.

sac_gini_profile

distance
     0.636176
   0.636060
  0.623794
  0.585519
  0.536802
  0.499355
  0.472811
  0.452414
  0.436664
  0.424351
  0.412981
Name: Gini, dtype: float64

As such, the profile is easy to plot:

sac_gini_profile.plot()

<Axes: xlabel='distance'>

A good way to compare multiscalar profiles is to plot them in the same figure. For example to compare profiles for gini and dissimilarity indices:

sac_dissim_profile = compute_multiscalar_profile(sacramento, segregation_index=Dissim,
                                                group_pop_var="BLACK", total_pop_var="TOT_POP", 
                                                distances= range(500,5500,500))

from libpysal.weights import DistanceBand

fig, ax = plt.subplots(figsize=(8,8))

sac_dissim_profile.plot(ax=ax)
sac_gini_profile.plot(ax=ax)
ax.legend()

<matplotlib.legend.Legend at 0x7f6bcfd95fd0>

The multiscalar profiles for Gini and Dissimilarity indices are very similar, but have slightly different shapes.

Network versus Euclidian Multiscalar Profiles¶

To calculate a multiscalar profile using travel network distance instead of Euclidian distance, simply pass a pandana.Network object to the function

Note: the network-distance workflow below relies on the optional pandarm package and a pre-built network file, so those cells are tagged skip-execution and are not run during automated testing.

import pandana as pdna

net = pdna.Network.from_hdf5("../40900.h5")

net_dissim_profile = compute_multiscalar_profile(sacramento, segregation_index=Dissim,
                                                group_pop_var="BLACK", total_pop_var="TOT_POP", 
                                                network = net,
                                                distances= range(500,5500,500))

fig, ax = plt.subplots(figsize=(8,8))

sac_dissim_profile.name='Dissim'
net_dissim_profile.name='Network Dissim'
sac_dissim_profile.plot(ax=ax)
net_dissim_profile.plot(ax=ax)
ax.legend()

<matplotlib.legend.Legend at 0x1b28f0d60>

In this case, comparing the two profiles reveals the role of travel infrastructure on the experience and measurement of segregation; the network-based dissimilarity profile falls slower, indicating that travel networks help insulate segregation at larger distances

Computing a Multi Group Profile¶

To calculate a multigroup index (e.g. the multigroup information theory index from the original paper), simply pass a MultiGroupIndex class to the function with multigroup arguments instead of singlegroup

from segregation.multigroup import MultiInfoTheory, MultiGini

multi_info_profile = compute_multiscalar_profile(sacramento, segregation_index=MultiInfoTheory, 
                                          groups=["HISP", 'BLACK', "WHITE"], distances=range(500,5000,500))

multi_gini_profile = compute_multiscalar_profile(sacramento, segregation_index=MultiGini, 
                                          groups=["HISP", 'BLACK', "WHITE"], distances=range(500,5000,500))

fig, ax = plt.subplots(figsize=(8,8))

multi_gini_profile.plot(ax=ax)
multi_info_profile.plot(ax=ax)
ax.legend()

<matplotlib.legend.Legend at 0x7f6bcfd9fb60>

Batch-Computing Profiles¶

from segregation.batch import batch_multiscalar_singlegroup, batch_multiscalar_multigroup

single_profs =  batch_multiscalar_singlegroup(sacramento,group_pop_var="BLACK", total_pop_var="TOT_POP", 
                                                distances= range(500,5500,500))

multi_profs = batch_multiscalar_multigroup(sacramento, distances=range(500,5000,500), groups=["HISP", 'BLACK', "WHITE"])

With several profiles to examine at once, it’s helpful to use an interactive plotting library like hvplot

Note: hvplot is an optional dependency used only for interactive plotting; the cells below are tagged skip-execution and are not run during automated testing.

import hvplot.pandas

single_profs.hvplot(width=850, height=450)

multi_profs.hvplot(width=850, height=550)