CHASM: A configurational measure of socio-spatial residential segregation

Abstract

Despite recent advances in the quantification of residential segregation, several important limitations persist. Zone-based measures have low resolution and treat all locations inside a zone as identical; oversimplify the possibility of interaction between zones; and underestimate the role of the street layout and how it can shape potential movement and exposure. Here, we propose a new measure of socio-spatial residential segregation called CHASM that estimates potential exposure between different social groups based on their positions in the street grid and comparing them to a hypothetical scenario in which all groups are evenly distributed (i.e., a situation of non-segregation). Depending on the type of centrality chosen for the analysis, its scores represent the degree to which the distances of a street segment to the different social groups are unevenly distributed or, alternatively, the degree to which different social groups tend to avoid sharing the same street segments in their trips. We tested CHASM’s validity through a random permutation test in a hypothetical scenario and a comparison with more traditional measures in a medium-sized Brazilian city. The results suggest that CHASM is indeed able to quantify residential segregation and: (a) better estimates distances, connections, and continuities between different areas of the city, including the implications of barriers that are overlooked in zone-based measures; (b) minimizes distortions introduced by zones’ arbitrary shapes; and (c) opens up new possibilities for testing alternative designs for the street system.

Keywords

Socio-spatial segregation residential segregation urban morphology street layout configuration

Introduction

In cities around the world, a variety of spatial strategies have been used to restrict contact between individuals from different social groups. Several negative consequences have been associated with these strategies: lower access to employment, education and health opportunities (Cutler and Glaeser, 1997; Marques, 2007), greater vulnerability to crime (Light and Thomas, 2019; Sampson and Levy, 2020), and perpetuation of poverty (Giddens, 2011; Massey, 1996; Vaughan, 2007), maintaining or accentuating the exclusion of already excluded populations.

Numerous measures were created to study socio-spatial segregation (Feitosa et al., 2023; White, 1983; Yao et al., 2019), and their performance and validity have been the subject of much debate over the decades. Several improvements have been made to capture the nuances of the phenomenon more fully and account more adequately for the role of space in segregation.

However, even these more recent generations of segregation measures still present important limitations. First, they adopt a representation of space based on discrete homogeneous zones, often with a high level of aggregation and low resolution. Second, they oversimplify the possibilities of interaction between zones, usually estimating it by their shape and the length of the common perimeter (Wong, 1993) or by Euclidean distances between centroids (e.g., Feitosa et al., 2007; Wong, 2005). Finally, they underestimate the role of the street grid and how it can shape movement (Knaap and Rey, 2023).

Because of these limitations, over the last few decades several studies have been looking at socio-spatial segregation from a different perspective, acknowledging the role of movement in a more explicit way, arguing that a large part of contacts and interactions with other people happen in activities performed outside the areas captured by zones (Kwan, 2013; Netto et al., 2015; Schnell and Yoav, 2001). One of the first studies in this tradition was carried out by Boal (1969), who found segregated daily movement patterns between Protestants and Catholics in Belfast. Schnell and Yoav (2001) proposed an index of segregation based, among other things, on individuals’ sociability practices and the time spent in such activities. Netto et al. (2015) compared the daily trajectories of individuals from different income groups and how much they overlapped. Maffini and Maraschin (2018) took a similar approach but generalized the trajectories by differentiating the origins by average income at the census tract level and using retail establishments as destinations.

However, approaches based on activity spaces also have their limitations. Data acquisition for individuals is costly and time consuming, which tends to limit sample size. Big data alternatives are increasingly viable (e.g., Netto et al., 2018) to enlarge sample size, but they are limited in describing the very characteristics of social groups upon which segregation emerges, such as race, ethnicity and income.

More recent works that explicitly propose the integration between socio-spatial segregation and configurational analyses also have important limitations, such as relying on visual comparisons or partial measures such as the proportion of high accessibility lines in areas with a predominance of different social groups (Rokem and Vaughan, 2018, 2019). One notable exception is Maffini et al. (2024), who used the residences of different social groups and non-residential establishments as weights for origins and destinations, respectively, in a configurational approach focusing on the overlapping of trajectories at the city scale.

Therefore, we propose a new configurational measure of socio-spatial segregation that takes into account the possibilities of exposure between individuals from different social groups afforded by the street layout configuration. Our model considers the potential of movement from places of residence both from the point of view of closeness and betweenness, comparing it with scenarios of non-segregation, allowing the characterization of the potential for shared destinations and trajectories. We argue that it provides greater resolution and avoids the coarse-grained definition of zones; better estimates distances and trajectories between different portions of the urban system; enables analyses at different scales in a more organic way than combining Euclidean distances between zones’ centroids; allows the combination of closeness and betweenness centralities; and opens up new opportunities for evaluating alternative design proposals not afforded by zone-based analyses.

Theoretical underpinnings

Socio-spatial and residential segregation: definitions

Building on Freeman’s (1978) definition of segregation, socio-spatial segregation is defined here as a process in which exposure (co-presence and face-to-face interaction) between members of different social groups is minimized, hindered or prevented as a result of intentional, spontaneous, or unpredicted spatial conditions. These conditions include—but are not limited to—distancing, separation, avoidances, visual obstruction, material, or symbolic territorial demarcations, and restrictions of access to and by different modes of transportation. Moreover, the term socio-spatial segregation is also used to denote the outcome of this process, that is, a concrete state of the aforementioned factors at a specific time and place.

According to this perspective, residential segregation is a specific form of socio-spatial segregation, in which the restriction of exposure between members of different social groups is achieved mainly through the separation of their places of residence in distinct areas of the city. It also circumscribes the focus of interest to one of the multiple ways through which segregation occurs, namely those conditions that restrict contacts in the public areas around and near the residences, as opposed, for instance, to those in the school, workplace or more central areas. This conception is consolidated in several important definitions in the literature, with one of the most notable being from Massey and Denton (1988: 282), who defined residential segregation as “the degree to which two or more groups live separately from one another, in different parts of the urban environment.” Many other authors adopt a similar definition, albeit often using different expressions such as “urban” (Feitosa et al., 2007), “spatial” (Reardon & O’Sullivan, 2004) or “neighborhood” segregation (Bruch, 2014).

Here, we use “exposure” as a general term that encompasses co-presence and interaction. Co-presence—being present at the same time and at the same place—is the material condition for more meaningful interactions (Netto et al., 2015). Other things being equal, higher co-presence is associated with higher levels of interaction, and thus may be used as a proxy for the latter. However, even when there is no verbal communication or other types of interaction, co-presence is an important component of exposure as it entails communication and exchange of meaningful signs (Goffman, 1963).

Segregation, movement, and the place of residence

Exposure between members of different social groups is intrinsically linked to their movements through space. The ease of accessing specific spaces and the routes they select significantly influence the likelihood of their encounters, either in the destinations of their trips or along the paths they take to get there. The place of residence plays a pivotal role in this regard, acting as a primary node for people’s movements (Watson et al., 2021).

Therefore, the relative location of each space (say, a street segment or a public open space) to the residences of members of different social groups is an important indicator of how likely they are to go to these places. All else being equal, spaces closer to one’s residence are more likely to be selected as destinations for trips originating there, whereas more distant spaces are less probable alternatives by comparison, especially if they walk to access them (Clifton et al., 2016). This, in turn, can be used as an estimator of how likely a space is to be used by members of different social groups, increasing or decreasing the likelihood of co-presence and interaction between them.

Another important aspect of movement patterns is the superposition of routes, that is, betweenness centrality. Spaces situated on the shortest paths between the origins and destinations of individuals from different social groups are more likely to facilitate their co-presence and interaction (Maffini & Maraschin, 2018; Netto et al., 2015, 2018). This is especially true of local scale movement by foot or bicycle that maximizes the exchange of visual and auditory information (Urry, 2002) and, thus, are the more relevant in the context of residential segregation.

There is yet another aspect of residential location that is relevant for its adoption as the point of reference for the proposed measure: the quality of exposure in the vicinity of one’s residence is different from those that happen, for instance, in more central areas or high streets. Co-presence and interactions in the vicinity of the residence suggest a more intimate feeling and are usually accompanied by a sense of repetition and routine that may help develop more long-lasting relationships through time. In contrast, meeting someone from a different social group in a high street does not bring the same sense of friendliness and conviviality, and possesses a much more random nature (although it is undoubtedly an important cultural resource—see Peponis, 1989).

Configurational measure of segregation (CHASM): Operational specification

The overall logic of our proposed measure is to calculate the configurational centralities of different social groups considering their positions in the street layout and compare them to a hypothetical scenario in which all groups are evenly distributed (i.e., a situation of non-segregation) (Figure S1 in the Supplementary Material). Each street segment will end up with a specific combination of centrality for each group in the experimental scenario, and the proportions of these centralities to the non-segregation scenarios are used to obtain a final measure of segregation.

Step 1: Assignment of social groups’ residential locations to street segments

The first step consists in obtaining a fine-grained description of each social group’s residential location at the level of street segments (Figures 1(a) and (b)). To do that, we must previously determine a classification of social groups according to one or more dimensions considered relevant to the analysis, such as income, race, ethnicity, religious affiliation or gender, among others. This classification can result in two or multiple groups and be expressed in absolute or percentual numbers of each social group population.

From these aggregated areas, a specific residential population should be estimated and assigned to each street segment. The best way to do that varies according to the specific characteristics of available data. In its simplest form, this procedure could consider solely the total number of street segments in the tract and distribute the population of each social group equally among them. Ideally, however, at least some proportionality criterion should be used, for instance considering the relative size of each street segment in proportion to the total length of all segments in the area. Even these simplified approaches have advantages over the basic representation by zones, as we discuss in more detail in the Conclusions. However, if more detailed data are available, such as segment or block-based data, they can also be used to better estimate the proportion of each group’s residences to be assigned to each segment.

In parallel to the description of the existing situation, a control scenario must also be created. This scenario represents a hypothetical situation of “non-segregation” in which every street segment has the same proportions of each social group as the study area as a whole. This is important because it will avoid interpretations of lower and higher centrality scores without considering lower and higher quantities of individuals or residences in each social group.

Step 2: Centrality analyses for each social group

The second step consists of the basic configurational analyses for each social group. The centrality analyses can capture two different configurational properties, closeness, and betweenness, as discussed above.

To perform the configurational analysis, we must first choose the definition of distance between street segments, since this will determine how the shortest paths are calculated. Usual definitions of distance in network systems are “metric,” “topological,” and “angular.” Metric distances consider the length of each street segment as a proxy of the cost to traverse it. Topological distances, popularized in the early stages of the Space Syntax tradition, assign a distance of 1 if two street segments (or, more commonly, axial lines) are directly connected. The distance between two spaces that are not directly connected is equivalent to the number of spaces between them plus one. Finally, angular distances consider the angle between segments, assigning higher costs to more acute angles, and approaching zero when the segments are perfectly aligned (Turner, 2007).

Another fundamental parameter is the radius within which the computations of centrality will be carried out. Like the different definitions of distance listed above, the radius may be set using metric, topological or angular measures, or not be defined at all, meaning that the whole system should be considered.

The choice of distance type for both the distance between pairs of segments and the radius of analysis depends on the goals and requirements of the analysis, as well as the theoretical framework informing it. However, Hillier and Iida (2005) found that metric distances between segments performed poorly when correlated with pedestrian (and vehicular) movement compared to topological and angular distances. Therefore, the combination of angular distances for determining shortest paths between pairs of segments and metric distances to limit the radius of analysis is currently considered to be the most appropriate in most cases (Hillier, 2009).

Closeness and betweenness centrality analyses are carried out for each social group separately (Figures 1(c) and (d)). For closeness centrality, the algorithm considers the origins where there are households of a specific social group and calculates the length of the shortest paths to all other segments. Weights are given according to the number of households of the social group at the origin, while destinations are considered as having equal and unitary weight. Therefore, street segments near to more street segments with households of this social group are considered more central; likewise, a street segment that is x units of distance of a street segment with 10 households is considered more central than another that is equally x units of distance from a segment that has only five households.

Betweenness centrality is calculated in a similar way: origins are weighted according to the number of households of a specific social group, and a weight of 1 is uniformly assigned to all destinations. However, for each pair of spaces, these weights are multiplied, and the result is distributed among all street segments that lie on all shortest paths between origin and destination (sometimes there are more than one shortest path). Therefore, higher betweenness centrality values correspond to those street segments that lie on the higher number of shortest paths between street segments with the higher number of households of a specific social group. Figures 1(c) and (d) show the betweenness for groups 0 and 2, respectively.

The same configurational analyses are run for the control scenario.

Step 3: Local configurational percentage (LCP)

We are now able to calculate the Local Configurational Percentage (LCP), given by the proportion of a social group centrality in relation to the sum of centralities of all social groups in the segment

{L C P}_{x j} = \frac{C_{x j}}{\sum_{m = 1}^{n} C_{m j}}

where

■ ${L C P}_{x j}$ = Local Configurational Percentage of social group X at segment j.

■ C_m_j = Centrality (closeness or betweenness) of social group m at segment j.

■ n = Total number of social groups.

Therefore, LCP approaches 0 if the centrality for the group is almost inexistent and approaches 1 if the social group centrality represents a large portion of all groups’ centralities in the segment combined. This index is also calculated for the control (non-segregated) scenario.

Step 4: Local configurational quotient (LCQ)

One shortcoming of the Local Configurational Percentage (LCP) is that it captures the predominance of a groups’ centrality in relation to all groups’ centralities, but it does not take into account the quantities of those groups in the area or in the city as a whole. Therefore, it might be the case that a group’s high LCP in a segment is due to it being more numerous in the city or in the vicinity of the segment, and not because of any configurational property that prevents other groups from accessing that location.

To overcome this limitation, we could divide each group’s LCP by its overall proportion and calculate a local quotient index (Brown and Chung, 2006; Brown et al., 1996; Isard et al., 1960). However, a better approach is to divide each group’s LCP by the same index computed for the control scenario. It can be calculated as follows

{L C Q}_{x j} = \frac{{L C P}_{x j}}{{L C P}_{x j (n s)}}

where

■ ${L C Q}_{x j}$ = Local Configurational Quotient of social group X at locality/segment j.

■ ${L C P}_{x j}$ = Local Configurational Percentage of social group X at locality/segment j.

■ ${L C P}_{x j (n s)}$ = Local Configurational Percentage of social group X at locality/segment j in the control (non-segregation) scenario.

The resulting Local Configurational Quotient (LCQ) captures the difference between the estimated prevalence of a social group in the segment and the expected prevalence of that social group in the same segment in the non-segregation scenario. This solves two problems: first, it avoids distortions caused by different group sizes by normalizing the Local Configurational Percentage (LCP) with the same measure calculated for a group of the same size. Second, it highlights how different the LCP of each group is from what would be expected in a situation of non-segregation. The Local Configurational Quotient (LCQ) is, thus, an important metric in itself, allowing analyses about the isolation and clustering of specific social groups (Figures 1(e) and 1(f)).

Its interpretation is simple: LCQ lower than 1 indicates that the group’s prevalence is below the expected prevalence in the control scenario and, conversely, LCQ values greater than 1 indicate that the prevalence in the experimental scenario is greater than the same social group’s prevalence in the corresponding non-segregated scenario.

Steps 5 and 6: Configurational socio-spatial segregation measure (CHASM)

The final steps combine the different Local Configurational Quotient indexes (LCQ) of each social group in a final aggregated measure of socio-spatial segregation. Any measure that captures the evenness of a set of proportions would work. Here, we follow Netto et al. (2018, p. 2) who calculate “social diversity on the streets” through Shannon (1948) entropy, but we use a normalized version of the entropy equation

E_{j} = (- 1) . \frac{\sum_{x = 1}^{n} p_{x j} . \ln p_{x j}}{\ln n}

where

■ E_j = Entropy for segment/location j.

■ n = Total number of social groups.

■ p_xj = Proportion of the Local Configurational Quotient of group x in segment/location j.

Since the equation deals with percentages, before applying it we must normalize the Local Configurational Quotient in such a way that it reflects its proportion in the segment considering the sum of all such indexes for all other groups, similarly to what Song et al. (2013) did in their weighed entropy measure. The resulting value for each group, called Local Configurational Quotient Percentage (LCQp), then replaces p_xj in the equation above. The formula is

L C {Q p}_{x j} = \frac{L C Q_{x j}}{\sum_{m = 1}^{n} L C Q_{m j}}

where

■ $L C Q p_{x j}$ = Local Configurational Quotient Percentage for group x in segment/location j.

■ $L C Q_{x j}$ = Local Configurational Quotient for group x in segment/location j.

Our configurational measure, CHASM, is the inverse of the evenness between groups and is obtained by

C H A S M = 1 - E_{j}

CHASM’s scores range from 0 to 1. The values approximate 1 when one group’s centrality accounts for a disproportionately large share of the centralities of all groups in the segment. In other words, the segment is disproportionately close to (in the case of closeness centrality) or in the shortest paths of (in the case of betweenness centrality) only one social group. Conversely, its values approach 0 when the centralities of all groups are more evenly distributed, meaning that none of them are too under- or over-represented. In spatial terms, this means that the segment is equally close to or in the shortest paths of all social groups.

Random permutation test

To test the index’s sensitivity to capture socio-spatial segregation, we calculated Moran’s Index of the Local Configurational Quotient for Group 0 (LCQ_0) for 100 random scenarios with the same overall quantities of households in each group as the experimental scenario. We then compared the results to the Moran’s Index of the experimental scenario depicted in Figure 1(e). In the context of this study, higher values mean that there are numerous street segments with high (or low) LCQ that are clustered with other similar segments. The Index thus captures the degree to which segments dominated by single groups are clustered together, that is, segregation.

Figure S2 in the Supplementary Material shows a histogram of Moran’s Indexes calculated for 100 random scenarios considering the LCQ of Group 0. The average value is 0.479 and the maximum value is 0.619. Moran’s Index for the Location Configurational Quotient for Group 0 in the experimental scenario was much higher: 0.971. This shows that this CHASM score is highly unlikely to have happened by chance and suggests that our measure is indeed sensitive to the logic of socio-spatial segregation.

Empirical application and convergent validation: The case of Blumenau, Brazil

We applied our new configurational socio-spatial segregation approach to Blumenau, a medium-sized city located in the state of Santa Catarina, south of Brazil. The social groups of interest were determined by a socioeconomic classification comprising low-, medium- and high-income households using income per capita to classify them in one of the three groups.

We considered as low-income households with per capita income of up to 0.5 minimum wage (MW) per month; and high-income those households with per capita income over 3 MW per month. Medium-income households were those falling between these thresholds. This classification is based on official Brazilian institutional programs and standards such as the Statistic Grid of the Brazilian Institute of Geography and Statistics (Instituto Brasileiro De Geografia e Estatística, 2010). Blumenau’s urban population is around 295,000 inhabitants, distributed in 123,186 households, of which 5.5% are low-income and 21.5% are high-income, according to the above criteria.

We combined two data sources to achieve a more precise characterization of the spatial distribution of these socioeconomic groups throughout the street segments. The first was the number of residences in the three ranges of income per capita at the census tract level, provided by IBGE for the 2010 Census. The second was the “block face,” a spatial unit also provided by IBGE which is roughly equivalent to street segments and shows the total number of residences in each block face, allowing a better approximation of their distribution inside each census tract. We used the first data source to calculate percentages for each group in the census tract, and then distributed the groups following these percentages among the block faces in such a way that each block face had the same proportions of social groups as the census tracts in which their centroid lied. We then assigned the proportional number of residences of each group to the segments that were closest to the block faces. The detailed socioeconomic group’s residential location by segments is shown in Figure S3 in the Supplementary Material.

Centrality measures

For space reasons, we report here only the betweenness centrality results. To calculate it, we used sDNA plugin (Cooper and Chiaradia, 2020) for QGIS that allows the assignment of different weights to both the origins and destinations of pairs of segments. Following Hillier et al.’s (2012) recommendations, we used angular distances to determine the shortest paths and a local metric radius of 1,000 m, roughly equivalent to 15 min of walking. The segment map was derived from OpenStreetMaps, downloaded by QGIS plugin QuickOSM and prepared for analysis by a graphical model developed by the authors following sDNA’s guidelines for network preparation.¹ The spatial unit of analysis, therefore, is the street segment, defined as the set of lines between intersections or between an intersection and a street end.

Figures S4a and S4c in the Supplementary Material show the configurational betweenness centrality mapping for low- (red gradient) and high-income (blue gradient) socioeconomic groups for the experimental scenario. Segments are classified by quantiles in 5 classes. Figures S4(b) and S4(d) show the configurational betweenness centrality for the control (non-segregation) scenario.

We then calculated the Local Configurational Percentage (LCP) of each social group in each street segment. It was then used as input to obtain the Local Configurational Quotient (LCQ) representing the under- and over-representation of the betweenness of each income group in relation to the non-segregation scenario. As we can see in Figure 2, the LCQ is much more able than raw centrality values to capture the unevenness of distributions of exposure potential in urban spaces and the likelihood of spatial clustering of the movement potential of each of the two extreme income groups. A strong contrast between a high-income clustering tendency in more central areas (blue color) and a dispersed and peripheric clustering of the low-income group (red colors) becomes immediately apparent.

Configurational socio-spatial segregation measure (CHASM)

In the final step, we calculated our configurational socio-spatial segregation measure (CHASM) as shown in Figure 3. The highest values (deep purple) indicate higher socio-spatial segregation in street segments, meaning, in this case, that the interplay of street layout and residential location of low-, medium- and high-income groups does not encourage their co-presence in local (1,000m) trips in these segments.

In the next section, we deepen our understanding of the measure and its validity through a comparison with more traditional segregation indices.

Convergent validation: Comparison with traditional residential segregation measures

Convergent validity involves assessing the extent to which a new measure aligns with or diverges from established measures when trying to quantify the same underlying concept or phenomenon (Adcock and Collier, 2001). If the scores of the new measure are too similar to those of the more established one, it is probably not adding much to the existing measure; if, on the other hand, the scores are completely different, it may suggest some problem with the new measure.

Therefore, in this section, we compare our CHASM scores to those of Feitosa et al. (2007), a more traditional zone-based measure of segregation built upon previous work by Sakoda (1981), Bell (1954), and Wong (2005, 1993), among others. The measures put forward by Feitosa et al. (2007) take into account the spatial location of groups by using kernel estimators to ascertain adjacency and proximity within a specified radius based on the centroids of the zones. This, in turn, is used to compose an index called “Local Population Intensity” that considers the proportions of social groups in each zone and of those within the radius, weighing the latter by the inverse of the distance between centroids. From that, they calculate several global and local measures, of which we compare two to our scores:

• Local Spatial Isolation measures the degree to which a specific social group is over-represented in the zone and in the adjacent zones.

• Spatial Dissimilarity Index measures the degree to which the proportion of groups in each zone is different from that of the city as a whole, on average. This was compared to our CHASM measure, since both aim at capturing the evenness dimension of segregation.

For both indices, we used the definition of low- and high-income groups used in the previous section. The scores for Local Spatial Isolation and Spatial Dissimilarity were calculated using the Segreg² plugin for QGIS at the census tract level with a 1,000m radius. They were then attributed to street segments through a spatial join in QGIS, and Spearman correlations were determined for each pair of corresponding measures.

In addition to the convergent validation, we also produced a difference map to visually compare them and gain more qualitative insight into how and why they are different in specific situations.

Evenness indices comparison: CHASM x Dissimilarity

Figure 4(a) shows the scores of the Dissimilarity measure by Feitosa et al. (2007) and Figure 4(b) shows the differences between the two scores at the street segment level.

The Spearman rank correlation between the two scores was 0.265 (p < .01). While it indicates some agreement between the two measures, the degree of association is poor. This suggests that CHASM is indeed capturing aspects that the traditional measure is not. To better understand these differences, we discuss in more detail two contrasting situations marked as “1” and “2” in Figure 4(b).

In situation 1, CHASM scores were two terciles lower than Dissimilarity. To understand why this happened we must first look at the shape of the census tract. In this case, it extends south and, in fact, only a small portion on the north of the tract is occupied by the street network (Figure 5(a)). This results in its centroid being located outside of the portion of the tract that is effectively occupied by the social groups, and close to other centroids in the south and east that have similar high proportions of high-income groups. The centroid-based Euclidian distances employed by this measure result in these tracts being considered within the 1,000m radius. Therefore, the proportions of their social groups are taken into account in the Dissimilarity measure, even if they are completely disconnected by the street layout in this radius. In fact, many of these centroids are on the other side of a major river, with no direct connections. For this reason, we can see in Figure 5(d) that this tract is assigned a high isolation index for the high-income group.

Our LQC (Figure 2(a)) and CHASM (Figure 3) scores, on the other hand, ignore these tracts to the south of situation 1 because they do not fall within the 1,000m threshold through the street network. They do consider, however, the potential of movement of the census tract immediately to the west, which has a high proportion of low-income groups. Therefore, the final CHASM score is much lower, proportionately, than that of the Dissimilarity Index.

Situation 2 illustrates the opposite: a predominantly high-income tract is surrounded by low-income tracts, thus yielding low Dissimilarity scores (Figure 4(a)). However, the configurational analysis shows that this proximity does not, in fact, exist. Most of the street segments in these other tracts are farther than 1,000m considering distances by the network. The “end of line” character of the area is also captured by the configurational approach and contributes to longer distances to the neighboring tracts, along with the disconnections caused by the river. It is worth noting, however, that the bridge that connects to the other side of the river, with low-income groups, has low CHASM, showing that the measure is indeed able to discriminate intra zones differences in the potential for movement-generated co-presence.

Conclusions

This work offered a new measure of socio-spatial segregation that seeks to overcome both the limitations of traditional zone-based measures and the operational difficulties imposed by ad-hoc individual data about trips and activities. To do this, we devised a configurational measure called CHASM which integrates the unevenness of the residential location of different social groups and the exposure potentials afforded by the street network within a specified radius. This opened several analytical possibilities: different scales of analysis in a less arbitrary way than using zones of different sizes, different definitions of distance through the network (metric, topological, and angular) and different algorithms to compute configurational accessibility (closeness and betweenness). These options may be used in combination to paint a more complete picture of the socio-spatial residential segregation under study.

A random permutation test suggested that it was indeed sensitive to capture segregation in the sense that the scores obtained by a hypothetical scenario clearly segregated were very unlikely to have arisen randomly. A second test involved comparing our measure to those put forth by Feitosa et al. (2007) and revealed that CHASM was able to capture more closely the actual distances and possibilities of movement of each social group as afforded by the street network, as expected. Our results suggest that the differences are still higher than those obtained by Knaap and Rey (2023), who also used distances by the street network to calculate segregation, but only between centroids. This is ever more important considering the growing juxtaposition and disconnectedness of different social groups in different parts of the city (Allegra et al., 2012) and the high levels of fragmentation and interpenetration of developed and vacant areas in urban peripheries around the world (Angel et al., 2012).

In addition, our configurational measure brought another benefit: it helped locate the households of social groups in a more correct position within the census tracts. This may be a point of contention, because it involves assigning data from a lower- to a higher-resolution spatial unit. However, a closer look at this procedure in our empirical case suggests that, even in cases where the segments are relatively well distributed inside the zone, assigning residences uniformly (or in proportion to their lengths) among the segments is a more faithful approximation of their distribution, from a probabilistic point of view, than the assumption that all of them are located at the zone’s centroid.

Being largely arbitrary abstractions, however, census tracts often have unusual shapes that do not conform to the area that is in fact occupied by streets and buildings, including environmentally protected areas, water bodies, brownfields and other types of underutilized land. In these cases, the advantages are still greater, since the centroid may fall completely outside of the populated portion and make the already poor estimations of distances to other zones even worse. Figure S3 in the Supplementary Material and accompanying text illustrate this point in more depth.

It also helped capture the effects of natural elements that act as barriers, such as rivers, hills, etc., although indirectly, since the street grid is usually responsive to their influence (for instance, through fewer connections across rivers and other natural barriers, and more deformed grids—and thus larger distances—on higher slopes).

Another contribution of CHASM is that it allows for scenario testing in the case of new subdivisions and even in interventions in consolidated areas. In both cases, alternative designs for the street grid may be tested to determine the one that contributes the most to minimize the effects of residential segregation.

Our measure also offers important advantages over other more closely related measures that rely on a configurational or near configurational approach. For instance, as opposed to the index proposed by Netto et al. (2015), CHASM provides a normalized and easily interpretable score and offers a way to calculate the potential for inter-group exposure for the whole city. It also advances Maffini et al.’s (2024) proposition by comparing the score of each street segment to its counterpart in a situation of non-segregation, instead of dividing all of them uniformly by the size of each group.

However, CHASM also has important limitations. First, it is essentially a measure of residential segregation. As such, it places little or no emphasis on other manifestations of socio-spatial segregation, such as those inside schools, shopping-centers, and other types of buildings, nor inside public spaces such as neighborhood parks. Our measure does, however, help quantify the degree to which collective spaces are in locations that tend to facilitate the co-presence of different social groups in relation to their places of residence.

Another important limitation is that it does not consider the opportunities and costs of movement afforded by other modes of transportation, such as cars, buses, and subways. Rokem and Vaughan (2018) point out that mobility by public transport may be an important factor in minimizing or intensifying the limitations of exposure imposed by residential segregation.

Therefore, other analytical tools could be used in conjunction with CHASM to achieve more complete results. It also can—and should—be used in combination with measures that capture other instances of restriction of contacts between members of different social groups, such as those mentioned above. Being a multi-dimensional and multiscalar phenomenon, socio-spatial segregation requires multiple points of view and frames of reference to measure it, as well as a coherent set of policies and actions of distinct types, scales and underlying mechanisms to overcome it.

Supplemental Material

Supplemental Material - CHASM: A configurational measure of socio-spatial residential segregation

Supplemental Material for CHASM: A configurational measure of socio-spatial residential segregation by Renato Tibiriçá de Saboya and Otavio Martins Peres in Environment and Planning B: Urban Analytics and City Science.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was partially supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); 311470/2022-0.

ORCID iD

Renato Tibirica de Saboya

Data availability statement

The data utilized in this manuscript, along with its documentation, are available at https://doi.org/10.5281/zenodo.10474856.

Supplemental Material

Supplemental material for this article is available online.

Notes

Renato Tibiriçá de Saboya Associate Professor of Architecture and Urbanism at the Federal University of Santa Catarina, Brazil. He received his Professional Degree in Architecture and Urbanism at UFSC (1997), a Master’s Degree in Urban and Regional Planning at UFRGS (2001) and a Doctor’s Degree in Civil Engineering at UFSC (2007). In 2020, he was a visiting researcher at Oxford Brookes University. He was the Director of Graduate Studies in Architecture and Urbanism at UFSC from 2016 to 2018 and is currently a CNPq Research Fellow – grant level 2. His main research areas include urban morphology and configuration, diversity, and segregation.

Otavio Martins Peres Adjunct Professor at the Faculty of Architecture and Urbanism (UFPel). Architect and Urban Planner from the Federal University of Rio Grande do Sul (2007), Specialist in Regional Water Resources Management (UFPel, 2009), Master in Architecture and Urbanism (UFPel, 2010). He studies urban growth processes and their relationships with the natural environment and socio-spatial structure, from a morphology and urban environmental modeling standpoint. He was Pro-Rector of Planning at UFPel between 2017 and 2020. He is currently a doctoral candidate at the Postgraduate Program in Architecture and Urbanism at the Federal University of Santa Catarina-UFSC.

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