MethodsMethods References

#  Human interaction networks reveal that large cities facilitate segregation

Hamed Nilforoshan∗,1 Wenli Looi∗,1 Emma Pierson∗,2 Blanca Villanueva3 Nic
Fishman1
Yiling Chen1 John Sholar1 Beth Redbird4,5 David Grusky6 Jure Leskovec†,1
${}^{1}\;$Department of Computer Science, Stanford University, Stanford, CA
94305, USA
${}^{2}\;$Department of Computer Science, Cornell Tech, New York, NY 10044,
USA
${}^{3}\;$Department of Biomedical Data Science, Stanford University,
Stanford, CA 94305, USA
${}^{4}\;$Institute for Policy Research, Northwestern University, Evanston, IL
60208, USA
${}^{5}\;$Department of Sociology, Northwestern University, Evanston, IL
60208, USA
${}^{6}\;$Department of Sociology, Stanford University, Stanford, CA 94305,
USA
${}^{*}\;$These authors contributed equally to this work
${}^{\dagger}\;$Corresponding author. Email<EMAIL_ADDRESS>

###### Abstract

A long-standing expectation is that large, dense, and cosmopolitan areas will
support diverse interactions and socioeconomic mixing[1, 2, 3, 4, 5, 6]. It
has been difficult to assess this hypothesis because past approaches to
measuring socioeconomic mixing have relied on static residential housing data
rather than real-life interactions among people meeting at work, in places of
leisure, and in home neighborhoods[7, 8]. Here we develop a new measure of
interaction segregation (IS) that captures the economic diversity of the set
of people that a given person meets in their everyday life. Leveraging cell
phone mobility data to represent 1.6 billion interactions among 9.6 million
people in the United States, we measure interaction segregation across 382
Metropolitan Statistical Areas (MSAs) and 2829 counties. When averaged across
all MSAs, interaction segregation is 38% lower than a conventional static
estimate, which means that people meet diverse others mostly when outside
their home neighborhoods. But, we also find that interaction segregation is
67% higher in the 10 largest Metropolitan Statistical Areas (MSAs) than in
small MSAs with fewer than 100,000 residents. We find evidence that because
large cities can offer a greater choice of differentiated spaces targeted to
specific socioeconomic groups, they end up promoting—rather than
reducing—everyday economic segregation. We also discover that this
segregation-increasing effect is countered when hubs of interaction (e.g.
shopping malls) are positioned to bridge diverse neighborhoods and thus
attract people of all socioeconomic statuses. Overall, our findings challenge
a long-standing conjecture in human geography and urban design, and highlight
how built environment can both prevent and facilitate diverse human
interactions.

Figure 1: Interaction segregation (IS) captures the likelihood of contact
between people of different economic backgrounds. (a) For 9.6 million
individuals (i.e. cell phones), we infer economic standing (rent or rent
equivalent) from home address, based on location at night. We then leverage
anonymized cell phone mobility data to identify _interactions_ between pairs
of individuals (where two individuals are defined to interact if they were
within 50 meters of each other within less than 5 minutes). (b) The nationwide
network of 1.6 billion interactions spans 2829 counties and 382 Metropolitan
Statistical Areas (MSAs). Our interaction network contrasts with a
conventional measure of economic segregation, the Neighborhood Sorting Index,
which assumes that people interact uniformly and only with other residents of
their home Census tract. Graphs based on a sample community of 50 individuals
from San Francisco, CA residing in 10 different census tracts. Nodes are
individuals; edges are interactions. As this sample illustrates, most
interactions happen when both persons are away from their home tract. These
cross-tract interactions are undetected by conventional segregation measures.
(c) For each geographic region (e.g. MSA, county), we estimate interaction
segregation, defined as the correlation between an individual’s economic
standing (ES) and the mean ES of those with whom they interact. 1 signifies
perfect segregation; 0 signifies no segregation. This definition is equivalent
to the conventional Neighborhood Sorting Index (NSI), but with the key
difference that it leverages real-life interactions from mobility data instead
of synthetic interactions from individuals grouped by Census tracts. For two
MSAs, we show the raw data; each point represents one individual. San
Francisco-Oakland-Hayward, CA is $2.2\times$ more segregated than Napa, CA.
(d) Top: Interaction segregation is 38% lower than the conventional
segregation measure NSI. Each point represents the interaction segregation
estimate in one MSA; vertical colored lines represent median across MSAs.
Bottom: breaking down interaction segregation into component parts.
Interactions where both people are within their home Census tract (green) are
over $2.5\times$ more segregated than interactions where at least one person
is outside their home Census tract (orange and red), reflecting the _homophily
effect_ in which people preferentially interact with those of similar ES in
their home tracts. Out-of-tract interactions (orange and red) are less
segregated, reflecting the _visitor effect_ in which visiting other tracts
exposes individuals to economically diverse individuals. Because a small
minority (2.4%) of interactions happen within home tract, the visitor effect
dominates the homophily effect and thus interaction segregation is lower than
conventional NSI. (e) Interaction segregation varies by location type. Each
point represents segregation in one MSA using only interactions occurring in a
given location type; boxes indicate the interquartile range across MSAs.
Segregation is highest at golf courses and country clubs, and lowest at
performing arts centers and stadiums.  Figure 2: Highly-populated metropolitan
areas are more segregated due to socioeconomic differentiation of spaces.
Contrary to the hypothesis that highly-populated metropolitan areas support
diverse interactions and socioeconomic mixing, we find that (a) Larger MSAs
are more segregated. Interaction segregation presented as a function of
population size; each dot represents one MSA; purple line indicates LOWESS
fit. Upward trend reveals that urbanization is associated with higher
interaction segregation (Spearman Correlation 0.62, N=382, p$<10^{-10}$). The
top 10 largest MSAs, by population size, are 67% more segregated than small
MSAs with less than 100,000 residents. Associations are robust to controlling
for potential confounders and are similar for population density and IS
(Extended Data Table 1, Supplementary Table S7). (b) Interaction segregation
across the 2829 US counties. Analysis limited to counties with at least 50
individuals. Interaction segregation varies significantly across counties in
the United States. Moreover, as with MSA-level, county-level interaction
segregation is also positively associated with both population size and
population density (Extended Data Figure 3). (c-e) A case study of full-
service restaurants illustrates the mechanism through which urbanization
produces interaction segregation. Highly-populated metropolitan areas are more
segregated not only because they offer a wider choice of venues but also
because these venues are more socioeconomically differentiated (e.g. in New
York City, one can spend $10, $100, or $1000 on a meal, depending on the
choice of restaurant[9, 10]). (c) Larger MSAs have more restaurants within 10
kilometers of the average resident, giving residents more options to self-
segregate. (d) Moreover, restaurants in larger MSAs vary more in the median ES
of their visitors, offering a greater choice of socioeconomically
differentiated restaurants. The coefficient of variation across restaurant ES
in 10 largest MSAs is 63% more than the coefficient of variation in small MSAs
(with fewer than 100,000 residents). (e) Consequently, interaction segregation
within restaurants is higher in larger MSAs. These relationships are also
detectable at the scale of interaction hubs (i.e. higher-level clusters of
POIs such as plazas and shopping malls) as well as at the neighborhood level
(Extended Data Figures 4-5).  Figure 3: Interaction segregation is lower when
interaction hubs bridge socioeconomically-diverse neighborhoods. (a) We
develop a Bridging Index (BI) that quantifies the extent to which interaction
hubs bridge socioeconomically diverse neighborhoods. The metric is constructed
by clustering homes by nearest interaction hub, then measuring the within-
cluster diversity of ES (Methods M3). Two plots illustrate that BI is distinct
from a conventional residential measure of segregation (i.e. Neighborhood
Sorting Index). BI ranges from 0.0 (no bridging; top) to 1.0 (perfect
bridging; bottom) while residential segregation is constant (high and low-ES
individuals are highly segregated by census tract, denoted by purple and
yellow bounding boxes). We compute BI with hubs of interaction defined as
commercial centers (e.g. shopping malls, plazas) because the majority (56.9%)
of interactions across all 382 MSAs occur in close proximity (within 1km) of a
commercial center, even though only 2.5% of land area is within 1km of a
commercial center. (b) BI strongly predicts interaction segregation (Spearman
Correlation $-0.78$, N=382, p$<10^{-10}$). The top 10 MSAs with the highest BI
are 53.1% less segregated than the 10 MSAs with lowest BI. Bridging Index
predicts segregation more accurately than population size, ES inequality, NSI,
and racial demographics, and is significantly associated with interaction
segregation after controlling for these variables and other potential
confounders (Extended Data Tables 2-3). (c-d) A case study of Fayetteville,
NC, an MSA with low interaction segregation (21st percentile) despite having
above-median population size (64th percentile) and income inequality (60th
percentile). (c) Interaction heat map of Fayetteville; all visually
discernible hubs are associated with one or more commercial centers. (d)
Interaction hubs are located in accessible proximity to both high and low ES
census tracts, leading to diverse interactions. An illustrative example of one
hub (Highland Center) in Fayetteville and a random sample of 10 interactions
occurring inside of it. Home icons demarcate individual home location (up to
100m of random noise added for anonymity); colors denote individual and mean
tract ES.

## Introduction

In the U.S., economic segregation is very high, with income affecting where
one lives[11], who one marries[12], and who one meets and befriends[13]. This
extreme segregation is costly: it reduces economic mobility[14, 15, 16, 17],
fosters a wide range of health problems[18, 19], and increases political
polarization[20]. Although there are all manner of reforms designed to reduce
economic segregation (e.g. subsidized housing), it has long been argued that
one of the most powerful segregation-reducing dynamics is rising
urbanization[21] and the happenstance mixing that it induces[1, 2, 3, 4, 5,
6].

As plausible as this “cosmopolitan mixing hypothesis” might seem, big cities
also provide new opportunities for self-segregation, given that they’re large
enough to allow people to seek out and find others like themselves[22]. These
contrasting hypotheses about the effects of urbanization on interaction remain
untested because it has been difficult to measure real-world interaction among
individuals. In most cases, analysts have treated residential housing
segregation as a proxy for the diversity of interaction[7, 23, 24, 25], an
approach that rests on the implausible assumption that people interact
uniformly with those in their neighborhood and do not interact with anyone
outside their neighborhood.

To understand how urbanization affects segregation, we instead need a measure
that captures where people go, when they go there, and with whom they come
into contact. We introduce a measure of interaction segretation (IS) by
leveraging anonymized cell phone geolocation data to construct a fine-grained,
dynamic network that captures 1.6 billion physical interactions (i.e. path-
crossings) between 9.6 million people in the United States. These data are
used to define a measure of _interaction segregation_ (IS) that extends a
traditional static segregation measure by capturing actual interactions in a
given geographic area. In recent years, cell phone networks have been used for
many research purposes[26, 27, 28, 29, 30, 31, 32, 33, 34], but a nationwide
study of economic mobility and urbanization has not been undertaken because of
difficulties in ascertaining individual-level economic status, determining
when dyadic interactions occur, and amassing the data needed to compare across
cities or counties[26, 27, 28, 30, 31, 32, 33, 34]. We undertake the first
credible test of the “cosmopolitan mixing hypothesis” and the mechanisms
underlying it by using cell phone data to link geolocated interactions with
individual-level economic status in 382 MSAs and 2829 counties.

## Results

We estimate _interaction segregation_ (IS), defined as the extent of contact
between individuals of different economic statuses, for each geographic area
in the U.S. (e.g. MSA, county). This entails building a dynamic _interaction
network_ with 9,567,559 nodes (representing individuals) and 1,570,782,460
edges (representing interactions/path-crossings in the physical space).

##### Developing a more realistic measure of socioeconomic segregation.

To estimate each person’s economic standing (ES), we first infer their night-
time home location from cell phone mobility data, and we then recover the
estimated monthly rent value of the home at this location (Methods M2). This
method is more accurate than the convention of proxying individual ES with
neighborhood-level Census averages[28, 29]. The economic segregation of each
geographic region is measured by the correlation between a person’s ES and the
mean ES of everyone with whom they interact. This correlation is estimated by
fitting a linear mixed effects model that eliminates attenuation bias (Methods
M3). The resulting measure of interaction segregation (Figure 1a-c), which
ranges from 0 (perfect integration) to 1 (complete segregation), is a
generalization of a widely used measure of socioeconomic segregation, the
Neighborhood Sorting Index (NSI)[7]. The NSI is equivalent to the correlation
between each person’s ES and the mean ES of all people in their Census tract,
whereas the IS is equivalent to the correlation between each person’s ES and
the mean ES of all people with whom they have interacted, either inside or
outside their census tract. Like the NSI, the IS measures cross-class contact
of any type, rather than ties that are persistent and possibly stronger (such
as friendship ties)[13].

##### Interaction segregation is lower than previously estimated.

We find that the median interaction segregation across all MSAs is 38% lower
than a conventional static estimate (NSI; Figure 1d top). To understand why,
we examine how segregation differs by interaction location (Figure 1d bottom).
We find that interactions that occur when both people are within their home
Census tract are 41% more segregated than under the hypothetical that
residents interact uniformly with all people in the same tract (as the NSI
assumes). This result illustrates the _homophily effect_ : even within their
own neighborhood, people interact with neighbors who are socioeconomically
most similar to them. By contrast, interactions where at least one person is
outside their home tract are far less segregated, meaning that people interact
with more heterogeneous populations when they visit non-home tracts for work,
leisure, or other activities. We refer to this phenomenon as the _visitor
effect_. Because these out-of-home-tract interactions are more frequent than
within-home-tract interactions (i.e. less than 2.5% of interactions are within
the same home tract), the visitor effect dominates the homophily effect and
interaction segregation is lower than conventional static measures imply.

##### Interaction segregation varies across leisure sites.

We validate and explore the IS metric by measuring variability in interaction
segregation across different points of interest (POIs). We do so by filtering
for interactions that occur within a single POI category and re-applying our
same mixed model (Methods M3; Figure 1e). The resulting estimates show, for
instance, that golf courses and country clubs have over 2$\times$ higher
interaction segregation than performing arts centers (in the median MSA). We
find that the degree to which POIs service small and socioeconomically
homogeneous communities explains much of this variability in POI-level
segregation (Extended Data Figure 2). The POIs that are numerous, embedded
locally within residential communities, and thereby serve economically
differentiated communities (e.g. churches) tend to be more segregated than
larger POIs that are designed to serve the entire city (e.g. stadiums). In
rare cases (i.e. golf courses), a POI with few venues may still be highly
segregated because cross-venue economic differentiation is generated through
other mechanisms, such as a public-private distinction.

##### Large cities facilitate segregation.

We discover that interaction segregation is higher in large MSAs (Figure 2),
which directly undermines the “cosmopolitan mixing hypothesis”. The Spearman
correlation between MSA population and MSA segregation is 0.62, and the 10
largest MSAs by population size are 67% more segregated than small MSAs with
less than 100,000 residents. This result is robust: we validate it by
recalculating the correlation with a measure of density rather than population
size (Spearman Correlation 0.45), by controlling for relevant covariates
(Extended Data Table 1 and Supplementary Table S7), by varying the granularity
of the analysis (Figure 2b, Extended Data Figure 3), and by testing a variety
of specifications of interaction segregation (Supplementary Table S6,
Supplementary Figures S2-S8). The consistent result that larger, denser cities
are more segregated runs counter to the hypothesis that such cities facilitate
diverse social interactions by attracting liberal cosmopolitans and by
constraining space in ways that oblige diverse individuals to come into
contact with each other[1, 2, 3, 4, 5, 6]. Our results support the opposite
hypothesis: big cities allow their inhabitants to seek out people who are more
like themselves.

##### Mechanisms producing higher interaction segregation in larger
metropolitan areas.

To understand why large metropolitan areas support these homophilous
tendencies, it is useful to explore interaction segregation within leisure
POIs. Full-service restaurants provide an illustrative example (Figure 2c,d,e)
of a segregation-inducing dynamic that holds widely across other leisure sites
(Figure S21). We find that larger MSAs offer their residents a greater number
of leisure choices: the average resident of one of the 10 largest MSAs has
150$\times$ more restaurants within 10 kilometers of their home than an
average resident of a small MSA (where a ”small MSA” is defined as one with
less than 100,000 residents; Figure 2c). These choices are also more
socioeconomically differentiated. When a restaurant’s ES is defined as the
median ES of all people who cross paths within it, the coefficient of
variation of “restaurant ES” in the 10 largest MSAs is 63% larger than that in
small ones (Figure 2d). Thus, large MSAs not only offer their residents a
larger choice of restaurants, but these restaurants are also more
socioeconomically differentiated. These processes combine to increase
interaction segregation by 29% at restaurants in the 10 largest MSAs relative
to those in small MSAs (Figure 2e). We also find analogous results at higher
levels of scale: interaction hubs (e.g. plazas, malls, shopping centers,
boardwalks) (Extended Data Figure 4) as well as neighborhoods (Extended Data
Figure 5) and across different many POI types (Supplementary Figure S21).

##### Mitigating segregation via urban design.

Our results so far suggest that segregation could be mitigated via urban
design by placing POIs of high interaction to act as bridges between diverse
neighborhoods, which would allow residents of nearby high-ES and low-ES
neighborhoods to easily visit and interact (Figure 3c)[35, 36, 37]. We develop
the _Bridging Index_ (BI; Methods M3) to assess whether interaction hubs (i.e.
highly-visited POIs) are located in such bridging positions. This index, which
measures the economic diversity of the groups that would interact if everybody
visited only their nearest hub, is computed by clustering individuals by the
nearest hub to their home and then measuring the economic diversity within
these clusters (Extended Data Figure 6). The resulting index ranges from 0 to
1, where 0 means that individuals near each hub have uniform ES, and 1 means
that individuals near each hub are as diverse as the overall area (Extended
Data Figure 7). We compute BI for commercial centers (e.g. plazas, malls,
shopping centers, boardwalks) because we find that they are common hubs of
interaction (see Figure 3c). The results show that BI is strongly associated
with interaction segregation (Spearman Correlation -0.78; see Figure 3d). The
top 10 MSAs with the highest BI are 53.1% less segregated than the 10 MSAs
with the lowest BI. This finding is again robust: the effect of BI is strong
and significant even after including controls for race, population size,
economic inequality, and many other variables (Extended Data Tables 2 and 3;
see also Supplementary Table S6; Supplementary Figures S2 and S8;
Supplementary Figure S11). It follows that policies that encourage developers
to locate hubs such as commercial centers between diverse residential
neighborhoods (e.g. zoning laws or subsidies) may reduce interaction
segregation. We have identified several large cities that increase integration
in this way (Supplementary Table S8) and present an illustrative example
(Figure 3c-d) in which well-placed interaction hubs bridge diverse individuals
in Fayetteville, North Carolina.

## Discussion

As big cities continue to grow and spread, it is important to ask whether they
are increasing socioeconomic mixing. Although it is often argued that big
cities promote mixing by increasing density, in fact we find that interaction
diversity and city size are negatively related. We find that the key mechanism
here is scale. Because large cities can sustain venues that are targeted to
thin socioeconomic slices of the population, they have become homophily-
generating machines that are more segregated than small cities. We also find
that some cities are able to mitigate this segregative effect because their
interaction hubs are located in bridging zones that can draw in people from
diverse neighborhoods. We were able to detect these pockets of homophily (and
the counteracting effects of bridging hubs) because we have developed a
dynamic measure of economic segregation that captures everyday interactions at
home, work, and leisure.

This new methodology for measuring interaction segregation, while an important
improvement over conventional static approaches, has limitations. We use close
physical proximity as a proxy for interaction. It is reassuring, however, that
our core results persist under stricter time, distance, and tie-strength
thresholds (Extended Data Figure 1(d)). It is likewise important to locate and
analyze supplementary datasets that cover subpopulations (e.g., homeless
subpopulations) that aren’t as well represented in our dataset[38]. The
available evidence indicates that our sample is representative on many key
racial, economic, and demographic variables[39], but cellphone market
penetration is still not complete. Lastly, our measure of economic standing
relies on housing consumption, an indicator that does not exhaust the concept
of economic status. It is again reassuring that our analytic approach, which
improves on conventional neighborhood-level imputations, is robust under a
range of alternative measures of economic standing (Supplementary Figure S3).

Our work advances the usual static approach to measuring economic segregation
to using large-scale mobility data and develops a dynamic notion of
quantifying segregation and diversity of mixing between people. The dynamic
approach that we have taken here could further be extended to examine cross-
population differences in the sources of segregation and to develop a more
complete toolkit of approaches to reducing segregation and improving urban
design.

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## Methods

In Methods M1, we explain the datasets used in our analysis; in Methods M2, we
explain data processing procedures we leverage to infer economic standing and
interactions; and in Methods M3, we explain the analysis underlying our main
results.

###  M1 Datasets

#### SafeGraph

Our primary mobility and location data comprise GPS locations from a sample of
adult smartphone users in the United States, provided by the company
SafeGraph. The data are anonymous GPS location pings from smartphone
applications which are collected and transmitted to SafeGraph by participating
userssafegraph. While the sample is not random sample, prior work has
demonstrated that SafeGraph data is geographically representative (e.g. an
approximately unbiased sample of different census tracts within each State),
and well-balanced along the dimensions of race, income, and
educationsquire2019, chang2021mobility. Furthermore, SafeGraph data is a
widely used standard in large-scale studies of human mobility across many
different areas including COVID-19 modelingchang2021mobility, political
polarizationchen2018effect, and tracking consumer
preferencesathey2018estimating. All data provided by SafeGraph was anonymized,
does not contain any identifying information, and was stored on a secure
server behind a firewall. Data handling and analysis was conducted in
accordance with SafeGraph policies and in accordance with the guidelines of
the Stanford University Institutional Review Board.

The raw data consists of 91,755,502 users and 61,730,645,084 pings (one
latitude and longitude for one user at one timestamp) from three evenly spaced
months in 2017: March, July, and November. The mean number of raw pings
associated with a user is 667 and the median number of pings is 12. We apply
several filters to improve the reliability of the SafeGraph data, and
subsequently link each user to an estimated rent (i.e. Zillow Zestimate) using
their inferred home location (i.e. CoreLogic address), as described in Methods
M2.

We apply several filters to improve the reliability of the SafeGraph data. To
ensure locations are reliable, we remove pings whose location is estimated
with accuracy worse than 100 meters as recommended by
SafeGraphsafegraph_visit. We filter out users with fewer than 500 pings, as
these are largely noise. Since we incorporate a user’s home value and rent in
measuring their economic standing, we filter out users for whom we are unable
to infer a home. Finally, to avoid duplicate users, we remove users if more
than 80% of their pings have identical latitudes, longitudes, and timestamps
to those of another user; this could potentially occur if, for example, a
single person in the real world carries multiple mobile devices. After the
initial filters on ping counts and reliability, we are able to infer home
locations for 12,805,490 users in the United States (50 states and Washington
D.C.), leveraging the CoreLogic database. Of users for whom we can infer a
home location, we are able to successfully link 9,576,650 to an estimated rent
value via the Zillow API. Section Methods M2 provides full details on the use
of CoreLogic database to infer home locations and the use of the Zillow API to
link these home locations to estimated rent values. Finally, after removing
users where $>80$% of their pings are duplicates with another user, we reduce
the number of users from 9,576,650 to 9,567,559 (i.e., we remove about 0.1% of
users through de-duplication).

#### CoreLogic

We use the CoreLogic real estate database to link users to home
locationscorelogic. The database provides information covering over 99% of US
residential properties (145 million properties), over 99% of commercial real
estate properties (26 million properties), and 100% of US county, municipal,
and special tax districts (3141 counties). The CoreLogic real estate database
includes the latitude and longitude of each home, in addition to its full
address: street name, number, county, state, and zip code.

#### Zillow

We use the Zillow property database to query for rent estimateszillow (our
primary measure of economic standing). The Zillow database contains rent data
(”rent Zestimate”) for 119 million US residential properties. We were able to
determine a rent Zestimate, the primary measure of economic standing (ES) used
in our analysis, for 9,576,650 out of 12,183,523 inferred SafeGraph user homes
(a 79% hit rate).

#### SafeGraph Places

Our database of US business establishment boundaries and annotations comes
from the SafeGraph Places databasesafegraph, which indexes the names,
addresses, categories, latitudes, longitudes, and geographical boundary
polygons of 5.5 million US points of interest (POIs) in the United States.
SafeGraph includes the NAICS (North American Industry Classification System)
category of each POI, which is standard taxonomy used by the Federal
government to classify business establishmentskelton2008using. For instance,
the NAICS code 722511 indicates full service restaurants. We identify relevant
leisure sites using the prefixes 7, which includes arts, entertainment,
recreation, accommodation, and food services, and supplement these POIs with
the prefix 8131 to include religious organizations such as churches. We
restrict our analysis of leisure sites to the top most frequently visited POI
categories within these NAICS code prefixes (Figure 1d): full service
restaurants, snack bars, limited-service restaurants, stadiums, etc. SafeGraph
Places also includes higher-level “parent” POI polygons which encapsulate
smaller POIs. Specifically, we identified interaction hubs with the NAICS code
531120 (lessors of non-residential real estate) which we find in practice
corresponds to commercial centers such as shopping malls, plazas, boardwalks,
and other clusters of businesses. We provide illustrative examples of such
interaction hubs in Supplementary Figures S14-S16.

#### US Census

We extract demographic and geographic features from the 5-year 2013-2017
American Community Survey (ACS)censusreporter. This allows us, as described
below, to link cell phone locations to geographic areas including census block
group, census tract, and Metropolitan Statistical Area (MSA), as well as to
infer demographic features corresponding to those demographic areas including
median household income.

A census block group (CBG) is a statistical division of a census tract. CBGs
are generally defined to contain between 600 and 3,000 people. A CBG can be
identified on the national level by the unique combination of state, county,
tract, and block group codes.

A census tract is a statistical subdivision of a county containing an average
of roughly 4,000 inhabitants. Census tracts range in population from 1,200 to
8,000 inhabitants. Each tract is identified by a unique numeric code within a
county. A tract can be identified on the national level by the unique
combination of state, county, and tract codes.

Census tracts and block groups typically cover a contiguous geographic area,
though this is not a constraint on the shape of the tract or block group.
Census tract and block group boundaries generally persist over time so that
temporal and geographical analysis is possible across multiple censuses.

Most census tracts and CBGs are delineated by inhabitants who participate in
the Census Bureau’s Participant Statistical Areas Program. The Census Bureau
determines the boundaries of the remaining tracts and block groups when
delineation by inhabitants, local governments, or regional organizations is
not possible census_glossary.

A Metropolitan Statistical Area (MSA) is a US geographic area defined by the
Office of Management and Budget (OMB) and is one of two types of Core Based
Statistical Area (CBSA). A CBSA comprises a county or counties associated with
a core urbanized area with a population of at least 10,000 inhabitants and
adjacent counties with a high degree of social and economic integration with
the core area. Social and economic integration is measured through commuting
ties between the adjacent counties and the core. A Micropolitan Statistical
Area is a CBSA whose core has a population of between 10,000 and 50,000; a
Metropolitan Statistical Area is a CBSA whose core has a population of over
50,000. In our primary analysis, we follow Athey et alathey and focus on
Metropolitan Statistical Areas, excluding Micropolitan Statistical Areas due
to data sparsity concerns.

#### TIGER

Road and transportation feature annotations come from the Census-curated
Topologically Integrated Geographic Encoding and Referencing system (TIGER)
databasetiger. The TIGER databases are an extract of selected geographic and
cartographic information from the U.S. Census Bureau’s Master Address File /
Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER)
Database (MTDB). We use the MAF/TIGER Feature Class Code (MTFCC) from the
TIGER Roads and TIGER Rails databases to identify road and railways. TIGER
data is in the format of Shapefiles, which provide the exact boundaries of
roads and railways as latitude/longitude coordinates.

###  M2 Data processing

For each individual, we first infer their home location and subsequently
estimate economic standing based on their home rent value (see _Inferring home
location_ and subsequently _Inferring economic standing_). We then calculate
all interactions between individuals (see _Constructing interaction network_),
which we then annotate based on the location, i.e. if the interaction occurred
in both, one, or neither individual’s home tract, and whether it occurred
inside of a fine-grained POI such as a specific restaurant or a “parent” POI
such as an interaction hub (see _Annotating interactions_). Details on all
inferences and interaction calculations are provided below.

#### Inferring home location

We first infer a user’s home latitude and longitude using the latitude and
longitude coordinates of their pings during local nighttime hours, based on
best practices established by SafeGraph[safegraph_pattern]. We first remove
users with fewer than 500 pings to ensure that we have enough data to reliably
infer home locations. We then interpolate each person’s location at each hour
(eg, 6 PM, 7 PM, and 8 PM) using linear interpolation of latitudes and
longitudes, to ensure we have timeseries at constant time resolution. We
filter for hours between 6 PM and 9 AM where the person moves less than 50
meters until the next hour; these stationary nighttime observations represent
cases when the person is more likely to be at home. We filter for users who
have stationary nighttime observations on at least 3 nights and with at least
60% of observations within a 50 meter radius. Finally, we infer home latitude
and longitude as the median latitude and longitude of these nighttime home
locations (after removing outliers outside the 50 meter radius). We choose the
thresholds above because they yield a good compromise between inferring the
home location of most users and inferring home locations with high confidence.
Overall, we are able to infer home locations for 70% of users with more than
500 pings, and these locations are inferred with high confidence; 89% of
stationary nighttime observations are within 50 meters of the inferred home
latitude and longitude.

#### Inferring economic standing from home latitude and longitude

Having inferred home location from nighttime GPS pings, we link their latitude
and longitude to a large-scale housing database (Zillow) to infer the
estimated rent of each user’s home, which we use as a measure of economic
standing. We do this in two steps. First, we link the inferred user’s home
latitude and longitude to the CoreLogic property database (Methods M1), a
comprehensive database of properties in the United States, by taking the
closest CoreLogic residential property (single family residence, condominium,
duplex, or apartment) to the user’s inferred home latitude and longitude.
Second, we use the CoreLogic address to query the Zillow database, which
provides estimated home rent and price for each user. (The Zillow database
does not allow for queries using raw latitude and longitude, which it is
necessary to leverage to CoreLogic to obtain an address for each user.) We use
Zillow’s estimated rent for the user’s home as our main measure of economic
standing. We apply several quality control filters to ensure that the final
set of users we use in our main analyses have reliably inferred home locations
and economic standings: 1) we remove a small number of users whose inferred
nighttime home latitude and longitude are identical to another user’s, since
we empirically observe that these people have unusual ping patterns; 2) we
remove users for whom we are lacking an Zillow rent estimate, since this
constitutes our primary economic standing measure; 3) we winsorize Zillow rent
estimates which are greater than $20,000 to avoid spurious results from a
small number of outliers; 4) we remove a small number of users who are missing
Census demographic information for their inferred home location; 5) we remove
users whose Zillow home location is further than 100 meters from their
CoreLogic home location, or whose CoreLogic home location is further than 100
meters from their nighttime latitude and longitude; 6) we remove a small
number of users in single family residences who are mapped to the exact same
single family residence as more than 10 other people, since this may indicate
a data error in the Zillow database.

The set of users who pass these filters constitute our final analysis set of
9,567,559 users. We confirm that the Census demographic statistics of these
users’ inferred home locations are similar to those of the US population in
terms of income, age, sex, and race, suggesting that our inference procedure
yields a demographically representative sample.

Any individual quantitative measure provides only a partial picture of a
person’s economic standing. Recognizing this, we conduct robustness checks in
which rather than using the Zillow estimated rent of the user’s home as a
proxy for economic standing, we use 1) the median Census Block Group household
income in that area; and 2) the percentile-scored rent of the home, to account
for long-tailed rent distributions. Our main results are robust to using these
alternate measures of economic standing (Supplementary Figure S3).

#### Constructing interaction network

We construct a fine-grained, dynamic interaction network $\mathcal{G}$ between
all 9,567,559 individuals across 382 MSAs and 2829 counties, which is
represented as an undirected graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$
with time-varying edges. Each node $v_{i}\in\mathcal{V}$ in the graph
represents one of the $N=9,567,559$ individuals in our study, such that the
set of nodes is $V=\\{v_{1},v_{2},...,v_{N}\\}$. Each node $v_{i}$ has a
single attribute $x_{i}$, representing the inferred economic standing
(estimated rent) of the individual.

Individuals $v_{i}$ and $v_{j}$ are connected by one edge
$e_{i,j,k}\in\mathcal{E}$ per interaction, with $k$ indicating the $k$th
interaction between individuals $v_{i}$ and $v_{j}$. Each edge $e_{i,j,k}$ has
three attributes $t_{i,j,k}$, $lat_{i,j,k}$, $lon_{i,j,k}$ indicating the
timestamp, latitude, and longitude of the interaction respectively. We now
focus our discussion on explaining how each of the interactions edges of the
network is calculated.

We define an _interaction_ to occur when two users have GPS pings which are
close (according to a fixed threshold) in both physical proximity and time.
Specifically if user $v_{i}$ has a GPS ping with $t_{i},lat_{i},lon_{i}$
(indicating the timestamp, latitude, and longitude of the ping respectively),
and user $v_{j}$ has a GPS ping with $t_{j},lat_{j},lon_{j}$, then we users
are said to have shared an interaction if $|t_{i}-t_{j}|<T$ and
$distance((lat_{i},lat_{i}),(lat_{j},lat_{j}))<D$, where $T$ represents the
time threshold (i.e. maximum time distance the two pings can be apart to count
as an interaction) and $D$ represents the distance threshold (i.e. maximum
physical distance the two pings can be apart to count as an interaction). We
filter for both distance and time simultaneously to ensure that our
interaction network only includes pairs of users who are likely to have come
into contact with each other. This contrasts to other methods which consider
all individuals to visit the same location, irrespective of
timemoro2021mobility, to have an equal likelihood of interaction, an
assumption which may prove unrealistic in many cities (e.g. demographics of
individuals visiting public parks varies starkly by time of
daymadge1997public). We use a threshold $T$ of 5 minutes, which is a stringent
threshold on time as the mean number of pings per person per hour during day
time is approximately one ping; we use a distance threshold $D$ of 50 meters,
following prior work which shows that even exposure to individuals from afar
is linked to long term outcomesbrown2021childhood. Our network is validated by
correlation to external, gold-standard datasets (Extended Data Figure 1(d)).
Furthermore, we show through a series of robustness checks that our key
results in Figure 1, Figure 2, and Figure 3 are highly robust to varying
thresholds (i.e. 1 minute or 2 minutes time threshold, as well as 10 meters or
25 meters distance threshold), as well as additional criteria to increase tie
strength (i.e. requiring multiple consecutive interactions, or multiple
interactions on unique days)—and under all observed circumstances the main
findings remain consistent (see Supplementary Table S6, Supplementary Figures
S2-S8).

To efficiently calculate the interactions between all users, we implement our
interaction threshold as a k-d treebentley1975multidimensional, a data
structure which allows one to efficiently identify all pairs of points within
a given distance of each other. In total, we identify 1,570,782,460
interactions. The timestamp $t_{i,j,k}$ of the interaction is the minimum ping
timestamp in the pair of individuals’ ping timestamps ($t_{i}$,$t_{j}$), and
the location $lat_{i,j,k}$, $lon_{i,j,k}$ of the interaction is the average
latitude and longitude of pair of pings belonging to the two individuals
($lat_{i}$,$lat_{j}$) and ($lon_{i}$,$lon_{j}$).

#### Annotating interactions

Interactions are annotated to indicate whether they occurred at or near
features of interest: e.g., near a user’s home. Annotations are not mutually
exclusive in that an interaction may be simultaneously tagged as having
occurred near multiple features from multiple data sources. We describe the
specific annotations below.

We annotate a user’s interaction as having occurred in their home if it occurs
within 50 meters of the user’s home location. An interaction is annotated with
a TIGER road/railway if it occurs within 20 meters from that feature. An
interaction is annotated as having occurred within a SafeGraph Places point-
of-interest (POI) if the interaction occurs within the polygon defined for the
POI. Polygons are provided by the SafeGraph Places database for both fine-
grained POIs (e.g. individual restaurants) as well as “parent” POIs (e.g.
interaction hubs). We focus our analysis of fine-grained POIs (Figure 1e,
Extended Data Figure 2) on the most visited fine-grained POIs: full-service
restaurants, snack bars, limited-ervice restaurants (e.g. fast food),
stadiums, etc (see Figure 1e for full list). These categories roughly align
with those used by prior work athey.

###  M3 Analysis

#### Interaction Segregation

We define the interaction segregation (IS) of a specified geographical area
(i.e. Metropolitan Statistical Area, County) as the Pearson correlation
between the economic standing (ES) of individuals residing in that
geographical area, and the mean ES those that they come into contact with.

$\displaystyle Interaction\>Segregation$
$\displaystyle=Corr(ES,\overline{ES}_{interactions})$

Our metric captures the extent to which an individual’s ES predicts the ES of
their immediate interaction network. Thus, in a perfectly integrated area in
which individuals interact randomly with others regardless of ES, interaction
segregation would equal 0.0. In a perfectly segregated area in which
individuals interact with only those of the exact same ES, interaction
segregation would equal 1.0.

Interaction segregation nests a classic definition residential segregation,
the Neighborhood Sorting Indexjargowsky1996take, jargowsky2005measure (NSI),
which is equivalent to the Pearson correlation across between each person’s ES
and the mean ES in their Census tract. The NSI is widely used because it can
be calculated directly from Census data on the ES of people living in each
tract. However, a fundamental limitation of NSI as a measure segregation is
that the Census tract in which people live is a weak proxy for who they
interact with. Census tracts are static and artificial boundaries which fail
to capture interactions as individuals move throughout the cityscape during
work, leisure time, and schooling.

We design our interaction segregation (IS) metric such that it accommodates
any interaction network, and thus NSI is a special case of our metric.
Specifically, if interaction segregation is computed for a synthetic
interaction network under the unrealistic assumptions that a) people only
interact with those in their home Census tract and b) they do so uniformly at
random—then it is equivalent to NSI (Supplementary Figure S17). However,
constructing such a synthetic interaction network from Census tracts has
limited applicability to measuring segregation in the real world, because
people may also interact with more heterogeneous populations as they visit
other Census tracts for work, leisure, or other activities, a phenomenon we
refer to as the _visitor effect_. Furthermore, even within home tract,
individuals may interact non-uniformly as they seek out people of similar
economic standing; we refer to this as the _homophily effect_. Thus, we
instead leverage dynamic mobility data from cell phones to captures the extent
of contact between diverse individuals throughout the day, and apply our
metric, interaction segregation (IS), to this real-world interaction network.
An advantage of interaction segregation is that it allows for direct
comparability to NSI, because both measures are of the same underlying
statistical quantity, but differ in their definition of the interaction
network. Our results indicate that this choice of interaction network matters;
IS is a stronger predictor of upward economic mobility (Extended Data Figure
1(d)) as the two metrics are shown to be distinct (Supplementary Figure S18).

To calculate the interaction segregation of a specified geographical area
(i.e. Metropolitan Statistical Area, County), we first select the set of all
individuals who reside in area: $\mathcal{V}_{A}\subset\mathcal{V}$. For
instance, to calculate Interaction Segregation for Napa, California (Figure 1c
Top), $\mathcal{V}_{A}$ is the 3707 individuals with home locations inside the
geographical boundary of the Napa, CA MSA. Subsequently, for each individual
resident of the area $v_{i}\in\mathcal{V}_{A}$ we query the population
interaction network ($\mathcal{G}=(\mathcal{V},\mathcal{E})$) for the ES of
the set of individuals they interact with, $\mathcal{Y}_{i}$:
$\\{x_{j}\in\mathcal{V}|e_{i,j,k}\in\mathcal{E}\\}$. We then aim to estimate
the Pearson correlation between the ES of each individual $x_{i}$ and the mean
ES of those they interact with, $y_{i}=mean(\mathcal{Y}_{i})$.

#### Mixed model

We use a linear mixed effects model to accurately estimate interaction
segregation: the Pearson correlation coefficient between a person’s ES and the
mean ES of the people they interact with. A statistical model is required to
estimate interaction segregation because naively computing the correlation
based on limited data (in counties or MSAs with low population sizes) results
in estimates that are downward biased. 111By “naive” estimation of the Pearson
correlation, we intend to convey calculating the correlation using the sample:
$\displaystyle\frac{{}\sum_{i=1}^{n}(x_{i}-\overline{x})(y_{i}-\overline{y})}{\sqrt{\sum_{i=1}^{n}(x_{i}-\overline{x})^{2}(y_{i}-\overline{y})^{2}}}$
By contrast, our linear mixed effects model is an unbiased estimator of the
Pearson correlation. We compare the unbiased estimates from our linear mixed
effects model to naive estimates of interaction segregation in Methods Figure
2. To illustrate why naive estimates of interaction segregation are downward
biased, imagine that we compute the correlation between a person’s ES and the
“true” mean ES of the people they interact with. Now, we add noise to the mean
ES values, which represents the noisy mean estimates given limited data. As
the noise is increased, the correlation is decreased. Thus, because estimates
of each person’s mean ES will be more noisy in geographical areas with less
data, there will be a downward bias to naive estimates of the Pearson
correlation in these areas.

Figure 2: Mixed model estimate compared with naive estimates of the Pearson
correlation. We took people who interacted with at least 500 other people and
computed the Pearson correlation coefficient (the “gold standard estimate”).
Then, for each person we randomly sampled 5, 10, 50, 100, and 200 people from
the 500+ people and computed segregation estimates based on the reduced sets
of people. The left plot shows the ratio of the estimates to the gold
standard, for each MSA. The right plot shows the overall number of people in
the dataset with $\leq N$ interactions.

Our mixed model models the distribution of datapoints ($x_{i}$, $y_{ij})$
through the following equation:

$\displaystyle y_{ij}$
$\displaystyle=ax_{i}+b+\epsilon_{i}^{(1)}+\epsilon_{ij}^{(2)}$
$\displaystyle\text{where }x_{i}$ $\displaystyle=\text{ES of person $i$}$
$\displaystyle y_{ij}$ $\displaystyle=\text{ES of person $j$ who has
interacted with person $i$}$ $\displaystyle a,b$ $\displaystyle=\text{model
parameters}$ $\displaystyle\epsilon_{i}^{(1)}$ $\displaystyle=\text{person-
specific noise term}$ $\displaystyle\epsilon_{ij}^{(2)}$
$\displaystyle=\text{noise for each data point}$

The Pearson correlation coefficient between person $i$’s ES and the mean ES of
the people they interact with is then computed as follows. We assume that
$x_{i}$ has a variance of $1$ through data preprocessing and that $x_{i}$ is
uncorrelated with $\epsilon_{i}^{(1)}$.

$\displaystyle\mathrm{corr}\left(x_{i},ax_{i}+b+\epsilon_{i}^{(1)}\right)$
$\displaystyle=\mathrm{corr}\left(x_{i},ax_{i}+\epsilon_{i}^{(1)}\right)$
$\displaystyle=\frac{\mathrm{cov}\left(x_{i},ax_{i}+\epsilon_{i}^{(1)}\right)}{\sqrt{\mathrm{Var}\left(x_{i}\right)Var\left(ax_{i}+\epsilon_{i}^{(1)}\right)}}$
$\displaystyle=\frac{\mathrm{cov}\left(x_{i},ax_{i}\right)}{\sqrt{\mathrm{Var}\left(ax_{i}+\epsilon_{i}^{(1)}\right)}}$
$\displaystyle=\frac{a}{\sqrt{a^{2}+\mathrm{Var}\left(\epsilon_{i}^{(1)}\right)}}$

We estimate $a$ and $\mathrm{Var}\left(\epsilon_{i}^{(1)}\right)$ by fitting
the mixed model using the R lme4 package, optimizing the restricted maximum
likelihood (REML) objective.

#### Decomposing segregation by time

Each interaction edge ($e_{i,j,k}$) in our interaction network is timestamped
with a time of interaction $t_{i,j,k}$. This allows us to decompose our
overall interaction segregation into fine-grained estimates of segregation
during different hours of the day, by filtering for interactions that occurred
within a specific hour. In Supplementary Figures S19, we partition estimates
of segregation by 3 hour windows to illustrate how segregation varies
throughout the day (see Supplementary Information).

#### Decomposing segregation by activity

Each interaction edge ($e_{i,j,k}$) in our interaction network occurs at a
specific location $lat_{i,j,k}$, $lon_{i,j,k}$. Thus, it is possible to
annotate interactions by the fine-grained POI (e.g. specific restaurant) they
occurred in, as well as the by the higher-level “parent” POI (e.g. commercial
center) in which the POI was located (Methods M2). This allows us to decompose
our overall interaction segregation into fine-grained estimates of segregation
by specific leisure activity. We do so by filtering the network for all
interactions that occurred in a specific POI category, and re-calculating
interaction segregation for the MSA or county, using only those interactions.
In Figure 1e, we show the variation in interaction segregation by leisure
site, and further explain these variations in Extended Data Figure 2.

#### Bridging Index

We seek to identify a modifiable, extrinsic aspect of a city’s built
environment which may reduce interaction segregation. One promising candidate
is the location of a city’s hubs of interaction. We define a new measure, the
_Bridging Index_ (BI), which measures the extent to which a particular set of
interaction hubs (i.e. high-interaction POIs, $\mathcal{P}$) facilitate the
integration of individuals of diverse economic standing within a geographic
area (i.e. MSA or county). Specifically, BI measures the economic diversity of
the groups that would interact if everybody visited only their nearest hub
from $\mathcal{P}$—based on the observation that physical proximity
significantly influences which hubs individuals visit[35, 36, 37].

We compute the Bridging Index (BI) via two steps (Extended Data Figure 6).

  1. 1.

Cluster all individuals who live in an area (i.e. MSA or county residents,
$\mathcal{V}_{A}$) into $K$ clusters
($\mathcal{C}_{1},\mathcal{C}_{2},...,\mathcal{C}_{K}$) according to the
interaction hub from $\mathcal{P}$ closest to their home location. $K$ is the
number of hubs in $\mathcal{P}$.

  2. 2.

Bridging Index is computed as the weighted average of the economic diversity
(i.e. Gini Index) of these clusters of people, relative to the area’s overall
economic diversity.

$\displaystyle Bridging\>Index\>(BI)$
$\displaystyle=\frac{Within\>Hub\>Economic\>Diversity}{Overall\>Economic\>Diversity}$
$\displaystyle=\frac{\sum_{i=1}^{K}|\mathcal{C}_{i}|\cdot
Gini\>Index(\mathcal{C}_{i})}{|\mathcal{V}_{A}|\cdot
Gini\>Index(\mathcal{V}_{A})}$

We illustrate the intuition for BI and how it captures the relationship
between home and hub locations in Extended Data Figure 7. A BI of 1.0
indicates that if everybody visits their nearest interaction hub, each person
will be exposed to a set of people _as economically diverse as the overall
city they reside in_. Thus, a BI of 1.0 signifies perfect bridging, i.e. even
if individuals live in segregated neighborhoods, hubs are located such that
individuals must leave their neighborhoods and interact with diverse others.
On the other hand, a BI of 0.0 signifies the opposite extreme; a city with a
BI of 0.0 is one in which, if everybody visits the nearest interaction hub,
each person will be exposed to only people of the exact same economic
standing.

The economic diversity of each cluster $\mathcal{C}_{i}$ is quantified using
the Gini Index: $Gini\>Index(\mathcal{C}_{i})$, a well-established measure of
economic statistical dispersion (Extended Data Figure 6c)dorfman1979formula,
although results are robust to choice of economic diversity measure such as
using variance instead of Gini Index (Supplementary Figure S12). The
denominator of BI normalizes for the baseline economic diversity observed in
the city, allowing for direct comparisons between cities.

In our primary analysis, we identify hubs of interaction via commercial
centers (e.g. shopping malls, plazas, etc. which are higher-level clusters of
individual POIs) because they are associated with a high density of
interactions. Specifically, the majority (56.9%) of interactions happen inside
of or within 1km of a commercial center (e.g. shopping mall, plaza, etc.) even
though only 2.5% of the land area of MSAs is within 1km of a commercial
center. We thus compute BI using the set $\mathcal{P}$ of all commercial
centers within each MSA. We discover that BI strongly predicts interaction
segregation (Spearman Correlation $-0.78$, Figure 3d). The top 10 MSAs with
the highest BI are 53.1% less segregated than the 10 MSAs with the lowest BI.
BI predicts segregation more accurately than population size, racial
demographics ES inequality, NSI, and racial demographics, and is significantly
associated with segregation $({p}{<}{10^{-8}})$ after controlling for all
aforementioned variables (Extended Data Tables 2-3).

naturemag main

## Extended Data

(a)

(b)

(c)

(d)

Figure 1: This studies’ interaction network predicts population-scale
friendship formation and upward economic mobility outcomes. We measure the
external validity of our definition of interaction, by linking our interaction
network to outcomes across two gold-standard, large-scale, datasets. We find
at the zip code, county, and MSA-level, our interaction network mirrors
population-scale outcomes resulting from dynamic human processes: (a-b) the
Facebook Social Connectedness Index[bailey2018social] measures the relative
probability of a Facebook friendship link between a given Facebook user in
location $i$ and a given user in location $j$. FB Social Connectedness Index
has been used social segregation[bailey2020social], and has also been linked
to economic[bailey2021international, kuchler2020social] and public health
outcomes[kuchler2021jue]. We reproduce the Social Connectness Index using our
interaction network
($\frac{\\#InteractionPairs_{i,j}}{\\#Individuals_{i}\cdot\\#Individuals_{j}}$)
at the county (a) and zip code (b) level, and find strong correlations across
county pairs (Spearman Correlation 0.85, $N=121,595$, $p<10^{-10}$) and zip
code pairs (Spearman Correlation 0.73, $N=1,053,539$, $p<10^{-10}$). (c-d) The
Chetty et al. Intergenerational Mobility dataset quantifies upward economic
mobility from federal income tax records for each MSA as the mean income rank
of children with parents in the bottom half of the income distribution
[chetty2014land]. We find that interaction segregation at the MSA-level (c)
correlates to upward economic mobility (Spearman Correlation -0.37, $N=379$,
$p<10^{-10}$), and does so significantly more strongly ($p<0.0001$, Fisher’s
z-test) than (d) the conventional segregation measure NSI (Spearman
Correlation -0.12, $N=379$, $p<0.05$)

.

Figure 2: Understanding why interaction segregation varies significantly across leisure sites. We identify three primary facets of socioeconomic differentiation between POIs which explain the heterogeneous segregation levels of different leisure POIS (Figure 1e): (a) localization, (b) quantity, and (c) stratification. (a) Localization strongly predicts segregation across all POI categories (Spearman Correlation -0.77, N=17, p$<$0.01). POIs which are more locally embedded into neighborhoods (e.g. religious organizations) are more segregated than activities in which POIs are serve multiple neighborhoods (e.g. stadiums). We operationalize localization as the average distance from each indvidual in the MSA to the nearest POI of that category. (a) The quantity of POIs also explains segregation (Spearman Correlation 0.64, N=17, p$<$0.01). Leisure activities with more options (e.g. restaurants) have differentiated venues catering to a specific economic standing (e.g. Michelin-star restaurants) compared to POIs which are small in number and cater to the overall city (e.g. stadiums) (c) Golf courses and country clubs (golf clubs) are an anomaly in that they have a small number of unlocalized POIs, but are highly segregated. We conduct a case study in which look at top and bottom golf clubs by mean visitor ES in 5 of the 10 largest MSAs. We find that the high segregation of golf clubs is due to extreme stratification between venues; for instance the minimum cost to play at the high-ES golf course in Miami, FL is 11717$\times$ higher than at the lowest-ES golf course. By contrast, the average cost of a MacDonalds Big Mac ($5.65[bigmac]) is only 63$\times$ higher than the average cost of a Michelin 3-star restaurant ($357[michelin]). Finally, these findings foreshadow Bridging Index (BI), which captures POI localization, quantity, and stratification (Extended Data Figure 7). Figure 3: Large, dense counties are more segregated. We compute interaction segregation across 2829 USA counties (94% of the counties in the USA), excluding counties in which there are less than 50 individuals in our dataset. We find that at the county-level, interaction segregation is also positively correlated with population size (Spearman Correlation 0.45, N=2829, p$<10^{-10}$) and population density (Spearman Correlation 0.45, N=2829, p$<10^{-10}$). These correlations reveal that the association between large, dense cities and interaction segregation (Figure 2a) is likely an artifact of city boundaries, and may in fact be an emergent property from dynamics of individuals residing highly populated, dense geographic areas, which persists across multiple scales of granularity. |  Dependent variable: Interaction Segregation
---|---
| (1) | (2) | (3) | (4) | (5) | (6)
Intercept |  0.355∗∗∗ |  0.355∗∗∗ |  0.355∗∗∗ |  0.355∗∗∗ |  0.355∗∗∗ |  0.355∗∗∗
| (0.004) | (0.004) | (0.003) | (0.003) | (0.003) | (0.003)
Log(Population Size) |  0.059∗∗∗ |  |  0.041∗∗∗ |  0.044∗∗∗ |  0.026∗∗∗ |  0.028∗∗∗
| (0.004) |  | (0.004) | (0.004) | (0.004) | (0.004)
Gini Index (Estimated Rent) |  |  0.064∗∗∗ |  0.050∗∗∗ |  0.051∗∗∗ |  0.045∗∗∗ |  0.047∗∗∗
|  | (0.004) | (0.004) | (0.004) | (0.003) | (0.003)
Political Alignment (% Democrat in 2016 Election) |  |  |  | 0.004 |  | 0.004
|  |  |  | (0.004) |  | (0.004)
Racial Demographics (% non-Hispanic White) |  |  |  | 0.001 |  |  0.006∗
|  |  |  | (0.004) |  | (0.003)
Mean ES (Estimated Rent) |  |  |  |  -0.012∗∗∗ |  | -0.005
|  |  |  | (0.004) |  | (0.004)
Walkability (Walkscore) |  |  |  |  | 0.002 | 0.001
|  |  |  |  | (0.003) | (0.003)
Commutability (% Commute to Work) |  |  |  |  |  -0.011∗∗∗ |  -0.010∗∗∗
|  |  |  |  | (0.003) | (0.004)
Conventional Segregation (NSI) |  |  |  |  |  0.042∗∗∗ |  0.041∗∗∗
|  |  |  |  | (0.003) | (0.003)
Observations | 382 | 382 | 382 | 376 | 382 | 376
$R^{2}$ | 0.350 | 0.419 | 0.567 | 0.578 | 0.704 | 0.705
Adjusted $R^{2}$ | 0.348 | 0.417 | 0.565 | 0.573 | 0.701 | 0.698
|  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table 1: Population size is significantly associated with interaction segregation, after controlling for MSA income inequality (Gini Index), political alignment (% Democrat in 2016 election), racial demographics (% non-Hispanic White), mean ES, walkability (Walkscore[walkscore]), commutability (% of residents commuting to work), and residential segregation (NSI). Here we show the coefficients (after normalizing via z-scoring to have mean 0 and variance 1) from the primary specifications estimating the effect of population size on interaction segregation across all MSAs. Columns (1-5) are models specified with different subsets of covariates; Column 6 shows model specification with all covariates. Differences between sample size in models is due to missing data for several covariates in a small number of MSAs (Walkscores were not available for all MSAs). (*p $<$ 0.1; **p $<$ 0.05; *** p $<$ 0.01). |  Dependent variable: Interaction Segregation
---|---
| (1) | (2) | (3) | (4) | (5)
Intercept |  0.355∗∗∗ |  0.355∗∗∗ |  0.355∗∗∗ |  0.355∗∗∗ |  0.355∗∗∗
| (0.003) | (0.003) | (0.003) | (0.003) | (0.003)
Bridging Index |  -0.078∗∗∗ |  -0.059∗∗∗ |  -0.058∗∗∗ |  -0.035∗∗∗ |  -0.036∗∗∗
| (0.003) | (0.005) | (0.005) | (0.006) | (0.006)
Log(Population Size) |  | 0.003 |  0.008∗ |  0.010∗∗ |  0.017∗∗∗
|  | (0.004) | (0.005) | (0.004) | (0.006)
Gini Index (Estimated Rent) |  |  0.031∗∗∗ |  0.032∗∗∗ |  0.035∗∗∗ |  0.036∗∗∗
|  | (0.003) | (0.003) | (0.003) | (0.003)
Political Alignment (% Democrat in 2016 Election) |  |  | 0.001 |  | 0.002
|  |  | (0.004) |  | (0.004)
Racial Demographics (% non-Hispanic White) |  |  | 0.003 |  | 0.005
|  |  | (0.003) |  | (0.003)
Mean ES (Estimated Rent) |  |  |  -0.009∗∗ |  | -0.005
|  |  | (0.004) |  | (0.003)
Walkability (Walkscore) |  |  |  | 0.002 | 0.001
|  |  |  | (0.003) | (0.003)
Commutability (% Commute to Work) |  |  |  |  -0.011∗∗∗ |  -0.009∗∗
|  |  |  | (0.003) | (0.004)
Conventional Segregation (NSI) |  |  |  |  0.028∗∗∗ |  0.026∗∗∗
|  |  |  | (0.004) | (0.004)
# of Interaction Hubs |  |  |  |  | -0.006
|  |  |  |  | (0.005)
Observations | 382 | 382 | 376 | 382 | 376
$R^{2}$ | 0.620 | 0.686 | 0.693 | 0.733 | 0.736
Adjusted $R^{2}$ | 0.619 | 0.684 | 0.688 | 0.729 | 0.729
|  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table 2: Bridging Index (BI) is significantly associated with interaction
segregation, after controlling for population size, # of hubs, MSA income
inequality (Gini Index), political alignment (% Democrat in 2016 election),
racial demographics (% non-Hispanic White), mean ES, walkability
(Walkscore[walkscore]), commutability (% of residents commuting to work), and
residential segregation (NSI). Here we show the coefficients (after
normalizing via z-scoring to have mean 0 and variance 1) from the primary
specifications estimating the effect of population size on interaction
segregation across all MSAs. Columns (1-4) are models specified with different
subsets of covariates; Column 5 shows model specification with all covariates.
Differences between sample size in models is due to missing data for several
covariates in a small number of MSAs (Walkscores were not available for all
MSAs). (*p $<$ 0.1; **p $<$ 0.05; *** p $<$ 0.01).

Measure |  Spearman $\rho^{2}$ |  Pearson $R^{2}$
---|---|---
Bridging Index | 0.60 | 0.62
Log(Population Size) | 0.39 | 0.35
Gini Index (Estimated Rent) | 0.41 | 0.42
Political Alignment (% Democrat in 2016 Election) | 0.06 | 0.05
Racial Demographics (% non-Hispanic White) | 0.09 | 0.05
Mean ES (Estimated Rent) | 0.09 | 0.05
Walkability (Walkscore) | 0.01 | 0.02
Commutability (% Commute to Work) | 0.04 | 0.03
Conventional Segregation (NSI) | 0.44 | 0.42
# of Interaction Hubs | 0.44 | 0.16

Table 3: Bridging Index (BI) strongly predicts interaction segregation and
does so more accurately than population size, # of hubs, MSA income inequality
(Gini Index), political alignment (% Democrat in 2016 election), racial
demographics (% non-Hispanic White), mean ES, walkability
(Walkscore[walkscore]), commutability (% of residents commuting to work), and
residential segregation (NSI)

.

Figure 4: At higher levels of scale, spaces in large cities are more
differentiated and consequently segregated: interaction hubs. (a-c) Conducting
an analogous analysis to that for restaurants in Figure 3c-e for interaction
hubs (i.e. commercial centers which are higher-level clusters of restaurants,
grocery stores, etc.). We find that higher segregation is driven by an
increase in highly differentiated choice of interaction hubs in large cities:
(a) Larger MSAs have more interaction hubs, giving residents more options to
self-segregate (Spearman Correlation 0.81, N=382, p$<10^{-10}$). (b)
Consequently, hubs in larger MSAs vary more in terms of the mean ES of their
visitors (Spearman Correlation 0.58, N=382, p$<10^{-10}$) and as a result, (c)
interaction segregation within hubs is higher in larger MSAs (Spearman
Correlation 0.64, N=382, p$<10^{-10}$). Overall, this analysis suggests that
across multiple levels of scale, large cities offer a greater choice of
differentiated spaces targeted to specific socioeconomic groups, promoting
everyday segregation in interactions.

(a)

(b)

(c)

(d)

Figure 5: At higher levels of scale, spaces in large cities are more
differentiated and consequently segregated: home neighborhoods. (a-c)
Conducting an analogous analysis to that for restaurants in Figure 3c-e, we
find that higher segregation is driven by an increase in highly differentiated
choice of neighborhoods in large cities: (a) Larger MSAs have more census
tracts, giving residents more options to self-segregate (Spearman Correlation
0.97, N=382, p$<10^{-10}$). (b) Consequently, census tracts in larger MSAs
vary more in terms of the mean ES of their residents (Spearman Correlation
0.58, N=382, p$<10^{-10}$) and as a result, (c) both conventional NSI and
interaction segregation are higher (Spearman Correlations 0.52 and 0.35,
N=382, p$<10^{-10}$ and p$<10^{-5}$). However, (c) also shows that interaction
segregation (green series) rises more slowly with population than conventional
segregation (blue series), suggesting that within-home-tract homophily, which
increases interaction segregation but not conventional segregation, is _not_
more pronounced in large MSAs. Substantiating this, (d) shows that when home
tract interaction segregation is computed using an alternate ES measure so it
captures only within-home-tract-homophily, it is no higher in large MSAs
(Spearman Correlation -0.01, N=382, p$>0.1$). (The alternative ES measure is
computed by subtracting the mean ES in each Census tract; see Methods.)
Overall, this analysis suggests that the higher home tract segregation in
large MSAs is driven by people’s greater choice of neighborhoods of varying ES
in which to live, but not by a greater tendency to interact homophilously
within their own neighborhood. Figure 6: Computing Bridging Index (BI).
Illustration of our analytical pipeline for calculating BI. (a) BI is computed
from the locations and number of POIs in the MSA which are expected to be hubs
of interaction, as well the locations and economic standing values of all
homes within MSA boundaries. We intentionally develop BI without using
mobility data, with the intention of identifying a modifiable extrinsic aspect
of an MSA that can be intervened on to _impact_ mobility patterns and decrease
interaction segregation (b) In order, we (1) cluster all homes by nearest
interaction hub (using straight line distance from home to hub), partitioning
all homes into $K$ clusters, where $K$ is the number of hubs in the MSA (2)
compute the weighted average economic diversity (i.e. Gini Index) of the
clusters, normalized by the overall economic diversity of the MSA to allow for
comparisons between different MSAs of varying baseline levels of economic
diversity (Extended Data Table 1) (c) The graphical definition of Gini Index
is provided, which is a standard measure of economic
dispersion[dorfman1979formula]. Results are robust to the definition of
economic diversity, and holds true when using variance in ES instead of Gini
Index (Supplementary Figure S12). Figure 7: Understanding the determinants of
BI. The Bridging Index (BI) is a single metric which captures three important
factors of built environment (see Supplementary Figure S11 for contributions
of these factors to explaining interaction segregation):
(1) The locations of interaction hubs — If hubs are located in between diverse
neighborhoods, BI will be high as hubs will bridge together diverse
individuals.
(2) The # of interaction hubs — as # of hubs decreases, BI increases (e.g if
there is only 1 hub in a city, BI will be 1.0 as all individuals are unified
by a single hub)
(3) Residential segregation, i.e. the locations of homes and their associated
economic standing — as residential segregation decreases we can expect that
individuals residing near each hub will be more diverse.
This figure builds intuition for BI by showing how BI may vary for a single
simulated city, consisting of highly segregated neighborhoods. We hold
residential segregation (3) constant, and vary the location (1) and number (2)
of interaction hubs across panels (a), (b), (c), (d), in order of increasing
BI. Note that BI in (c) is substantially higher than BI in (b), because hubs
in (c) are better positioned to bridge diverse neighborhoods—even though the
number of hubs remains constant. Figure 8: Montgomery, AL. We conduct an
analogous analysis to Figure 3a,b but for Montgomery, AL, which has nearly
identical population (374K vs 385K residents) and income inequality (55th vs
60th percentile Gini Index) to Fayetteville, NC but is 74% more segregated
(88th percentile vs. 21st percentile interaction segregation). We find that
the difference in segregation is explained by Montgomery, AL having a
significantly higher BI compared to Fayetteville, NC (65th vs. 13th
percentile). In Montgomery, AL interaction hubs (i.e. commercial centers) are
differentiated by ES which results in high-ES individuals and low-ES
individuals visiting separate hubs and prevents them from engaging in cross-ES
interactions. (a) shows that, as with all MSAs, commercial centers (e.g.
shopping malls, plazas, etc.) are hubs of interaction. We illustrate that in
Montgomery, AL all visually discernible hubs are associated with one or more
commercial centers. (b) In Montgomery, AL, interaction hubs are located in
different locations which cater separate to high and low ES residents, leading
to segregated interactions. As an illustrative example, we show a zoomed-in
map of one hub (Chantilly Center) in Montgomery, AL, and display a random
sample of 10 interactions occurring inside of it. Chantilly Center in
Montgomery, AL is located accessibly for high ES individuals but is far apart
from low-ES tracts. As a result, the sample shows that the majority of
interactions are middle-upper ES, and only a few low-ES individuals visit
Chantilly Center and interact with these high-ES individuals. Home icons
demarcate individual home location (up to 100 meters of random noise added to
preserve anonymity); home colors denote individual ES; arcs indicate an
interaction inside of the hub; background colors indicate mean census tract
ES.

## Supplementary Information

|  | Accurate pings
---
| Unique days
---
| Distinct user pairs
---
interact
| Interactions
---
| Accurate pings
---
| Distinct user pairs
---
who interact
| Interactions
---
count | 8,609,406 | 8,609,406 | 8,527,115 | 8,527,115 | 382 | 382 | 382
mean | 3,273 | 35 | 184 | 363 | 73,757,695 | 2,577,322 | 4,845,144
std | 16,507 | 20 | 374 | 1,073 | 163,848,305 | 8,872,464 | 16,838,938
min | 11 | 2 | 1 | 1 | 2,196,084 | 27,326 | 53,350
10% | 570 | 13 | 8 | 17 | 8,398,875 | 140,251 | 313,803
50% | 1,471 | 30 | 76 | 141 | 22,054,930 | 504,525 | 1,031,691
90% | 5,857 | 63 | 436 | 785 | 175,295,175 | 4,573,152 | 8,954,800
max | 4,755,081 | 95 | 42,323 | 193,193 | 1,605,070,032 | 94,140,015 | 215,183,409
Table S1: Combined descriptive statistics for all individuals residing in 382
Metropolitan Statistical Areas (MSAs). 8,609,406 individuals reside in a
Metropolitan Statistical Area (90% of the overall 9,567,559 individuals in our
study). The remaining 958,153 users live outside of MSAs, influencing the
interaction segregation of an MSA by coming into contact with MSA residents.
Descriptive statistics are grouped by individual (left) and MSA (right). At
least one of two users in each interaction pair must live in an MSA to be
included in this table. Figure S1: Descriptive statistics of path crossings.
(a) Ten Metropolitan Statistical Areas (MSAs) with the highest and lowest
median users crossed per user.
(b) Overall distribution of median users crossed per user over MSAs. display_name | # POIs (25%) | # POIs (50%) | # POIs (75%) | # POIs (max) | # POIs (mean) | # POIs (min) | # POIs (std)
---|---|---|---|---|---|---|---
Full-Service Restaurants | 75.5 | 160.0 | 424.0 | 24,689.0 | 609.8 | 12.0 | 1,820.05
Snack Bars | 18.0 | 40.0 | 110.0 | 6,266.0 | 169.76 | 1.0 | 511.17
Limited-Service Restaurants | 33.0 | 60.0 | 145.5 | 4,847.0 | 192.14 | 5.0 | 434.78
Stadiums | 1.0 | 2.0 | 4.0 | 43.0 | 3.67 | 1.0 | 4.32
Performing Arts Centers | 1.0 | 2.0 | 4.0 | 28.0 | 3.25 | 1.0 | 3.41
Fitness/Recreation Centers | 10.0 | 25.0 | 72.0 | 4,877.0 | 126.6 | 1.0 | 414.26
Historical Sites | 1.0 | 2.0 | 7.0 | 206.0 | 9.16 | 1.0 | 21.65
Theme Parks | 1.0 | 3.0 | 6.0 | 158.0 | 7.64 | 1.0 | 16.77
Bars/Drinking Places | 2.0 | 5.0 | 13.0 | 447.0 | 19.52 | 1.0 | 45.91
Parks | 3.0 | 6.0 | 17.0 | 793.0 | 28.69 | 1.0 | 80.44
Religious Organizations | 7.0 | 16.0 | 41.25 | 2,644.0 | 63.28 | 1.0 | 196.97
Bowling Centers | 2.0 | 4.0 | 8.0 | 204.0 | 9.77 | 1.0 | 20.52
Museums | 1.0 | 3.0 | 6.0 | 137.0 | 6.78 | 1.0 | 13.99
Casinos | 1.0 | 3.0 | 7.0 | 188.0 | 8.05 | 1.0 | 17.22
Independent Artists | 1.0 | 2.0 | 5.0 | 130.0 | 7.55 | 1.0 | 17.42
Other Amusement/Recreation | 1.0 | 2.0 | 7.0 | 525.0 | 10.17 | 1.0 | 36.13
Golf Courses and Country Clubs | 2.0 | 3.0 | 7.0 | 101.0 | 8.07 | 1.0 | 13.77
Table S2: POI descriptive statistics (# of POIs in each MSA) for each of the fine-grained POI categories in Figure 1e. display_name | POI ES (25%) | POI ES (50%) | POI ES (75%) | POI ES (max) | POI ES (mean) | POI ES (min) | POI ES (std)
---|---|---|---|---|---|---|---
Full-Service Restaurants | 1,210.96 | 1,395.0 | 1,674.27 | 3,628.06 | 1,493.04 | 763.0 | 430.99
Snack Bars | 1,229.73 | 1,412.35 | 1,684.69 | 3,621.34 | 1,513.61 | 788.12 | 433.86
Limited-Service Restaurants | 1,174.84 | 1,351.64 | 1,587.4 | 3,501.19 | 1,440.15 | 771.34 | 410.95
Stadiums | 1,310.0 | 1,500.0 | 1,775.0 | 3,585.25 | 1,593.21 | 795.0 | 424.77
Performing Arts Centers | 1,395.0 | 1,583.1 | 1,832.4 | 3,632.78 | 1,659.56 | 875.0 | 431.06
Fitness/Recreation Centers | 1,230.03 | 1,431.79 | 1,703.94 | 3,749.05 | 1,528.73 | 700.0 | 453.4
Historical Sites | 1,325.0 | 1,527.94 | 1,793.75 | 3,618.58 | 1,627.62 | 757.5 | 452.96
Theme Parks | 1,300.0 | 1,498.75 | 1,750.0 | 3,900.0 | 1,612.58 | 700.0 | 501.79
Bars/Drinking Places | 1,220.02 | 1,420.25 | 1,676.4 | 3,656.17 | 1,505.86 | 750.0 | 440.08
Parks | 1,279.82 | 1,470.15 | 1,748.12 | 3,748.11 | 1,562.62 | 725.0 | 454.13
Religious Organizations | 1,269.27 | 1,459.86 | 1,677.08 | 3,670.38 | 1,529.02 | 754.0 | 428.42
Bowling Centers | 1,180.08 | 1,368.75 | 1,621.15 | 3,504.36 | 1,457.96 | 725.0 | 434.56
Museums | 1,275.0 | 1,490.83 | 1,775.36 | 3,606.66 | 1,585.92 | 800.0 | 474.37
Casinos | 1,200.0 | 1,400.0 | 1,655.54 | 3,606.17 | 1,503.88 | 725.0 | 469.68
Independent Artists | 1,374.38 | 1,611.5 | 1,904.6 | 3,691.68 | 1,725.42 | 850.0 | 528.33
Other Amusement/Recreation | 1,266.0 | 1,450.0 | 1,700.74 | 4,053.39 | 1,549.13 | 758.0 | 462.03
Golf Courses and Country Clubs | 1,399.06 | 1,648.4 | 1,964.19 | 4,248.5 | 1,765.92 | 900.0 | 542.13
Table S3: POI descriptive statistics (average POI economic standing in an MSA) for each of the fine-grained POI categories in Figure 1e. POI economic standing is operationalized as the median visitor ES of the POI. display_name | IS (25%) | IS (50%) | IS (75%) | IS (max) | IS (mean) | IS (min) | IS (std)
---|---|---|---|---|---|---|---
Full-Service Restaurants | 0.22 | 0.27 | 0.32 | 0.48 | 0.27 | 0.08 | 0.07
Snack Bars | 0.2 | 0.25 | 0.31 | 0.5 | 0.25 | 0.01 | 0.08
Limited-Service Restaurants | 0.24 | 0.29 | 0.34 | 0.47 | 0.29 | 0.04 | 0.08
Stadiums | 0.14 | 0.17 | 0.22 | 0.36 | 0.18 | 0.02 | 0.06
Performing Arts Centers | 0.14 | 0.16 | 0.19 | 0.27 | 0.17 | 0.05 | 0.05
Fitness/Recreation Centers | 0.2 | 0.26 | 0.31 | 0.47 | 0.25 | 0.03 | 0.08
Historical Sites | 0.15 | 0.2 | 0.27 | 0.43 | 0.21 | 0.0 | 0.09
Theme Parks | 0.16 | 0.2 | 0.25 | 0.42 | 0.2 | 0.02 | 0.08
Bars/Drinking Places | 0.18 | 0.23 | 0.3 | 0.42 | 0.23 | 0.06 | 0.08
Parks | 0.19 | 0.26 | 0.33 | 0.47 | 0.26 | 0.05 | 0.09
Religious Organizations | 0.24 | 0.32 | 0.38 | 0.55 | 0.31 | 0.05 | 0.1
Bowling Centers | 0.16 | 0.21 | 0.26 | 0.44 | 0.22 | 0.03 | 0.08
Museums | 0.18 | 0.22 | 0.28 | 0.45 | 0.24 | 0.06 | 0.08
Casinos | 0.2 | 0.26 | 0.32 | 0.47 | 0.26 | 0.02 | 0.09
Independent Artists | 0.13 | 0.2 | 0.27 | 0.39 | 0.21 | 0.02 | 0.09
Other Amusement/Recreation | 0.18 | 0.25 | 0.31 | 0.71 | 0.25 | 0.02 | 0.12
Golf Courses and Country Clubs | 0.33 | 0.41 | 0.5 | 0.62 | 0.4 | 0.2 | 0.11
Table S4: POI descriptive statistics (Interaction Segregation within-category) for each of the fine-grained POI categories in Figure 1e. Interaction Segregation is calculated for each POI category by filtering for only interactions which occurred inside of the POI category, before estimating interaction segregation (Methods). display_name | # Interactions (25%) | # Interactions (50%) | # Interactions (75%) | # Interactions (max) | # Interactions (mean) | # Interactions (min) | # Interactions (std)
---|---|---|---|---|---|---|---
Full-Service Restaurants | 23,060.75 | 54,219.5 | 156,645.0 | 19,540,673.0 | 398,304.04 | 6,112.0 | 1,634,147.68
Snack Bars | 15,582.0 | 38,954.0 | 120,225.0 | 14,128,466.0 | 291,523.01 | 5,233.0 | 1,205,873.07
Limited-Service Restaurants | 16,485.5 | 38,444.0 | 106,515.0 | 10,453,353.0 | 227,378.5 | 4,122.0 | 878,243.0
Stadiums | 53,077.5 | 96,487.5 | 336,479.75 | 8,942,618.0 | 348,920.85 | 17,024.0 | 988,719.72
Performing Arts Centers | 66,712.0 | 120,256.0 | 384,770.0 | 6,972,326.0 | 403,378.22 | 27,589.0 | 932,589.88
Fitness/Recreation Centers | 11,165.25 | 21,541.5 | 62,380.5 | 5,630,299.0 | 158,025.53 | 3,740.0 | 573,788.93
Historical Sites | 18,351.5 | 47,793.0 | 98,385.5 | 6,362,665.0 | 187,978.09 | 5,147.0 | 684,470.65
Theme Parks | 34,989.0 | 61,553.0 | 135,744.0 | 1,883,136.0 | 157,622.73 | 14,460.0 | 290,329.93
Bars/Drinking Places | 11,592.5 | 21,401.0 | 63,929.0 | 1,266,235.0 | 84,752.14 | 4,553.0 | 181,978.58
Parks | 10,050.75 | 22,301.0 | 61,492.75 | 1,520,092.0 | 88,789.84 | 5,383.0 | 193,888.94
Religious Organizations | 6,014.0 | 13,002.0 | 35,157.25 | 2,206,316.0 | 60,683.34 | 2,739.0 | 212,948.46
Bowling Centers | 16,423.5 | 26,517.0 | 65,563.5 | 1,030,970.0 | 92,515.06 | 5,874.0 | 174,876.21
Museums | 14,807.5 | 27,802.0 | 66,729.75 | 681,994.0 | 87,797.02 | 4,310.0 | 146,495.57
Casinos | 13,844.0 | 23,109.0 | 60,222.0 | 826,676.0 | 68,012.52 | 7,474.0 | 124,063.14
Independent Artists | 8,795.0 | 23,789.5 | 56,736.75 | 1,106,402.0 | 87,662.95 | 3,951.0 | 198,394.53
Other Amusement/Recreation | 6,923.0 | 14,349.0 | 42,793.0 | 365,436.0 | 38,640.52 | 2,929.0 | 56,964.16
Golf Courses and Country Clubs | 4,765.75 | 7,836.5 | 15,555.0 | 58,348.0 | 13,047.42 | 2,636.0 | 13,348.76
Table S5: POI descriptive statistics (number of interactions occurring inside POI category) for each of the fine-grained POI categories in Figure 1e. | Pearson Corr. w/ Primary | Spearman Corr. w/ Primary | Median | Mean
---|---|---|---|---
Interaction Segregation Measure |  |  |  |
Primary Measure | — | — | 0.35 | 0.35
Primary Measure (+ Up-weight Multiple Interactions) | 0.89 | 0.91 | 0.46 | 0.45
ES Definition: Rent Zestimate Percentile | 0.78 | 0.80 | 0.46 | 0.45
ES Definition: Within-MSA Rent Zestimate Percentile | 0.81 | 0.83 | 0.54 | 0.53
ES Definition: Census Median Household Income | 0.75 | 0.77 | 0.47 | 0.46
Exclude Pri/Sec Roads | 0.99 | 0.99 | 0.37 | 0.37
Exclude Roads | 0.98 | 0.98 | 0.37 | 0.37
Exclude Same-home interactions | 0.98 | 0.98 | 0.34 | 0.34
Work/Leisure (Neither in Home Tract) | 0.93 | 0.93 | 0.31 | 0.31
Leisure (inside POI) | 0.85 | 0.84 | 0.28 | 0.29
Minimum Distance Between Pings: $<$ 25 meters | 0.98 | 0.99 | 0.36 | 0.36
Minimum Distance Between Pings: $<$ 10 meters | 0.95 | 0.96 | 0.37 | 0.36
Minimum Time Between Pings: $<$ 2 minutes | 0.99 | 0.99 | 0.36 | 0.36
Minimum Time Between Pings: $<$ 60 seconds | 0.99 | 0.99 | 0.36 | 0.36
Minimum Tie Strength: $2$ consecutive interactions | 0.94 | 0.95 | 0.35 | 0.35
Minimum Tie Strength: $3$ consecutive interactions | 0.83 | 0.83 | 0.37 | 0.37
Minimum Tie Strength: $2$ unique days of interaction | 0.88 | 0.90 | 0.47 | 0.46
Minimum Tie Strength: $3$ unique days of interaction | 0.73 | 0.76 | 0.56 | 0.54
Dist. $<$ 25 meters, Time $<$ 2 min., $>=$ 2 consec. interactions | 0.93 | 0.94 | 0.35 | 0.35
Dist. $<$ 25 meters, Time $<$ 2 min., $>=$ 2 unique days | 0.88 | 0.89 | 0.46 | 0.45
Dist. $<$ 10 meters, Time $<$ 60 sec., $>=$ 3 consec. interactions | 0.80 | 0.80 | 0.38 | 0.37
Dist. $<$ 10 meters, Time $<$ 60 sec., $>=$ 3 unique days | 0.73 | 0.75 | 0.52 | 0.50
Table S6: Robustness checks overview. We find that our definition of
interaction segregation is robust to varying many parameters: weighting of
repeated interactions between the same users, definition of economic standing,
inclusion/exclusion of roads and same-home interactions, filtering location of
interaction, minimum distance, minimum time, and minimum tie strength (as well
as the intersection of distance, time, and tie strength). The above variants
all are strongly correlated to our primary measure (all have Spearman Corr.
$>=$ 0.75). We also find that our primary findings that (1) large, dense
cities facilitate segregation and (2) interaction hub locations accessible to
diverse individuals may mitigate segregation are robust across all definitions
of Interaction Segregation (Supplementary Figures S2-S7). Note that we exclude
same-home interactions in robustness checks that vary minimum time, distance,
or require repeated interactions, to ensure that results are not influenced by
interactions with members of the same household (these interactions ordinarily
have minimum influence on Interaction Segregation, as shown by the robustness
check which excludes same-home interactions and results in virtually identical
metric (Spearman Corr. 0.98); however, the influence of same-home interactions
is higher after more conservative filters are applied to the definition of
interactions, such as requiring a minimum tie strength of 3 consecutive
interaction).

(a)

(b)

Figure S2: Robustness of primary study findings to weighting of repeated
interactions. We find that our primary study findings that, (1) large, dense
cities facilitate segregation and (2) interaction hub locations accessible to
diverse individuals may mitigate segregation, are robust to the choice of
whether to upweight repeated interactions in our interaction network. We
compare the results of:
_Primary Measure:_ Interactions are defined as pairs of users who have ever
interacted within the study observation window (three months of 2017). We
deduplicate repeated interactions, as frequency of pings varies across
smartphone users, to reduce bias from users with a higher frequency of pings.
For instance, if an individual A with an individual B (ES $1000) two times and
individual C (ES $2000) one, we compute the mean ES of individual A’s network
as $1500.
_Upweight Repeated Interactions:_ Repeated interactions are unweighted when
calculating the mean ES of an individual’s interaction network. For instance,
if an individual A with an individual B (ES $1000) two times and individual C
(ES $2000) once, we compute the mean ES of individual A’s network as $1333.

(a)

(b)

(c)

(d)

Figure S3: Robustness of primary study findings to definition of economic
standing. We find that our primary study findings that, (1) large, dense
cities facilitate segregation and (2) interaction hub locations accessible to
diverse individuals may mitigate segregation, are robust to the definition of
economic standing. We compare the results of:
_Primary Measure:_ Our primary measure leverages estimated monthly rent value
(Zillow Rent Zestimate).
_Census Block Group (CBG) Median Household Income:_ We define the ES of an
individual is the median household income in the CBG in which they reside.
_Rent Zestimate Percentile:_ We normalize Rent Zestimate values across all
individuals.
_Primary measure Relative to MSA:_ We normalize Rent Zestimate values across
all individuals within an MSA, independent of other MSAs, to account for
differences in cost of living across cities.

(a)

(b)

(c)

(d)

(e)

Figure S4: Robustness of primary study findings to exclusion of interactions
within roads, exclusion interactions with residents of the same home, and
exclusion of non-work/leisure interactions. We find that our primary study
findings that, (1) large, dense cities facilitate segregation and (2)
interaction hub locations accessible to diverse individuals may mitigate
segregation, are robust to filtering for a subset of interactions. We compare
the results of:
_Primary Measure:_ Our primary measure includes all interactions, aiming to
give a complete account of an individual’s interaction network including path
crossings on roads as well as those they share a home with.
_Excluding roads:_ We define the ES of an individual is the median household
income in the CBG in which they reside.
_Rent Zestimate Percentile:_ We normalize Rent Zestimate values across all
individuals.
_Primary measure Relative to MSA:_ We normalize Rent Zestimate values across
all individuals within an MSA, independent of other MSAs, to account for
differences in cost of living across cities.
_Work/Leisure:_ We filter to include only interactions likely to take place in
the context of work or leisure, by excluding interactions which occurred when
either individuals were located within their home tracts.
_Leisure:_ We filter for leisure interactions by including only interactions
ocurring inside of the POIs categorized as related to leisure (Figure 1e).

(a)

(b)

(c)

Figure S5: Robustness of primary study findings to minimum distance required
between two GPS pings for individuals to be considered interacting. We find
that our primary study findings that, (1) large, dense cities facilitate
segregation and (2) interaction hub locations accessible to diverse
individuals may mitigate segregation, are robust to the time threshold used in
our definition of interaction:
_Primary Measure:_ Our primary measure uses a threshold of 50 meters, based on
prior literature which shows that even distant exposure to diverse individuals
is predictive of long-term behaviors[20].
_Alternative measures:_ We alternatively consider more conservative thresholds
of 25 meters and 10 meters, with 10 meters being the lowest threshold due to
limitations of GPS ping accuracy[merry2019smartphone, menard2011comparing].

(a)

(b)

(c)

Figure S6: Robustness of primary study findings to minimum time elapsed
between two pings to constitute an interaction. We find that our primary study
findings that, (1) large, dense cities facilitate segregation and (2)
interaction hub locations accessible to diverse individuals may mitigate
segregation, are robust to the time threshold used in our definition of
interaction:
_Primary Measure:_ Our primary measure uses a threshold of 5 minutes, to be
inclusive of users with sparse pings (e.g., for a subset of users, we only
have 1 ping per day, while for others we have 100+ pings per day) while
maintaining a reasonable confidence that an interaction may have occurred.
_Alternative measures:_ We alternatively consider more conservative thresholds
of 2 minutes and 1 minute.

(a)

(b)

(c)

(d)

(e)

Figure S7: Robustness of primary study findings to minimum tie strength
required to constitute an interaction. We find that our primary study findings
that, (1) large, dense cities facilitate segregation and (2) interaction hub
locations accessible to diverse individuals may mitigate segregation, are
robust regardless of the minimum tie strength threshold between two
individuals to be constitute an interaction:
_Primary Measure:_ Our primary measure only requires a single pair of pings
between users to constitute an interaction, to be inclusive of users with
sparse pings (e.g., for a subset of users, we only have 1 ping per day, while
for others we have 100+ pings per day).
_Alternative measures:_ We alternatively consider more conservative thresholds
of 2 or 3 consecutive interactions, as well as 2 or 3 interactions across
unique days. Requiring consecutive interactions increases the likelihood that
individuals actually came into contact together; interactions across unique
days increases the likelihood that interactions are not merely path crossings,
but social interactions between individuals who are familiar with each other.
(continued on next page)

(a)

(b)

(c)

(d)

Figure S8: (continued from previous page). We find that our primary study
findings that, (1) large, dense cities facilitate segregation and (2)
interaction hub locations accessible to diverse individuals may mitigate
segregation, are _robust to the combination of the minimum time, minimum
distance, and minimum tie strength threshold parameters_. To account for
interactions between threshold parameters, we also consider combinations of
parameter variants. For instance, the most conservative robustness check
defines an interaction as two individuals being $<$ 10 meters apart within a
$<$ 60 second window, and for this to have occurred either for either 3
consecutive minutes (second figure from the bottom) or across 3 unique days
(bottom figure).

(a)

(b)

Figure S9: Alternative homophily mechanisms do not explain segregation in
large cities. We consider the possibility of two alternative hypotheses which
may explain the trend towards high segregation in large cities
(a) _Constant Homophily_ : i.e. individuals have the same proclivity for
interacting with individuals of similar ES regardless of if they live in large
or small cities, and it is instead change in distribution of economic standing
that drives segregation in large cities (e.g. in large cities there may be a
greater supply of people in the same economic class available to interact
with). We test this hypothesis via a null network model, in which which we
preserve network nodes (individuals and their ES values) but randomize
edges[barabasi2013network, maslov2002specificity]. We randomly assign
interactions between pairs of people, weighting the likelihood of interaction
between people of similar ES higher according to a constant homophily
function. Specifically, the probability of interaction ($p_{i,j}$) between two
individuals of $ES_{i}$ and $ES_{j}$ is weighted by their similarity in ES,
defined as the complement of the normalized Euclidean distance in ES:
$p_{i,j}\propto
Similarity(ES_{i},ES_{j})=1-\frac{|ES_{i}-ES_{j}|}{max(ES)-min(ES)}$. We
choose 75 interactions per person such that the mean number of interactions
per person is 150, which corresponds to Dunbar’s number[dunbar2010many]. We
find that under this null model, there is no positive association between
interaction segregation and population size; in fact, larger cities are less
segregated on average, as there is an increase in supply of diverse
individuals in economic standing in larger cities. These findings are also
robust to a variety of null model specifications (Supplementary Figure S10).
(b) _Between Activity Homophily_ : i.e. it is not the differentiation of
individual venues that drives segregation, but rather that in large cities
individuals choose different categories of activities which results in
segregation (e.g. in small cities, there are less country clubs so everybody
visits restaurants to socialize, whereas in large cities high-ES individuals
segregate by spending a higher proportion of time in exclusive venues such as
country clubs). We test this hypothesis via a configuration
model[barabasi2013network, maslov2002specificity], a prominent null network
model in which node degree is preserved. Specifically, by applying a
configuration model to reconfigure network edges for each leisure category
separately, we preserve network nodes (individuals and their ES values) as
well as the number of interactions they had in each category of POI (node
degree), but randomize the specific venue in which each interaction occurred.
For instance, if an individual interacts with 5 people inside of restaurants
and 100 people inside of a fitness center, they will be randomly assigned to
interact with 5 people from all of those who visited restaurants, and 100
people from all of those who visited fitness centers. This null model
preserves between-activity homophily which results from activity choices (e.g.
whether to visit a country club or restaurant), but erases within-activity
homophily (e.g. individuals who visit any restaurant are equally likely to
interact). We find that under this null model, there is no positive
association between interaction segregation and population size; in fact,
there is minimal segregation across all cities as variation between activity
categories is insufficient to retain segregation. This is further supported by
Supplementary Table S3, which shows relatively small differences in ES between
participants in different categories of leisure activity (e.g. the lowest ES
activity, limited service restaurants has a median visitor ES of $1,352, the
highest ES activity, golf courses and country clubs has a median visitor ES of
$1,648.4).  Figure S10: Baseline Homophily null model results are robust to
varying null model specifications. We re-run the analysis in Supplementary
Figure S9a under a variety of null model specifications, and find that _in all
cases there is no evidence to suggest that the Constant Homophily hypothesis
explains the high segregation observed in large cities_. (a-c) We first
consider varying the extent of homophily by adding a constant parameter $H$ to
the homophilous weighting of edges, to exponentially increase/decrease the
extent of homophily in our null model for the probability of individuals $i$
and $j$ interacting: $p_{i,j}\propto Similarity(ES_{i},ES_{j})^{H}$. We find
that regardless of if we (a) decrease homophily (H=0.5) or (b-c) increase
homophily mildly (H=2) or strongly (H=25), there is no positive association
between population size and segregation in our simulations. In fact, larger
cities are less segregated on average, as there is an increase in supply of
diverse individuals in economic standing in larger cities. We also consider
alternative null model specifications such as (d) a softmax homophily function
$p_{i,j}\propto\frac{e^{Similarity(ES_{i},ES_{j})}}{\sum_{k=1}^{N}e^{Similarity(ES_{i},ES_{k})}}$
, (e) applying the original null model to percentile-scored values economic
standing (f) applying the original null model to percentile-scored values
economic standing, and calculating Interaction Segregation using percentile-
scored values economic standing. This suggests that the high segregation in
large cities is due to a change in resident behavior, facilitated by the built
environment of large cities, and not an artifact the economic standing
distribution in large cities.  Figure S11: Understanding why BI explains
Interaction Segregation. We show via an ablation study that interaction hub
locations, in addition to number of hubs and residential segregation,
contributes to the explanatory power of BI. As illustrated in Extended Data
Figure 7, BI captures three factors of built environment: (1) locations of
interaction hubs (2) number of interaction hubs and (3) residential
segregation. In this analysis, we aim to disentangle how these three factors
contribute to the ability of BI to explain interaction segregation (as
measured by $\rho^{2}$, the squared Spearman correlation with interaction
segregation). We find that number of hubs (orange, $\rho^{2}=0.436$) and
residential segregation (blue, $\rho^{2}=0.437$) are each correlated with
interaction segregation. To measure the combined explanatory power of these
two factors within BI, independent of interaction hub locations, we conduct an
ablation study in which we calculate Bridging Index for each MSA, using the
actual home location data and number of interaction hubs for each MSA, but
randomize hub locations (light purple, $\rho^{2}=0.486$). For each MSA, we
estimate this value over 1000 random trials. We find that calculating BI using
randomized hub locations is a significantly weaker predictor (p=0.0008$<$0.01,
Fisher’s z-test) compared to BI values computed using actual hub locations
(dark purple, $\rho^{2}=0.604$). This demonstrates that hub locations
contributes to the explanatory power of BI, i.e. BI explains interaction
segregation because it captures the extent to which the locations of hubs in
different cities facilitate the interaction of diverse individuals. Figure
S12: Robustness of BI to definition of ES diversity. We calculate a version of
Bridging Index which uses variance in to operationalize economic diversity:
$Bridging\>Index\>(BI)=\frac{\sum_{i=1}^{K}|\mathcal{C}_{i}|\cdot
Var(\mathcal{C}_{i})}{|\mathcal{V}_{MSA}|\cdot Var(\mathcal{V}_{MSA})}$. This
variant of BI explains interaction segregation comparably (Spearman Corr.
-0.75 vs. -0.78, both N=382, both p$<10^{-10}$) to our primary measure of BI
which uses Gini Index to operationalize economic diversity. Thus, we find that
the ability of Bridging Index to explain interaction segregation is robust to
the definition of ES diversity. Figure S13: We consider alternative mechanisms
through which built environment may mitigate interaction segregation. (a)
Following the inverse relationship between POI localization and segregation
established in Extended Data Figure 2a, we consider whether the de-
localization of interaction hubs alone can provide an alternative to BI. We
compute mean distance to nearest interaction hub for each MSA, which is the
same measure in Extended Data Figure 2a but calculated for interaction hubs.
We find that while hub localization is inversely correlated with interaction
segregation (Spearman Corr -0.44, N=382, p$<10^{-7}$), this correlation is
significantly less ($p<0.0001$, Fisher’s z-test) than the correlation between
BI and interaction segregation (Spearman Corr -0.78, N=382, p$<10^{-10}$).
This suggests that hub bridging, as quantified by BI may be a more promising
direction to investigate as a potential mitigator of segregation. (b) We also
consider whether fine-grained POIs may function as bridges between diverse
individuals. For each of the fine-grained leisure POI categories in Figure 1e,
we calculate a Bridging Index across all MSAs (using the same procedure to
calculate BI as shown in Extended Data Figure S12, except using fine-grained
POI locations instead of interaction hub locations). For instance, to
calculate the Bridging Index for restaurants, we cluster all homes by the
nearest restaurant location, and then calculate:
$(Restaurant)\>Bridging\>Index\>=\frac{\sum_{i=1}^{K}|\mathcal{R}_{i}|\cdot
Gini\>Index(\mathcal{R}_{i})}{|\mathcal{V}_{MSA}|\cdot
Gini\>Index(\mathcal{V}_{MSA})}$. After calculating the bridging index for all
fine-grained POI categories and for each of the 382 MSAs, we then measure the
correlation between each bridging index and interaction segregation across all
MSAs (as measured by $\rho^{2}$, the squared Spearman correlation). We find
that BI for hubs provides a stronger correlation ($\rho^{2}=0.604$, horizontal
line), than all other bridging indices which are plotted as points on the
scatter-plot in (b). Further, we find that POI categories which are often
located inside or near interaction hubs (co-location, X-axis) have bridging
indices which are stronger predictors of interaction segregation (e.g. for
fitness/recreation centers, snack bars etc.). The high correlation between
(Spearman Correlation -0.82, N=17, $p<0.001$) between co-location of POIs and
bridging index predictive ability demonstrates asymptotic convergence between
all other predictive bridging index metrics and our primary BI measure. This
further suggests that bridging of interaction hubs should be the primary
metric of interest for mitigators of segregation, because other bridging
indexes computed for fine-grained POI locations are at best proxies for BI
which leverages higher-level interaction hub locations. Supplementary Figures
S14-S16 illustrate the frequent co-location between hubs and other fine-
grained POIs. Figure S14: Examples of interaction hubs in coastal cities of
(a) San Francisco Bay Area and (b) Boston, MA. Hubs frequently contain a
diverse assortment of POIs including restaurants, fitness centers/gyms,
grocery stores, etc. and are also frequently hubs around which other POIs are
located nearby. Figure S15: Example of a major hubs in Fayetteville, NC (a)
zoomed-out view of hub and surrounding co-located POIs (b) zoomed-in view of
the hub core and businesses contained inside. We find that in Fayetteville, a
city with a high Bridging Index, large hubs contain a variety of POIs which
cater to diverse individuals of both high and low-ES. Figure S16: Examples two
hubs in Montgomery, AL which have visitors of predominantly (a) high economic
standing (b) low economic standing. We find that in Montgomery, AL a city with
a low Bridging Index, smaller hubs exist which contain POIs which cater to a
narrow band of individuals in a specific economic stratum. For instance, we
find that the nearby grocery store (a) is a Whole Foods Market in the high-ES
hub, in contrast to the (b) Walmart Supercenter in the low-ES hub. Figure S17:
Our model with simulated uniform within-tract crossings is equivalent to the
conventional neighbourhood sorting index (NSI). Each point is a Metropolitan
Statistical Area (MSA). The y-axis shows the interaction segregation estimate
from the mixed model with a simulated path crossing between every person in a
tract (in our dataset). The x-axis shows the correlation between a person’s ES
and the average ES of people in their tract, which is the neighbourhood
sorting index (NSI). As these measures are equivalent, Spearman Corr = 1.0 and
Pearson Corr. = 1.0. Figure S18: Our segregation measure versus a conventional
residential segregation, neighborhood sorting index (NSI). Each point is a
Metropolitan Statistical Area (MSA). Regardless of whether we compare the
numerical segregation values (Pearson Correlation 0.67) or the MSA ranking
(Spearman Correlation 0.66), only moderate correlation indicates that our
measure is different in kind from residential segregaiton as measured
conventionally by NSI. Figure S19: Segregation decomposed by time.As described
in Methods M3, our fine-grained interaction network allows us to decompose our
overall interaction segregation into estimates of segregation during different
hours of the day, by filtering for interactions that occurred within a
specific hour. In Supplementary Figure S19, we partition estimates of
segregation by 3 hour windows to illustrate how segregation varies throughout
the day (see Supplementary Information). We observe that segregation increases
by 61% between the afternoon and early morning hours. Segregation is lowest
during commute and work hours, indicating higher levels of interaction with
people of different SES while at work or otherwise away from home. Segregation
is higher during nighttime hours. This is driven by individuals returning to
their home neighborhoods, which are more homogeneous in economic standing, as
we well as mechanically a result of ES being is defined by rent value, such
that people who live in the same household will have the same ES (and thus
will be highly segregated).

(a) Full-Service Restaurants

(b) Snack Bars

(c) Limited-Service Restaurants

(a) Stadiums

(b) Performing Arts Centers

Figure S21: Across many activities, POIs in large cities are more differentiated and consequently more segregated. This figure shows that the trend towards more options, increased differentiation, and consequently higher segregation is consistent across many prominent POI categories. Here we find similar results for the 5 most frequently visited fine-grained Safegraph place features. The analyses for full-service correspond to Figures 2c-e, and we additionally show the same trend for snack bars, limited-service restaurants, stadiums, and performing arts centers (ranked 2-5 after full-service restaurants in terms of most frequently visited POIs among Safegraph places). Across the board, large, densely populated metropolitan areas are associated with increased options and economic differentiation of POIs, which may facilitate higher self-segregation. |  Dependent variable: Interaction Segregation
---|---
| (1) | (2) | (3) | (4) | (5) | (6)
Intercept |  0.355∗∗∗ |  0.355∗∗∗ |  0.355∗∗∗ |  0.356∗∗∗ |  0.355∗∗∗ |  0.355∗∗∗
| (0.005) | (0.004) | (0.004) | (0.004) | (0.003) | (0.003)
Population Density |  0.039∗∗∗ |  |  0.024∗∗∗ |  0.022∗∗∗ |  0.017∗∗∗ |  0.017∗∗∗
| (0.005) |  | (0.004) | (0.004) | (0.004) | (0.004)
Gini Index (Estimated Rent) |  |  0.064∗∗∗ |  0.058∗∗∗ |  0.059∗∗∗ |  0.049∗∗∗ |  0.050∗∗∗
|  | (0.004) | (0.004) | (0.004) | (0.003) | (0.003)
Political Alignment (% Democrat in 2016 Election) |  |  |  |  0.009∗ |  | 0.006
|  |  |  | (0.005) |  | (0.004)
Racial Demographics (% non-Hispanic White) |  |  |  | -0.005 |  | 0.003
|  |  |  | (0.004) |  | (0.003)
Mean ES (Estimated Rent) |  |  |  |  -0.009∗ |  | -0.003
|  |  |  | (0.005) |  | (0.004)
Walkability (Walkscore) |  |  |  |  | 0.002 | 0.001
|  |  |  |  | (0.003) | (0.004)
Commutability (% Commute to Work) |  |  |  |  |  -0.012∗∗∗ |  -0.013∗∗∗
|  |  |  |  | (0.004) | (0.004)
Conventional Segregation (NSI) |  |  |  |  |  0.048∗∗∗ |  0.047∗∗∗
|  |  |  |  | (0.003) | (0.003)
Observations | 382 | 382 | 382 | 376 | 382 | 376
$R^{2}$ | 0.151 | 0.419 | 0.475 | 0.490 | 0.682 | 0.680
Adjusted $R^{2}$ | 0.149 | 0.417 | 0.472 | 0.483 | 0.678 | 0.673
|  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S7: Population density is significantly associated with interaction
segregation, after controlling for MSA income inequality (Gini Index),
political alignment (% Democrat in 2016 election), racial demographics (% non-
Hispanic White), mean ES, walkability (Walkscore[walkscore]), commutability (%
of residents commuting to work), and residential segregation (NSI). This table
is from an analogous regression to the regression shown in Extended Data Table
1, using population density instead of population size (we look at each
separately due to co-linearity between population size and density). Here we
show the coefficients (after normalizing via z-scoring to have mean 0 and
variance 1) from the primary specifications estimating the effect of
population density on interaction segregation across all MSAs. Columns (1-5)
are models specified with different subsets of covariates; Column 6 shows
model specification with all covariates. Differences between sample size in
models is due to missing data for several covariates in a small number of MSAs
(Walkscores were not available for all MSAs). (*p $<$ 0.1; **p $<$ 0.05; *** p
$<$ 0.01).