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Beyond Distance Decay: Discover Homophily inSpatially Embedded Social Networks
Yang Xu, Paolo Santi & Carlo Ratti
To cite this article: Yang Xu, Paolo Santi & Carlo Ratti (2021): Beyond Distance Decay: DiscoverHomophily in Spatially Embedded Social Networks, Annals of the American Association ofGeographers, DOI: 10.1080/24694452.2021.1935208
To link to this article: https://doi.org/10.1080/24694452.2021.1935208
Published online: 28 Jul 2021.
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Beyond Distance Decay: Discover Homophily inSpatially Embedded Social Networks
Yang Xu,�
Paolo Santi,† and Carlo Ratti‡
�Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong
†Senseable City Laboratory, Massachusetts Institute of Technology, USA, and Instituto di Informatica e Telematica delCNR, Italy
‡Senseable City Laboratory, Massachusetts Institute of Technology, USA
Existing studies suggest distance decay as an important geographic property of online social networks.
Namely, social interactions are more likely to occur among people who are closer in physical space. Limited
effort has been devoted so far, however, to quantifying the impact of homophily forces on social network
structures. In this study, we provide a quantitative understanding of the joint impact of geographic distance
and people’s socioeconomic characteristics on their interaction patterns. By coupling large-scale mobile
phone, income, and housing price data sets in Singapore, we reconstruct a spatially embedded social network
that captures the cell phone communications of millions of phone users in the city. By associating phone
users with their estimated residence, we introduce two indicators (communication intensity and friendship
probability) to examine the cell phone interactions among places with various housing price values. Our
findings suggest that, after controlling for distance, similar places tend to have relatively higher
communication intensity than dissimilar ones, confirming a significant homophily effect as a determinant of
communication intensity. When the analysis is focused on the formation of social ties, though, the
homophily effect is more nuanced. It persists at relatively short distances, whereas at higher distances a
tendency to form ties with people in the highest social classes prevails. Overall, the results reported in this
study have implications for understanding social segregation in cities. In particular, the physical separation of
social groups in a city (e.g., residential segregation) will have a direct impact on shaping communication or
social network segregation. The study highlights the importance of incorporating socioeconomic data into
the understanding of spatial social networks. Key Words: distance decay, homophily, mobile phone data,segregation, social network.
In the past two decades, Internet and telecommu-
nication technologies have permeated almost
every aspect of human life, transforming the ways
in which people conduct their daily activities. One
important dimension of human life that has changed
dramatically is social interaction. Technological
advancements have created a “virtual space” (Strate
1999), where new forms of social communications
are emerging and evolving. These new social
channels—such as mobile phones, e-mails, and
online social media—empower people to connect
with others who are thousands of miles away. Unlike
face-to-face communications that require people to
go out and meet in physical space, social interactions
in virtual space hardly demand any travel and seem
to be not constrained by geographic distance. On
the other hand, the dynamics according to which
social ties are created and evolve in an online net-
work have only started to be unveiled, and it is
reasonable to assume that preexisting social ties
based on face-to-face relationships have a strong
influence on the formation of ties in online social
networks. So, although formally there is no geo-
graphic constraint on the formation of ties in online
social networks, it is possible that geographic proper-
ties also play a role in online social networks due to
their tight connections with preexisting (physical)
social networks (Larsen, Axhausen, and Urry 2006;
Carrasco, Miller, and Wellman 2008; Calabrese
et al. 2011).
Debates have emerged on how or whether new
information technologies will change the geographic
properties of human social interactions. The reflec-
tions on the “death of distance” (Cairncross 1997)
and “the end of geography” (Graham 1998) are
among the early works that call for a reconceptuali-
zation of space and place in the information age.
Although relevant debates are still ongoing, it is
Annals of the American Association of Geographers, 0(0) 2021, pp. 1–17 # 2021 by American Association of GeographersInitial submission, September 2020; revised submissions, March and April 2021; final acceptance, April 2021
Published by Taylor & Francis, LLC.
widely acknowledged—sometimes as common
sense—that human social interactions do not occur
in parallel in physical and virtual space. Instead,
they are continuously blending into each other. In
other words, “only by maintaining linked, relational
conceptions of both new information and communi-
cations technologies and space and place will we
ever approach a full understanding of the inter-rela-
tionships between them” (Graham 1998, 181).Inspired by these reflections, scholars started
exploring the geographic properties of various online
and mobile social networks, with considerable focus
on the “distance decay” effect. This distance effect
has been observed across different types of data sets
and networks, such as Facebook communities
(Goldenberg and Levy 2009; Backstrom, Sun, and
Marlow 2010), networks of bloggers (Liben-Nowell
et al. 2005), and telecommunications (Lambiotte
et al. 2008; Krings et al. 2009; Gao et al. 2013).
One consensus reached by these studies is that the
intensity or probability of human communications
between places decays with geographic distance.
This observation suggests that the relationship
between virtual and physical space is strong: Social
interactions are more likely to occur among people
who are closer in physical space.The research finding is not too surprising because
we have fewer opportunities to know someone who
is far away. In other words, the lack of physical
interactions has a notable impact on the geographic
dispersal of social networks. One important issue
that has not been addressed, however, is whether
the observed distance decay effect is purely a reflec-
tion of the decreasing opportunities for potential
human interactions. As human beings, we tend to
connect with similar others. The presence of homo-phily plays an important role in shaping social net-
work structures (McPherson, Smith-Lovin, and Cook
2001). Then, an interesting question worth investi-
gating is this: How do the socioeconomic character-
istics of people and their distribution in physical
space—for example, in a city—affect the geographic
properties of online social networks?Answering this question has many implications
for urban planning. Social segregation—a long-
standing research topic in geography and sociology
(Massey and Denton 1987; Leo et al. 2016; Le
Roux, Vall�ee, and Commenges 2017; Musterd et al.
2017; Q. Wang et al. 2018)—is a good example. If
online social networks exhibit a distance decay
effect, then a city where rich and poor people are
highly separated and meanwhile clustered are likely
to suffer from a certain level of segregation. The
implication is beyond the traditional understanding
of residential segregation (Massey and Denton
1988). It would imply that the physical separation of
social groups will directly contribute to the emer-
gence of a “communication segregation” in the vir-
tual space. Hence, a secondary question worth
investigating is whether the socioeconomic configu-
ration of a city is the sole driving force of online
social segregations. To be more specific, do people
connect simply because they are close? With dis-
tance being equal, are people more likely to interact
with similar others?To answer these questions, we perform a case
study in Singapore by analyzing a large-scale mobile
phone data set that captures the communication pat-
terns of 2.6 million people during a period of fifty -
days. A spatial social network is established by
embedding phone users into geographic space based
on their estimated residence. We explore the geo-
graphic properties of the network by examining the
communication intensity and probability of social
ties among different places. By further integrating
income data and a high-resolution housing price
data set, we examine whether places with similar
socioeconomic characteristics tend to maintain
higher levels of cell phone interactions. Different
from previous studies that focus on the distance
decay effect, this study aims to unravel the joint
impact of geographic distance and homophily on the
social network structure. We argue that people’s
social interactions are affected not only by their
physical proximity but also by forces of homophily
in the society. The research findings have many
implications for policymaking that aim to foster
social integration in cities. The research framework
can be applied or extended to better understand
other types of spatial social networks.
Theoretical Context
A social network provides a structural representa-
tion of human relations and interactions. As a
fundamental concept in social science, it has gener-
ated broad interests across many disciplines (e.g.,
sociology, geography, transportation, physics, and
computer sciences). Social networks emerge as a
reflection of personal relations in societies (Fischer
2 Xu, Santi, and Ratti
1982). Such relations are created or maintained
through different kinds of human activities, many of
which would take place, or are empowered by what
happened, in physical space. Therefore, studies of
social networks often consider a spatial context of
social structure, whether explicit or implicit.
Over the years, many studies have incorporated a
spatial dimension into social network analysis
(Stewart 1941; Liben-Nowell et al. 2005; Cranshaw
et al. 2010; Andris 2016). These efforts involve the
conceptualization of social actors (i.e., people), rela-
tions (i.e., social ties), and their linkage with built
environment. Studies of spatial social networks often
link social actors with physical locations—like one’s
home or neighborhood—such that contextual infor-
mation can be leveraged to better understand the
factors that contribute to or hamper the formation
of social relationships.Enabling a spatial view of social networks is essen-
tial. A typical example is the discovery of a distance
decay effect on social relations (Stutz 1973).
Namely, people tend to socialize more with ones
who are close to them. Because face-to-face interac-
tion is a key form in maintaining social relations,
the distance effect can partly be explained by the
travel cost that is incurred for conducting social
activities. Thus, travel behavior or mobility is con-
sidered an important dimension that explains the
interplay between social relations and distance
(Carrasco, Miller, and Wellman 2008; Cho, Myers,
and Leskovec 2011; D. Wang et al. 2011).In the past two decades, many online (e.g.,
Facebook) and mobile social networks have emerged.
Studies found that the chances that people form rela-
tions in these networks are still notably affected by geo-
graphic distance (Liben-Nowell et al. 2005; Goldenberg
and Levy 2009; Backstrom, Sun, and Marlow 2010).
Although online social interactions in principle can
occur without a need to travel in the physical space,
the rediscovery of a distance effect suggests that online
social networks partly mirror preexisting social ties,
which are shaped by various constraints in the physical
world. Thus, the spatialization of online social networks
could provide additional insights into human interac-
tions in an online–offline setting.
Beyond reflecting existing social structures, social
networks have been found to influence future activi-
ties and travels (Carrasco, Miller, and Wellman
2008). For example, studies found that telecommuni-
cations between phone users are indicative of their
colocation patterns, a reflection of their social inter-
action potentials (Calabrese et al. 2011; Xu et al.
2017). Therefore, mobile and online social networks
would have an impact on travel behavior and physical
activities, which in turn further affect network dynam-
ics and evolution. Thus, there is a mutual effect
between human travel and online social interactions.Social relations are not only constrained by geo-
graphic distance. Studies suggest that homophily, or
similarities in people’s sociodemographic characteristics,
is a catalyst of social interactions (McPherson, Smith-
Lovin, and Cook 2001). From the perspective of travel
behavior, great satisfaction might be obtained from
interactions between people with similar background
and therefore individuals are “willing to trade-off extra
(travel) cost” (Stutz 1973, 142) for these interactions.
Because one’s social background can be largely
explained by the underlying built environment (e.g.,
income, racial makeup), the homophily principle would
imply stronger social connections among locations with
similar characteristics.Although the distance and homophily effects have
been studied separately, their joint impact on social net-
work structures remains underexplored. In particular,
there is a lack of research on quantifying such impact at
intraurban scales and over social networks empowered by
modern information and communications technologies.
This is partially due to the difficulty of coupling large-
scale human interactions with fine-grained sociodemo-
graphic data. Filling this research gap, as this study
attempts to do, has important implications for cities. For
instance, if stronger social connections (e.g., telecommu-
nications) are observed among similar places (e.g., by
income or housing price) after geographic distance is con-
trolled for, this would imply more social travels in the
past or more interaction potential in the future. In other
words, socioeconomic configurations in cities would have
an impact on human interactions in the online space, on
their future travel behavior (in physical space), and, more
important, on socioeconomic segregation in the urban
environment (Farber et al. 2015; Leo et al. 2016; Q.
Wang et al. 2018).
Research Design
From Mobile Phone Data to City-ScaleSocial Network
The call detail record (CDR) data set was col-
lected from a major mobile phone operator in
Beyond Distance Decay 3
Singapore. The anonymized data set tracks the com-
munication patterns and location footprints of 4.4
million phone users during a period of fifty days in
2011. When a phone call or text message was initi-
ated by a user, a record was generated by the tele-
communication system, documenting the unique ID
of the caller and the callee, the event type (i.e., call
or text message), the associated timestamp, and the
cell towers to which the users were connected. Such
information allows us to not only extract social net-
work structure but also infer the frequented locations
of users (e.g., home), from which the social network
can be embedded into geographic space.Note that CDRs are passively generated and the
observations for some users can be quite sparse. By
measuring the number of days with records for each
user, we find a large variation of the level of activity
across the population (Figure 1A). To control the
data sparsity issue, this study focuses on a subset of
users who have at least ten active days of phone
usage. On the one hand, this choice allows us to
focus more on local residents by filtering short-term
subscribers such as tourists. On the other hand, it
would ensure that the number of observation days
for the retained users is high enough to support a
reliable estimation of home location. After this fil-
tering, we are left with a data set of 2.6 million
phone users.We then extract the social network structure by
measuring the communication patterns among cell-
phone users. Social ties (links) are established
between users (nodes) who have at least one
reciprocal contact during the study period. The asso-
ciated tie strength is measured as the total number
of calls or text messages. Note that we only retain
reciprocal contacts because some of the one-way
communications do not necessarily reflect human
interactions (e.g., robocalls). Performing this step
gives us a social network with a skewed degree distri-
bution (Figure 1B). The average and median number
of social contacts per person are 9.7 and 7.0,
respectively.
Embedding Social Network into Geographic Space
We embed the social network into geographic
space based on the spatial properties of the nodes.
Previous studies have suggested that social ties are
more likely to be observed at shorter distances,
because individuals tend to interact more with their
spatial neighbors (Goldenberg and Levy 2009;
Scellato et al. 2011). One usual practice, therefore,
is to assign a “home location” to users to embed
nodes into geographic space (Scellato et al. 2011).
This study adopts this strategy by first estimating the
home location of each phone user. The estimated
location is then used as the node property for spa-
tial embedding.Inferring home location from CDR data has been
investigated extensively (Ahas et al. 2010; Isaacman
et al. 2011; Xu et al. 2015; Xu et al. 2017). In this
study, we adopt the method from Xu et al. (2017),
which estimates each user’s home location as the
most used cell phone tower before 06:00 and after
Figure 1. (A) The distribution of number of active days of users. (B) Degree distribution of the extracted social network.
4 Xu, Santi, and Ratti
19:00. After performing the home location estima-
tion, we compute the number of phone users in each
planning area of Singapore1 and correlate it with the
official census population from the Singapore
Department of Statistics (2020). As shown in Figure
2A, we observe a strong correlation between the two
variables, which indicates the robustness of the esti-
mation. Following this step, we perform the spatial
embedding by assigning users to their estimated
home cell phone towers (Figure 2B).
Extracting Social–Spatial Properties of theEmbedded Network
We introduce two indicators, namely, the normal-ized communication intensity and friendship probability,to investigate the spatial properties of social network
connections. Given any two cell phone towers Liand Lj in the embedded network, the normalized
communication intensity between them, IðLi, LjÞ, is
defined as the total communication intensity among
all phone users concerned, normalized by the total
possible friend pairs between these two locations:
IðLi, LjÞ ¼ StrengthðLi, LjÞNðLiÞ �NðLjÞ : (1)
Here StrengthðLi, LjÞ denotes the total number of
calls or text messages exchanged between phone
users assigned to Li and Lj. Note that within-cell
communications are not counted. NðLiÞ and NðLjÞrefer to the total number of phone users (nodes)
assigned to Li and Lj, respectively. In other words,
NðLiÞ �NðLjÞ describes the total possible social links
that can be established between the two locations.IðLi, LjÞ measures the likelihood of communica-
tions between a pair of locations, and the value is
largely affected by the tie strength, or the communi-
cation frequency between social links. Therefore, we
compute another measure, the friendship probability,
by considering only the presence of social ties:
FðLi, LjÞ ¼ TiesðLi, LjÞNðLiÞ �NðLjÞ : (2)
Unlike other online social networks (e.g., Facebook)
in which social ties are well defined, cell phone
communications can only provide an indication of
people’s social relationships. To address this chal-
lenge, we define social links as cell phone user pairs
with at least one reciprocal contact during the study
period. Although this is not a perfect measure, a pre-
vious study based on large-scale telecommunication
data suggests that a significant proportion of phone
users with at least one reciprocal contact have
shared the same place with each other at the same
time (Calabrese et al. 2011). These colocation pat-
terns are indicative of coordination calls and face-to-
face interactions. Therefore, the definition of social
links here provides a reasonable proxy of existing
Figure 2. (A) By aggregating phone users based on their estimated home location, we compute the number of users at the level of
Singapore’s planning area. The numbers are highly correlated with the official census population (Pearson’s r¼ 0.96, p value < 0.001).
(B) The social network is embedded into geographic space by assigning phone users to their home cell phone tower (Voronoi cells are
used to approximate towers’ service areas).
Beyond Distance Decay 5
social ties between phone users and also excludes
one-way communications (e.g., advertisements, robot
calls) that do not reflect interpersonal relationships.Thus, TiesðLi,LjÞ in Equation 2 denotes the total
number of social links between phone users assigned to
Li and Lj. Because the distance between cell phone
towers can be easily computed, the two indicators (Iand F) can thus be used to examine the spatial proper-
ties (e.g., distance decay) of social network connections.
Incorporating Socioeconomic Characteristicsof Locations
To evaluate the impact of locations’ socioeconomic
similarities on the social network structure, we con-
sider another housing price data set. The data set,
which is acquired from a private company (99.co
2012) in Singapore, includes information of thousands
of residential properties collected between 2011 and
2012. Each record in the data set documents the infor-
mation of a single housing property, such as the prop-
erty type (condo, landed, or Housing Development
Board [HDB]2), geographic coordinates (latitude and
longitude), and the total sale price of one housing
unit. Because users are assigned to their home loca-
tions, the housing price data set can be used to reflect
the socioeconomic characteristics of places and the
corresponding phone users.We use the housing price data set instead of
income data collected by census because individual
housing properties provide a fine-grained view of the
socioeconomic characteristics of the places. The data
set can be well integrated with the spatial social net-
work at the cell phone tower level. The income data
from the census are usually reported at a coarser resolu-
tion and cannot capture well the spatial heterogeneity.
Before we use the data set to label locations in
the network, we perform a correlation analysis
between housing price and income at the level of
planning areas. The income data are acquired from
the 2012 Household Interview Travel Survey
(HITS) provided by the Singapore Land Authority
(2012). By extracting individuals from HITS who
reported their monthly income (12,111 in total), we
compute the average monthly income of respondents
in each planning area. We then compute the average
sale price of housing units in each area. We find that
the two variables match each other relatively well
except for a few outliers (Figure 3A). Through further
exploration, we think this inconsistency is partially
caused by the sampling bias during the household
interview survey. For example, only two respondents
were sampled in Southern Islands and both of them
reported a monthly income of 500 Singapore dollars
(SGD). The island is well known for its many luxury
residential neighborhoods, however. After removing
these three outliers, the Pearson’s correlation coeffi-
cient between the two variables increases to 0.88 (p <0.001), which suggests that housing price could well
indicate the socioeconomic level of places (Figure 3B).In this study, we use the average housing price to
label each cell phone tower. Because cell phone
Figure 3. (A) The relationship between mean housing price and average monthly income at the level of Singapore’s planning area. (B)
The correlation between the two variables after removing the three outliers. Note: SGD¼Singapore dollars; HITS¼Household
Interview Travel Survey.
6 Xu, Santi, and Ratti
towers are point features, we use Voronoi cells to
approximate their service areas (Figure 2B). We
then identify the housing properties that fall within
each cell and compute the average housing price to
label the corresponding cell phone tower. After this
step, each cell phone tower Li will be labeled using a
housing price value PrðLiÞ: This value empowers us
to examine the normalized communication frequency
and friendship probability between places with vary-
ing socioeconomic characteristics. Note that for
each Voronoi cell we have computed the standard
deviation of the housing price values (within-cell
standard deviation), and compared it with the over-
all standard deviation of the city. We find that the
median ratio of within-cell standard deviation and
overall standard deviation is 0.16. This result sug-
gests that housing price values are relatively homo-
geneous within the Voronoi cells and our approach
could capture the heterogeneity of residential hous-
ing prices in Singapore.
Results
Distance Decay Effect of Cell PhoneCommunication Network
In this section, we examine the distance decay
effect of the cell phone communication network.
Following the definitions of IðLi, LjÞ and FðLi, LjÞ,we measure normalized communication intensity and
friendship probability by aggregating pairs of cell
phone towers separated at different distance values
(d). The functions of I(d) and F(d) allow us to
explore the impact of geographic distance on the
network structure. As shown in Figure 4, both func-
tions show a linear trend at the log–log scale, which
indicates that each of the two variables (I(d) and
F(d)) and geographic distance (d) generally follow a
power law. Fitting the two functions yields an expo-
nent of �0.82 and �0.74, respectively. In particular,
the likelihood of cell phone communications among
people who live at a distance of d follows a distance
decay IðdÞ � d�0:82, whereas the probability of social
ties at a given distance follows FðdÞ � d�0:74: Note
that the observed exponents (�0.82 and �0.74) are
larger than the ones derived from some other studies
using online social networks. For example, a study
finds that friendship probability observed from the
LiveJournal network follows a distance decay
pðdÞ � d�1:2 (Liben-Nowell et al. 2005). Another
study based on Facebook data found that friendship
probability is inversely proportional to geographic
distance pðdÞ � d�1:0 (Backstrom, Sun, and Marlow
2010). Compared to these online social networks,
cell phone communications observed in this study
decay more slowly with geographic distance.The distance decay effect suggests that cell phone
communications (I) or social connections (F) are
more likely to occur among people whose residences
are close to each other. An intuitive interpretation
of IðdÞ � d�0:82 is that neighborhoods separated at a
distance of 10 km tend to exhibit only 15 percent
Figure 4. (A) Normalized communication intensity decays with geographic distance. Fitting the data with a power law function yields
IðdÞ � d�0:82: (B) The probability of friendship also shows a distance decay effect, FðdÞ � d�0:74:
Beyond Distance Decay 7
(10�0:82 � 0:15) of the communication strength
compared to neighborhoods that are 1 km apart.
Similarly, friendship probability between neighbor-
hoods decreases to 18 percent (10�0:75 � 0:18) whendistance reaches 10 km. Note that I(d) decays faster
than F(d), meaning that people tend to preserve
more friendship with distance. The intensity of com-
munication with these friends, however, is weaker
than that with closer friends (i.e., “good friends are
close to home”).The distance decay effects have notable implica-
tions for socioeconomic segregation in cities. If a
city has a high level of residential segregation—
namely, residents with similar socioeconomic charac-
teristics tend to live close to each other—the city is
likely to have a certain level of communication (or
social network) segregation. In other words, informa-
tion tends to spread among similar others in a city
with severe residential segregation.
To better understand the spatial configuration of
housing prices in Singapore, we measure the spatial
autocorrelation based on the average housing price
derived at the Voronoi cells (Figure 5A). In particu-
lar, we compute the global Moran’s I using the built-
in function provided by ESRI’s ArcGIS product. We
use Euclidean distance to measure the distance
between cells and the inverse distance method to
conceptualize their spatial relationships. As shown
in Figure 5B, the analysis yields a Moran’s index of
0.29 with a z score of 68.63. This indicates that
housing prices—which highly reflect the income
level of residents (Figure 3B)—are highly clustered.
The clustering patterns suggest that neighborhoods
with similar housing price values are generally closer
than dissimilar ones. Given the distance decay effect
of cell phone communications, the clustering pat-
terns would imply more interactions between these
similar neighborhoods, which contributes to a cer-
tain level of communication segregation.
Impact of Socioeconomic Characteristics onCommunication Intensity
Previous studies have discussed the existence of
homophily in social networks, namely, people’s
social connections tend to be homogeneous with
regard to many sociodemographic characteristics
(McPherson, Smith-Lovin, and Cook 2001). Given
the distance decay of cell phone communications
observed from the mobile phone data set, an intrigu-
ing question is whether people tend to connect with
similar others when geographic distance is con-
trolled. Although this cannot be investigated at an
individual level due to lack of personal socioeco-
nomic data, we examine whether places with similar
housing prices would have relatively more interac-
tions with each other than what would be predicted
by a distance decay effect.To achieve this, we sort the Voronoi cells based
on the average housing price derived previously. We
Figure 5. (A) The spatial patterns of average housing price at the level of Voronoi cells. (B) Global Moran’s I is computed over the
housing prices at these Voronoi cells. The analysis and report are derived from ESRI’s ArcGIS product.
8 Xu, Santi, and Ratti
divide them into five classes such that each class ofcells covers 20 percent of the population (i.e., phoneusers). We label them from C1 to C5, with averaging
housing price sorted in ascending order. In otherwords, C1 denotes areas with the lowest averagehousing price and C5 generally points to the rich
neighborhoods. We adopt this classification methodinstead of other alternatives (e.g., separating the top1 percent of population from others) such that each
class covers adequate amounts of phone users orVoronoi cells. It ensures that we have enough obser-vations of cell phone communications among differ-
ent classes at varying distance values.For each pair of class Ci and Cj, we measure their
normalized communication intensity at different dis-tance values. Figure 6 shows the results. Each sub-
plot demonstrates the communication intensity fromeach class to the five classes. Similar to the findingin Figure 4A, the communication intensity between
classes decays with geographic distance. Interestingly,though, when looking at the interactions among clas-ses, we find that cells with similar housing prices tend
to have higher communication intensities when dis-tance is controlled. For instance, C1 tends to interactmore with their own or nearby classes at a variety of
distance values (Figure 6A). This homophily effect iseven more obvious when looking at C5 (Figure 6E),which consistently maintains the highest level of
interaction within their own class.To further elaborate this, we visualize, for each
class, the classes that have the most and second
most interactions with them at different distancevalues. The results are shown in Figure 7. As can beseen, C1 and C2 tend to interact more with theirown or nearby classes at most of the distance values.
Again, class C5 exhibits a relatively stronger homo-phily effect compared to other classes. When dis-tance is being controlled, these places will always
Figure 6. Normalized communication intensity among the five classes.
Beyond Distance Decay 9
have the strongest interactions with their peers.
Class C4 presents a pattern that is different from the
other classes. We find that those in class C4 do not
exhibit the highest level of interaction with them-
selves. Rather, they tend to interact more with clas-
ses one or two steps downward. It is possible that
C4, which points to many people in the upper mid-
dle class, tends to interact more with lower socioeco-
nomic classes. For instance, many occupations that
are well paid (e.g., doctors, lawyers) have frequent
communications with different socioeconomic tiers.
For class C5, however, which points more to the
extreme wealth, a clear “rich club” effect can be
observed. Summarizing, we can conclude that,
although homophily seems to have a significant
effect on the intensity of communication, other
factors such as social structures are likely to have a
significant, and possibly heterogeneous across social
classes, effect as well.
Formation of Social Ties
The communication intensities among the five
classes have demonstrated the impact of homophily
on the social network structure. Another interesting
question is whether the formation of social ties
would follow the homophily principle. To investi-
gate this question, we perform another analysis by
replacing communication intensity (I) with friend-
ship probability (F), the measure that describes the
formation of social ties. By deriving the friendship
probability among the five classes at different
Figure 7. The classes that interact most and second most with each of the five classes at a given distance. The size of the dot is
proportional to the normalized communication frequency between the corresponding classes.
10 Xu, Santi, and Ratti
distance values, we find that the effect of homophily
still persists but only when geographic distance is
relatively short (Figure 8). Strikingly, when distance
increases to a large value (e.g., over 10 km), the clas-
ses that have the highest friendship probability with
a given class tend to be C4 or C5. This observation
is reaffirmed by Figure 9, which demonstrates the
classes that have the highest and second highest
friendship probabilities with each of the five classes
at a given distance.The results reveal an interesting aspect of social
dynamics beyond the homophily principle. When
people’s residencies are far away from each other,
the upper classes in the society are more likely to
know or to be known by others. In other words, the
formation of “long-range” ties tends to favor privi-
leged people. Again, this might be related to the
occupations of the upper classes as well as the over-
whelming attention they receive from other social
groups. For example, it is difficult for someone to
connect with a regular person who is geographically
distant. It is easier for a famous or rich person to be
known by others regardless of where he or she
resides in a city, however. This also connects to
Milgram’s (1967) small-world experiment and the
theory of six degrees of separation. Namely, it is
enough to have a “famous” friend reasonably close to
be able to reach many other people in the world.
Our results suggest that these “famous” and well-con-
nected people are likely to be rich.Note that although the formation of long-range
ties tends to favor the upper classes, the intensities
of cell phone communications at large distances are
still higher among similar social classes (shown in
Figure 6 and Figure 7). This indicates that for the
wealthy populations, their connections with the
middle and lower classes are more likely to be weak
ties (Granovetter 1977) and the majority of their
interactions are still with similar others (e.g., other
rich people).
Figure 8. Friendship probability among the five classes.
Beyond Distance Decay 11
Homophily Distance
The results presented so far have demonstrated
the joint impact of geographic distance and homo-
phily on people’s cell phone communications. Given
this, it is possible that two neighborhoods with simi-
lar socioeconomic characteristics—but geographically
distant—could have a higher communication inten-
sity than two close neighborhoods with different
characteristics. Figure 10A shows an example of this
scenario. To explicitly quantify this effect, we adopt
the concept of homophily distance (Xu et al. 2019)
and compute this metric between two classes. Given
two classes Ci and Cj, the homophily distance Dh is
defined as the geographic distance such that the
communication intensity between Ci and its peers
(Ci) at Dh is roughly equal to the communication
intensity between Ci and Cj at the minimal distance
(i.e., when they are in close proximity). A largevalue of Dh suggests that Ci would overcome thefriction of geographic distance to communicate with
similar others. Here, we define the minimal distanceas 1 km to reflect the concept of close proximity. Tocalculate Dh of Ci (from class) and Cj (to class), we
fit a linear function of communication intensity withdistance at the log–log scale (Figure 6). The pointwhere the communication intensity at the minimal
distance (1 km) intersects with the fitted line givesthe value of Dh.
We compute Dh for all combinations of classes.The results are shown in Figure 10B. Almost all
values are above 1 km, indicating that places of thesame class tend to maintain an adequate level ofcommunication even when they are far apart. For
Figure 9. The classes that have the highest and second highest friendship probabilities with each of the five classes at a given distance.
The size of the dot is proportional to the friendship probability between the corresponding classes.
12 Xu, Santi, and Ratti
instance, the homophily distance from C1 to C5 is
2.25 km, meaning that the communication intensity
between C1 and its peers that are Dh ¼ 2.25 km
away is comparable to the intensity between C1 and
C5 at a distance of 1 km. This homophily effect is
more pronounced when looking at the value from
C5 to C1 (Dh ¼ 3.75 km). Note that the five classes
are defined using the average housing price at the
Voronoi cells and some of them could point to
mixed-income neighborhoods. Thus, the homophily
distances might be even higher if measured at the
household or individual level. We are not able to
measure this, however, due to lack of individual-
level socioeconomic data. The results suggest that
colocation or geographic proximity does not always
ensure frequent communications. The socioeconomic
similarity between places and the underlying popula-
tions plays an equally important role in shaping the
structure of the cell phone communication network.
Discussion and Conclusion
In this study, we establish a spatially embedded
social network by coupling large-scale information
on people’s cell phone communications, residential
locations, and socioeconomic characteristics. The
findings suggest that cell phone interactions of peo-
ple in Singapore are affected by not only geographic
proximity but also how social groups are distributed
in the urban environment. We argue that the spatial
organization of social groups in a city, which is often
directed by urban planning policies (e.g., zoning
strategies; Jacobs 2016), will have a direct impact on
how people communicate in the virtual or
online space.By embedding phone users into urban space based
on their estimated residence, we explore the geo-
graphic properties of the cell phone communication
network. The results show that both communication
intensity and friendship probability among places fol-
low a power law decay with geographic distance.
That means that communications are more likely to
occur among people who live close to each other.
By further exploring the average housing price across
places—which highly reflects the income level of
residents in Singapore (Figure 3)—we find that the
housing price values are highly clustered (Figure 5).
Such an uneven distribution along with the distance
decay effect tends to cause an imbalance of cell
phone communications among social classes. The
results indicate that physical separation of social
groups in a city (e.g., residential segregation) will
have a direct impact on shaping communication or
social network segregation.By further examining cell phone connections
among places with different housing price values, we
Figure 10. (A) Given the effect of distance decay and homophily, it is possible that two neighborhoods with similar socioeconomic
characteristics but geographically distant could have an even higher communication intensity than two close neighborhoods with
different characteristics. (B) The value of homophily distance for all combinations of classes.
Beyond Distance Decay 13
find that it is not only geographic proximity but also
the principle of homophily that govern people’s cell
phone communications. In particular, places tend to
have a higher communication intensity with ones that
have similar housing price values when distance is con-
trolled (Figure 6 and Figure 7). This homophily effect
is reaffirmed by looking at the homophily distances
among social classes (Figure 10). For instance, the com-
munication intensity between the upper class (C5) and
its peers at a distance of 3.75km is comparable to the
level between C5 and the lowest class (C1) who are
immediately nearby. That means that social classes
would overcome the friction of distance or resist the
“convenience of colocation” to connect with similar
others. Note that we also observe this homophily effect
when examining friendship probability, the indicator
that describes the formation of social ties (Figure 8).
Interestingly, though, the homophily effect is observed
primarily at short distance values, or across all distance
values for the upper class C5. When distance is large,
the middle upper classes (C4 and C5) are always the
ones that have the most connections with other socio-
economic tiers (Figure 9). The result reveals a
“celebrity effect” on the formation of social ties.The findings on the homophily effect suggest that
neighborhoods with similar characteristics, even
when they are far apart, could contribute to the
emergence of social network segregation. Therefore,
traditional placed-based measures, such as creating
mixed-income neighborhoods, might not be enough
per se to accomplish a high degree of social mixing
in the online space. Novel online activities that can
actively bridge different social classes can possibly
promote social cohesion of cities given the preva-
lence of social media platforms and the recent public
health emergency (COVID-19; Oliver et al. 2020)
that further restricts physical human interactions.Our study suggests that geographic proximity and
homophily are two notable forces that jointly shape the
structures of social networks. Although this study
focuses on Singapore, we believe these two forces have
a far-reaching impact on human interactions in cities.
Because classic spatial interaction models (e.g., gravity
models) have a specific focus on modeling the distance
effect, future work that aims to model or explain spatial
social networks could incorporate socioeconomic char-
acteristics as a generic factor.We want to point out a few limitations of this
research. First, social ties in this study are defined as
cell phone user pairs with at least one reciprocal
contact during the study period. Although this mea-
sure, as suggested by a previous study in Portugal
(Calabrese et al. 2011), was indicative of face-to-
face interactions and therefore some sort of social
relationships, this evidence does not immediately
generalize to the city of Singapore, which is the sub-
ject of this study. Hence, we acknowledge that the
definition based on reciprocal phone contact pro-
vides a coarse indication of social ties in Singapore.
Second, social interactions in this study are mea-
sured using phone calls and text messages. Although
they accounted for a notable fraction of human com-
munications in 2011 (when the data set was col-
lected), people in Singapore were adopting social
media (e.g., Facebook, Twitter) at that time as new
channels of social interactions. In the future, it
would be meaningful to examine the robustness of
the findings by incorporating social media usage
(Crandall et al. 2010; Kumar, Novak, and Tomkins
2010; Xi, Calder, and Browning 2020) into the anal-
ysis (e.g., Twitter mentions and follower–followee
relationships). For instance, a recent work based on
geolocated Tweets (Heine et al. 2021) observed a
certain degree of mobility homophily in the city of
Stockholm, hinting at a possible robustness of our
findings to social media data sets. Third, this study
uses housing price as the variable to account for
homophily. There exist other factors, such as ethnic-
ity, that would affect people’s communication pat-
terns. Because our analysis is conducted at the cell
tower level, we are not able to obtain information
on ethnicity groups at such a fine spatial resolution.
Fortunately, the Singapore government introduced
the Ethnic Integration Policy (EIP) in 1989 for
HDB estates. The EIP sets limits on the total per-
centage of a block or neighborhood that can be
occupied by a certain ethnicity. Given that HDB
estates host more than 80 percent of residential pop-
ulation in Singapore, the EIP tends to neutralize the
impact of ethnic segregation on our results. We do
think it is important, though, to consider these
socioeconomic variables in future works (e.g., eth-
nicity and education background) to depict a more
holistic picture of homophily in spatial
social networks.This study demonstrates the importance of con-
ceptualizing and modeling social networks in geo-
graphic space (Andris 2016). It also calls for more
efforts on coupling physical and virtual (online)
spaces for studying human dynamics (Shaw and Sui
14 Xu, Santi, and Ratti
2020). Although exploratory in nature, this study
points to a few avenues for future research. For
instance, it would be meaningful to incorporate
socioeconomic similarity of places into spatial inter-
action models (Zipf 1946; Jung, Wang, and Stanley
2008; Simini et al. 2012) to better predict structures
of spatial social networks. It is also possible to detect
changes of socioeconomic environments (e.g., gentri-
fication) in cities by monitoring the interactions
among neighborhoods and how they evolve through
time and space (Zhu et al. 2020).
Acknowledgments
The authors thank Dr. Ling Bian and the
reviewers for their valuable comments and sugges-
tions that improved this article.
Funding
This research was jointly supported by the
Research Grant Council of Hong Kong (No.
25610118) and the Hong Kong Polytechnic
University Startup Grant (Project Code 1-BE0J).
ORCID
Yang Xu http://orcid.org/0000-0003-3898-022XPaolo Santi http://orcid.org/0000-0002-8942-8702
Notes
1. Planning areas, also known as DGPs, are the primarycensus divisions of Singapore created by the UrbanRedevelopment Authority (URA). There were a totalof fifty-five planning areas in Singapore at the timewhen the CDR data were collected (see https://en.wikipedia.org/wiki/Planning_Areas_of_Singapore).
2. HDB is a type of residential housing property thatis publicly governed and developed in Singapore.The HDB flats were built primarily to provideaffordable housing.
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YANG XU is an Assistant Professor in the
Department of Land Surveying and Geo-Informatics
at the Hong Kong Polytechnic University, Hung Hom,
Kowloon, Hong Kong. E-mail: [email protected] research interests include GIScience, human mobil-ity, and urban informatics.
PAOLO SANTI is Principal Research Scientist at
the MIT Senseable City Lab, Cambridge, MA.E-mail: [email protected]. There he leads the MIT/Fraunhofer Ambient Mobility initiative. He is also a
Research Director at the Istituto di Informatica eTelematica, CNR, Pisa, Italy. His research interest isin the modeling and analysis of complex systemsranging from wireless multihop networks to sensor
and vehicular networks and, more recently, smartmobility and intelligent transportation systems.
CARLO RATTI is a Professor and Director of the
MIT Senseable City Lab at the MassachusettsInstitute of Technology, Cambridge, MA. E-mail:[email protected]. He is also a founding partner of theinternational design office Carlo Ratti Associati.
Beyond Distance Decay 17