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nature cities
Perspective

https://doi.org/10.1038/s44284-023-00019-z

Defining a city: delineating urban areas using
cell-phone data
Received: 26 June 2023
Accepted: 4 December 2023
Published online: xx xx xxxx
Check for updates

Lei Dong 1, Fabio Duarte 2, Gilles Duranton3, Paolo Santi 2,4 ,Marc Barthelemy5,6, Michael Batty 7, Luís Bettencourt 8,
Michael Goodchild 9, Gary Hack3,10, Yu Liu 1, Denise Pumain 11,
Wenzhong Shi12, Vincent Verbavatz5, Geoffrey B. West13, Anthony Yeh& Carlo Ratti2

14What is a city? Researchers use different criteria and datasets to define it—from population density to traffic flows. We argue there is one dataset that
could serve as a proxy of the temporal and spatial connections that makecities what they are: geolocated data from the world’s more than 7 billion
cell-phone users. Cell-phone data are a proxy of people’s presence in a given
area and of their movement between areas. Combined with computational
methods, these data can support city delineations that are dynamic,
responding to multiple statistical and administrative requirements, tailoredto different research needs, thus accelerating ongoing work in urban
science.

Q1

The first cities emerged more than 5,000 years ago in ancient Sumeria,
where the agricultural surpluses led to the creation of marketplaces that
formed the seeds of an embryonic urban economy based on exchange1.
Cities grew up around these marketplaces, where populations serving their agricultural hinterlands were packed in close proximity sothat the costs of distribution could be minimized, and fortifications
were built to keep the city intact from invaders intent on capturing themarket and its resources. Until the Industrial Revolution, most cities
remained small, with the biggest barely exceeding a million people.
It took the invention of mechanical transportation technologies forcities to begin to exceed this limit for the first time. By the end of thenineteenth century, London had grown to over 6 million people and
New York to over 4 million people2. As a key factor, transportation andtechnological advances have further broken the historical boundaries
of cities. Populations began to spread out into their hinterlands, blurring the line between urban and rural. By the middle of the last century,
some large cities had begun to fuse with one another, creating megacities such as on the United States’ eastern seaboard3, while more recent

growth has led to urban complexes such as China’s Greater Bay Area,
which now exceeds 86 million people.
Q2 Q3
From a qualitative perspective, many scholars have addressed thequestion of ‘What is a city?’4,5; and from a quantitative perspective, in Q4 Q5
the 1960s, Berry developed the delineation of metropolitan areas using
Q6
commuting flows6,7, and the current boundaries of metropolitan areasin the United States and some other regions and countries are still basedon this methodology8,9. Morerecently, the United Nations Human
Settlements Programme (UN-Habitat) published a report under thepremise that, to achieve the Sustainable Development Goals, we needto propose solutions to key urban challenges, and to do so, we needa clear and globally agreed definition of what a city is10. This reportdiscusses two definitions: one defines the city by its urban extent, anduses satellite imagery to identify the morphology of human settlements
and the density of built-up structures; another defines the city by its
degree of urbanization11, based on population (density) using grid cells,
which is also endorsed by the United Nations Statistical Commission12.
Although laudable, two challenges still remain: one definition is based

Institute of Remote Sensing and Geographic Information Systems, School of Earth and Space Sciences, Peking University, Beijing, China. 2Senseable City
Laboratory, Massachusetts Institute of Technology, Cambridge, MA, USA. 3University of Pennsylvania, Philadelphia, PA, USA. 4The Institute of Informatics
and Telematics CNR, Pisa, Italy. 5Université Paris-Saclay, CNRS, CEA, Institut de Physique Théorique, Gif-sur-Yvette, France. 6Centre d’Analyse et deMathématique Sociales (CNRS/EHESS), Paris, France. 7University College London, London, UK. 8University of Chicago, Chicago, IL, USA. 9University ofCalifornia Santa Barbara, Santa Barbara, CA, USA. 10Massachusetts Institute of Technology, Cambridge, MA, USA. 11Université Paris 1 Panthéon-Sorbonne,
Paris, France. 12Hong Kong Polytechnic University, Hong Kong, China. 13Santa Fe Institute, Santa Fe, NM, USA. 14Hong Kong University, Hong Kong, China.
e-mail: psanti@mit.edu
1Nature Cities

Perspectiveon physical features and the other on granular population data, andneither consider flows—which we will discuss later. UN-Habitat also
pointed out that to operationalize any local or global policy, we needtimely data and metrics.
Unprecedented geospatial datasets, increased processing power
and recent advances in computational methods are now providing
opportunities to expand our understanding of cities, and to make thedelineation of cities more accurate and timely. In fact, a new scienceis rapidly emerging. Starting from such datasets and methods, it aims
to quantitatively describe cities and systems of cities13–20. Despite the‘discovery’ of some relatively robust urban laws (for example, gravity,
allometric scaling and rank-size), we are still at the very beginning of
elaborating this new science of cities, and what is still missing is a widely
accepted and thoroughly discussed methodology to delineate a city.
This Perspective discusses how scholars and policy officials havebeen making efforts to reach theoretically sound and operational definitions of the city; the challenges that these efforts are still facing; andhow the use of global, standardized datasets such as cell-phone records,
coupled with rigorous guidelines and methods for delineating cities
informed by such datasets, can help make substantial steps towards
widely agreed city delineations for urban science. A key argument of
this paper is that there is an essential feature that could unify the mostwell-accepted definitions of cities: the presence and flows of people. In
addition, we propose cell-phone data as a possible dataset representing a universal proxy for the presence and flows of people that definecities. After all, as Shakespeare said: “What is the city but the people?”(Coriolanus, Act 3, Scene 1).

Existing definitions

Before moving forward, we must pose an important clarification ofterminologies: ‘definition’ refers to the meaning, or how we explain
something; whereas ‘delineation’ refers to how we establish the boundaries of something—in our case, the definition is the set of rules one
applies and the delineation is the city boundaries resulting from theimplementation of these rules.

Definitions based on administrative boundaries
The administrative divisions traditionally used to delineate cities are
based on very different parameters. For example, Brazil has 5,570
municipalities, 68% of which have fewer than 20,000 inhabitants,
and Barcelos, slightly above this threshold, has an area larger thanNorth Korea or New York State; however, there are only about 300
prefecture-level cities in China, with an average population of nearly
4 million people21. These vastly different administrative delineationsof cities in different regions pose a major challenge for comparative
studies on a global scale.
To tackle this issue, national or transnational statistical offices
have long used quantitative definitions of metropolitan areas. One
common definition of a metropolitan area consists of core urban areasand commuting zones surrounding the center. From a labor market
perspective, this dependency is usually represented by a combination of population and commuting trips. For example, core-based
statistical areas (CBSAs) in the United States are defined by startingfrom a county containing a city of 10,000 to 50,000 (micropolitan
areas) or at least 50,000 (metropolitan areas) inhabitants, which grows
to encompass surrounding counties based on criteria that combine
population density and a minimum threshold of commuting flow to
the main city8. Using this definition, over 900 CBSAs are identified in
the United States, with New York–Newark–Jersey City being the largest,with over 20 million inhabitants.
In China, a quantitative definition of metropolitan areas was notavailable until very recently22. According to China’s National Development and Reform Commission, metropolitan areas are centered on
megacities (10 million people or more) or large cities (5 million) and arebounded by a 1-hour commuting buffer. With this high-population-size
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https://doi.org/10.1038/s44284-023-00019-z

criterion, the number of metropolitan areas in China is significantly
fewer than in the United States or the European Union (EU).
In an effort to facilitate international comparison, metropolitan
areas in the EU are defined using the notion of functional urban areas(FUAs)23,24. According to this definition, one must first identify an ‘urban
center’ based on a minimum total population of 50,000 and additional
density requirements. Then, surrounding centers are added to the
FUA based on a combination of population size and commuting flow
requirements. Following this definition, 828 FUAs are identified in the
EU, Switzerland, Iceland and Norway, with Paris being the largest witha population of over 13 million inhabitants.
While created to facilitate comparison, city definitions basedon fixed thresholds on population, density and so on, such as FUA,
address the problem of city delineation as a top-down, ‘one-size-fits-all’approach, which might imply, for instance, that the capital of a small
country such as Liechtenstein is not even considered a city. The notionof FUA also requires access to multiple data sources such as residential
and nighttime population, and commuting flows, which might further
hinder the wide application of such an approach to city delineation.
What is lacking then is a systematic methodology for determining
parametric thresholds (for example, total population, population
density and volume of commuting flows) to be used in combination
with universally accessible datasets.

Recent advances
With the advent and availability of granular geospatial data, newproposals and techniques of city delineation have emerged25,26. They
mostly fall into two categories, which we summarize as form-based
and function-based delineations.
Form-based approaches start by classifying the basic spatial unit
(for example, a geographic grid) as urban or non-urban using population, buildings, built-up area or nighttime light intensity, and thendefine cities as continuous urban units27–30. For example, it has beensuggested that a city is defined as a continuous cluster of more than X
inhabitants and/or Y nighttime light intensities. The choice of X and Y,
however, varies considerably among the different studies. Even when
the choice is made using statistical thresholds29, the arbitrariness is
reduced but not eliminated.
Function-based approaches start from the observation that areas
through which a significant fraction of people move within a given timeshould be considered part of the same city.In this case, the definitionof a city as a network of socioeconomic relationships can be proxiedby flows of people and goods within a certain space. This approach isespecially relevant to the complex network community, which seeks
to define and characterize cities as evolving networks of exchange
and interaction17,18. Examples of function-based delineations include
megaregions in the United States identified by commuting flows31,
metropolitan areas in Switzerland32 and functional areas in China33–35.
As mentioned earlier, whenever the notion of flow is involved, data canbecome a serious limitation.
Notably, the availability of remote-sensing imagery coupled withincreased computational power has led to the emergence of many
land classification studies in recent years36. These studies typicallyuse supervised machine learning models to perform classification of
remote-sensing data and label pixels of built-up areas as an importantland-use class37,38. Although land classification uses so-called groundtruth to determine whether a given pixel is urban (for example, buildings and roads) or not (for example, forest and rivers), deriving a delineation of the city as a whole from this information requires additional
analytical steps. For example, while the pixels of built-up areas identified by remote-sensing imagery need to be aggregated to define a city,
we must also determine how much of the contiguous built-up area isa city, and whether parks and green spaces, which are often classified
as non-built-up areas, are part of the city. More importantly, satellite
imagery mainly captures the physical and built environment of cities,

Q7

Perspective

https://doi.org/10.1038/s44284-023-00019-z

Box 1

Box 2

Drawbacks of existing city
definitions

Criteria for good city
definitions(1) There is a multiplicity of levels of administrative boundaries fromwhich it is hard to choose, and what each of these levels capturesdiffer across countries and even within countries.
(2) Both form-based and function-based approaches require somearbitrary parameters.
(3) Function-based definitions require data that were not readily
available before, especially for developing countries.
(4) Given the above points, it is very difficult to perform crossregional and cross-country comparisons between cities basedon existing definitions.

(1) A city definition should be easy to understand and easy to apply
by researchers and practitioners in the field.
(2) The data on which a city definition is built upon must be
universal, easy to access and self-explanatory.
(3) It should consider both urban form and function, which are theessential elements of a city.
(4) A definition should be based on careful control of the involved
parameters. Parameter choices should be clearly motivatedand, where possible, data driven, to avoid arbitrary choices. In
some cases, data-driven parameter setting might render themendogenous, thus making the city definition parameter free.
(5) The city delineations resulting from a definition should seeksome form of validation based on a procedure that should be
general and widely accepted by the urban science community.
Preferably, this procedure should include one or morequantitative criteria to assess the quality of a definition.
(6) Depending on the case studied, city delineations resulting
from a definition might be later combined with administrative
boundaries.

and it is difficult to estimate the movement of people in the city andthe resulting socioeconomic changes, which are arguably more criticalto defining cities.
The drawbacks of existing city definitions based on administrative
boundaries or solely on morphological or flow criteria are summarized
in Box 1.

Requisites of a good definition
To allow for comparative and universal analysis, we advance somecriteria for defining cities that could be widely accepted by the urban
science community. On the basis of the above discussion, and building
on previous work39,40, we propose six criteria, as shown in Box 2.
The first criterion states that the principles on which a city definition is based should be easy to understand by a non-specialized
audience. Also, the data processing and implementation procedures
used to empirically test this definition should be easily replicable, sothat a definition can be used in different contexts and by people withdiverse backgrounds and know-how. Note that it is quite common thata conceptually clean definition translates into highly non-trivial dataprocessing and implementation issues. In such cases, these non-trivial
procedures should be made open access and adequately documented
to facilitate use for as wide an audience as possible.
The second criterion describes the desirable characteristics ofthe dataset(s) on which a city definition should be based. By universal, we mean that the type of data used to ground a definition should
not be specific to or unique to a particular geography or country, butshould, to the maximum extent possible, be available in all cities. For
example, considering data related to the movement of people in thecity, a dataset pertaining to a specific travel mode would be useful only
for the definition of cities where such a specific travel mode exists.
Besides being universal, the datasets that can be used to delineate a city should be relatively easy to access. Ideally, one should
use data that are publicly available. Such wide accessibility would
allow any researcher, scholar or practitioner to collect and apply
the necessary data to delineate a city within its geography of interest. However, publicly accessible data are typically highly aggregated for reasons related to storage and/or computing costs as wellas privacy concerns, and do not have the granularity necessary for use
in quantitative city definition. Data with higher granularity require
extensive resources for storage and processing, are highly valuable
to the entity that generated or acquired them, and may raise highprivacy concerns. For these reasons, access to highly granular data
is often restricted, and getting access to them requires signing nondisclosure agreements and/or paying data access fees. Access to data
could hence become a major challenge in the quest for a universal,
Nature Cities

quantitative city definition—a topic that will be discussed further inthis paper.
The third property argues for the need to consider both formal
and functional features of a city. Clearly, how these features are incorporated into a city delineation depends on which aspects of a city weare interested in analyzing. Taking as an example the Greater Bay Area
in China, being interested in cities as labor markets might suggest
we focus on, say, ten spatial units (cities) in that area. In contrast, ananalysis focused on clusters of innovative activity might isolate only
three places (Hong Kong, Shenzhen and Guangzhou) within the same
area. Thus, the form and functional features to be considered in thecity delineations required for these two exemplary analyses should
be defined accordingly.
The fourth property points to the need to carefully select parameters and thresholds in defining a city. Arbitrary parameter selection
would de facto impair the ability to compare cities across regions andcountries and to address global research questions related to urbanization. For example, the UN Statistical Commission suggests defining
cities based on a total population of at least 50,000 and a minimum
population density threshold12. However, in the United States, the criteria for defining a city based on population vary by state, with somestates, such as Massachusetts, requiring at least 12,000 inhabitants, andothers, such as Iowa, having no minimum population requirement at all.
The UN approach12 uses an absolute definition, meaning that ahuman settlement would be classified in the same way across space
and time. The US cases are relative definitions that identify cities in acontext-dependent manner and thus vary across space and time. Whileabsolute definitions have many advantages, such as simplicity, stability
and ease of implementation, we must recognize that urbanization is a
dynamic process and varies greatly from country to country (a settlement of 5,000 people in the Congo is nowhere close to a settlement of
5,000 people in, say, the Netherlands). We, therefore, recommend therelative definition or a combination of relative and absolute definitions,with fixed parameters within a country and different parameters fordifferent countries. In such settings, the use of context-specific thresholds should be carefully controlled, and, if possible, it might be usefulPerspective

Box 3

A feasible process for citydelineation with cell-phonedata(1) Population density can be calculated from cell-phone data at
the grid cell level (a grid of about 1 km is recommended, taking
into account the resolution of cell-phone data and the scale ofpeople’s activities at the neighborhood level).
(2) Flow of people between grid cells can also be derived from cellphone data (Fig. 1a).
(3) Aggregate grid cells with population densities and flows abovecertain thresholds. One possible approach to set thresholds is
to exploit the critical characteristics of the urban system, which
could make these two thresholds endogenous and could bedetermined from the statistics or the phase diagram (that is,natural discontinuities). Another approach is goal oriented, forinstance, if the goal is to make the output as close as possible toa city delineation with desired features, such as reproducing FUA
boundaries.
(4) Multiple dimensional validations (for example, statisticalcharacteristics in urban systems, similarity to existing
metropolitan boundaries in terms of morphology, population
size and so on).

to establish data-driven methods to set parameters and thresholds
used in a city delineation. (An example of such a parameter-free method
used for computing thresholds to define city hotspots from cell-phonedata was proposed in ref. 41. More will be discussed in the next section).
The fifth property highlights the importance of seeking extrinsic
assessment methods for a city definition. This property is especially
important and challenging. One possibility would be to evaluate a city
definition both qualitatively and by checking whether some fundamental properties observed in multiple metropolitan regions of the world
also hold for the ‘cities’ resulting from the specific city definition athand. For example, recent studies of urban scaling laws have found thatmany fundamental scaling properties hold only within specific functional city boundaries42,43. As shown in Box 3, we suggest first computing
the population and area of a ‘city’ as defined by the specific definitionat hand, and then analyzing the properties of the ‘city’ population orarea distribution over a larger geography (for example, a country).
Lastly, depending on the case under study, administrative boundaries are inescapable, as usual statistical indicators (for example, population, economic or political indices) are generally collected at theadministrative level. This means that matching with existent politicalboundaries would allow the analyst to have access to a lot of data available, for instance, through census data. However, the benefit of thisadditional source of information heavily depends on the granularityof the smallest spatial unit used to aggregate such information, which
can range from a few blocks in a dense urban area in the United States,
to hundreds of square kilometers for countries such as Colombia. It
should also be noted that administrative boundaries do have a critical
impact on cities, given the role they play in ‘acting’ on the city throughplanning and policy-making—thus, the administrative boundaries driveor condition the presence and flows of people, as well as the city’s form
and functions. Therefore, in such cases where socioeconomic–politicalindicators are relevant, a good definition of a city should not overlook
the role of administrative boundaries. However, the delineation ofadministrative boundaries could be updated to better reflect the actual
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formal and functional characteristics of an urban area as defined by agood city delineation strategy. What we are looking for is a delineationthat attempts to find the best fit between a purely data-driven delineation and existing spatial boundaries.

Opportunities from using cell-phone data

We propose cell-phone data as the basic dataset in finding a solution to
the quest for standardized city definitions. Cell-phone data typicallycome in one of two forms: call detail records (CDR) or global positioning
system (GPS) records. CDR reports geolocate events such as sending atext, making or receiving a call, and so on. The record typically contains
at least an (anonymized) user ID, the time of the event and the ID of thecell tower to which the user is connected at the time of the event. GPSrecords provide more detailed spatiotemporal information, typicallyreporting at least the coordinates (latitude and longitude) of the data
point, the time and possibly other information, such as speed, heading
and so on. Note that we mainly consider the geospatial attributes ofcell-phone data, which have been widely used in the study of humanactivity and urban science in recent decades44,45. There are also a few
studies that use cell-phone communication information to study social
networks46. However, compared with location attributes, individuallevel cell-phone data with rich semantics are very difficult to access,so the cell-phone data used in this paper mainly refer to cell-phone
location data.
The main difference between the two types of cell-phone dataset
is in the spatial and temporal resolution of the information—as shownin Fig. 1. In the case of CDR, the spatial resolution is determined by thecoverage area of the cell tower, which ranges between a few hundred
meters in densely populated areas to a few tens of square kilometers in
low-density areas—with a tendency of reducing cell coverage area withnewer cellular communication technologies such as 5G. The temporal
resolution for CDR data depends on the frequency of recorded events,
which in turn is determined by how frequently the user uses the phone
for texting, calling, browsing the Internet and so on. GPS data have amuch higher accuracy in both time and space. Spatial accuracy is typically in the range of a few tens of meters, while the temporal recordingof events is typically quite regular, with sampling intervals ranging froma few seconds to a few minutes.
It is estimated that about 97% of the world’s population is coveredby a cellular network. Owing to this ubiquity and the worldwide availability of the Global System for Mobile communication standard, cellphone data provide a consistent collection mechanism across the world
and are independent of national censuses. This meets the requirementsof the second point described in Box 2. However, access to cell-phonedata is not easy, which might challenge the requirement for easy accessto data described in Box 2. The issue of access to cell-phone datasets isfurther discussed at the end of this paper.
Importantly, when it comes to city definition and delineation,
cell-phone data offer the ability to capture both form features (suchas nighttime and daytime presence of people in an area) and functional features (such as mobility flows between two areas)—as shownin Fig. 1. With well-established methods for estimating stay points andorigin–destination flows from trajectories47, cell-phone data can beused to compute both high-resolution population distributions andcommuting flows, becoming a valid alternative to classical labor market approaches that provide a satisfactory answer to only the second
point. Note that cell-phone data can be used to estimate flows in thecity more generally, allowing for an accurate picture of movement
patterns within a given geographical area, opening up the possibilityof defining functional cities with greater granularity.
Recent research based on cell-phone data and urban science has
also shed additional light on the fourth and fifth points described inBox 2, showing the potential of using cell-phone data to uncover foundational features of human movement that can provide a quantitative
ground for city delineation. For instance, Alessandretti et al.48 discovered

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a

Day and night populations
Calibration

Cell-phone location data

Data points

Thresholds

Stay points

Clustering

Dynamic mapping

Trajectories

OD flow
Spatiotemporal
aggregation

Thresholds

Anomaly detection

Temporalaggregation

Based on base stations

Commuting flow

or rule-based
approach

Trajectories

Optional

Towers

Gridding

Supervised learning

Home and work locations
Optional

Migrations

Based on GPS

b

3

8

2

5

4

1

7

6

1. Shenzhen
2. Guangzhou
3. Foshan
4. Dongguan
5. Huizhou
6. Zhuhai
7. Zhongshan
8. Jiangmen

Fig. 1 | Cell-phone data and process methods. a, Processing procedures for
CDR data and GPS data. For GPS data, the user’s activity points can be obtainedby clustering algorithms (for example, DBSCAN). Both the CDR data and the
GPS data are then passed through an anomaly detection process, which is used
to filter out noise (for example, false movements). Then, by setting a stay time(for example, 30 minutes), we can obtain the stay points of each user. With
stay points, user’s home and work locations can be estimated in a rule-based
approach, most commonly by calculating the locations that users visit mostduring the day on weekdays and most at night over a period of time. Note that
if there are users with known home and work locations, we can use supervisedmachine learning algorithms to infer those locations more accurately. With theuser’s home and work locations, it is easy to map the daytime and nighttime
population distributions and commuting flows within the city (where calibration
using census data might be necessary, as cell-phone data are a sampling of the
population). In addition to commuting flows, all cell-phone-estimated trips canbe calculated by stay points to obtain an origin–destination (OD) matrix between
locations. The OD matrix is one of the most important results, by which thespatiotemporal structure of the city can be obtained. b, The commuting flow in
Guangdong Province (China) calculated by the method illustrated in a.

that humans tend to perform a constant number of weekly movements
across different geographies, while Schläpfer et al.49 unveiled an inverse
square law between distance and frequency of trips. Other works following this line of research are by refs. 50,51.
Moreover, as the result of a process with self-organization characteristics, the city system has been found to exhibit discontinuouschanges—phase transitions17,52. One transition example was provided

by the hierarchical percolation on the British road network and on
its intersections, which show abrupt changes at critical parametervalues53. The clusters defined at these discontinuous thresholds were
found to be in good agreement with city boundaries estimated fromsatellite imagery. Similar percolation phenomena have been found incity systems in many parts of the world54,55. These characteristics allow
us to define cities using endogenous parameters—determined by the

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aDiscrete CCAbFlow aggregationc

3%

Parameter search (discontinuity)

15%

Count

900

600

300

0
2.5

3.0

3.5

4.0

4.5

log(Largest area)dBeijingChengduShanghai

Chongqing
Guangzhou
Dongguan
FoshanJiangmen

Huizhou

Zhongshan

ShenzhenZhuhaiFig. 2 | An illustration delineating cities using cell-phone data. a, A city
clustering algorithm (CCA)27 was applied to the discrete population density layer
estimated by cell-phone data to derive the continuous population clusters. This
step has two noteworthy points: first, the CCA can also be used for continuum
distribution datasets (not necessarily aggregated into grid cells); and second,
this step can also add other data sources (for example, nighttime lights, roads,
points of interest). Therefore, the grid cells that meet multiple (or any one)density conditions are used as candidate cells for city delineation. b, We calculate
the commuting flows between the continuous clusters obtained in the first stepand combine the clusters whose flow proportion exceeds a certain value. c, By
exploiting the critical characteristics of the urban system, it is possible to detect

phase transitions (that is, natural discontinuities), which could make population
density and flow thresholds endogenous. Here we calculate the area of thelargest cluster under different parameters, and find that under a certain set ofparameters, the area of the largest cluster would have a discontinuity (the dashedline). Another approach to set parameters is goal oriented, as shown in Box 3.
d, Cities defined by a–c steps. For comparison, we enlarged the map of theGreater Bay Area and added the boundaries of the existing prefecture-level cities(gray). As shown on the map, Guangzhou, Foshan and Jiangmen are connected
into one large metropolitan area, while Shenzhen, Dongguan and Huizhou form
another one. Data derived from ref. 40.

thresholds of the system, referred to as ‘critical’, which mark a phasetransition, making the thresholds in the definition process obtained
from the data, rather than purely arbitrary settings (the fourth point
in Box 2). It is worth noting that the commonly used sensitivity analysis
does not necessarily yield effective parameter thresholds. Because theresult can vary a lot when the threshold exceeds the phase-transition
point53, which is often not considered a good threshold in sensitivity
analysis.
In practice, the variability of form and function of cities in different
regions, and the quality of the data itself, make it not always possible
to find such discontinuities56. Even with critical parameter values,
we still need a set of metrics to evaluate whether the city boundaries
derived from cell-phone data are reasonable (the fifth point in Box 2).

In particular, Zipf’s law has been used in previous work as evidence ofgood delineation27. Yet, recent work57 has shown that Zipf’s law canbe problematic for city definition as the law’s exponents fluctuateconsiderably in empirical data58,59. With cell-phone data, we can do far
more than Zipf’s law to validate a city delineation. For example, we can
examine the allometric urban scaling laws Y ≈ Nβ, where N is the population in each city cluster and Y is the variable of area, interaction andoutput of each city cluster60. The scaling exponent β can be estimatedfrom cell-phone data and can be used to test whether the exponent
in the boundary quantified by cell-phone data is consistent with thetheoretical prediction40.
Returning to the global comparison, cell-phone data and the aforementioned characteristics of city systems provide an unprecedented

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Perspective
opportunity to consider both absolute and relative city definitions.
The consistency and universality of cell-phone data makes it easier toquantify cities using absolute thresholds. Importantly, the granularityof cell-phone data also allows us to set a ‘relative absolute threshold’.
For example, one can take the 95th percentile of distance to workand define local labor markets and corresponding city boundaries.
The methodology for doing this remains to be developed given thecontinuous nature of the data (Fig. 2 shows one possible way to findsuch thresholds). Yet, a big advantage here is that the distance bands
obtained by these statistical thresholds (absolute definition) will differ
across countries (relative definition).
As a summary, in Box 3 and Fig. 2, we outline a feasible process
for city delineation with cell-phone data. First, we use cell-phone data
to calculate the population density within a grid and merge continuous high-density grids into clusters. Second, also using cell-phonedata, we calculate the commuting flows between clusters and further
aggregate clusters with flows above a certain threshold. Note that
this step of the definition is similar to the FUAs, which also require
two parameters: population density and commuting ratio. Third, thecritical characteristics of the city system make these two parameters
endogenous and can be determined from the phase diagram. Afterthe above steps, we can obtain high-density and tightly connectedcity clusters. Fourth, the derived city clusters can be validated by using
a set of criteria (for example, scaling laws, similarity to the existing
metropolitan boundaries). Recall the last point in Box 2, to make theresults more useful in practice, we can further aggregate the clusters
at the administrative level.

Conclusions

To summarize, in this Perspective, we have extensively discussed why
we believe that the urban science community should carefully consider
the problem of how to define cities and metropolitan areas, and haveproposed a set of guidelines and widely accepted methods for delineating cities. We are not advocating here for a single definition, as we
believe that different ones will be needed depending on the specificproblem and research question being analyzed. Rather, we advocate
for the use of delineations that conform to the conceptual frameworkdescribed in Box 2, so that, regardless of the specific definition used
for the problem at hand, the requirement of universality, leveraging
standard and widely available data is still satisfied. This approach would
facilitate the replicability of studies and comparisons across different
geographies, bringing invaluable benefits to the research community.
We have also advocated the use of cell-phone data as a proxy forthe essential features of any city definition: urban form and function.
Cell-phone datasets are not the only example of standardized datathat can be used for this purpose. If needed, the integration of cellphone datasets with point-of-interest information, global road network
repositories such as OpenStreetMap, social network data, remotesensing imagery and so on could provide additional opportunities
for city delineation. However, a challenge in this context is that someof these complementary datasets may not be globally available in thesame format.
It is important to note here that the spatial and temporal resolution of the data is a critical factor when considering access to datathat is related to human ethics and privacy protection. While gaining
access to individual-level GPS trajectories might be extremely difficult,this level of detail is often not necessary in the process of delineatingcity boundaries. For this purpose, access to spatially and temporally
aggregated data (for example, how many people moved from area A
to area B in one day) is often sufficient. Generally speaking, the coarser
the level of spatiotemporal resolution, the easier it is to gain access to adataset. Thus, the question of which is the minimal resolution needed in
the context of city delineation is a prominent question that has mostly
been evaded so far in the literature. Note that there is no single answer
to this question since, as extensively argued in this paper, how to define
Nature Cities

https://doi.org/10.1038/s44284-023-00019-z

a city depends on the context and scope of the study, and so does theminimum data resolution needed to support a specific city definition.
Similarly, the data aggregation level and chosen spatial unit should besuited to the context and scope of the study.
Cell-phone datasets come with limitations related to the fact that
although cell-phone ownership is wide, some socioeconomic groups
tend to be overrepresented (younger, wealthier populations) or underrepresented (older populations). If we could have a globally covered
functional city dataset, scholars and policymakers in a variety of fields
such as urban planning, transportation, epidemiology and sustainability would benefit greatly. Yet, despite caveats and the uneven penetration of smartphones, the more than 18 billion cell phones projected to
be in use globally by 2025 are arguably the most widely spread proxy
for the presence and flows of people.
Global access to cell-phone data is a challenge: even if an increasing
number of open cell-phone datasets have been made available recently(such as the Data for Development (D4D) challenge, the Uber movement(https://movement.uber.com/) and Baidu Migration (https://qianxi.
baidu.com/)), the data in general are owned by private companies,
protected by non-disclosure agreements or access fees, strict privacy
regulations and so on. In this regard, we would encourage the urban
science community to join forces to develop satisfactory definitions ofcities based on cell-phone data or other standardized, global datasets,
and to work with international organizations, such as the International
Telecommunication Union, to make anonymized cell-phone data available more broadly, as a clear delineation of cities is critical to addressing
current and future urban problems affecting populations globally.
Collecting, pooling and analyzing such data on a global scale requires
nothing less than a collective effort, which we all call for.

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Acknowledgements

L.D. and Y.L. acknowledge the support of the National Natural Science
Foundation of China (No. 41830645). M. Batty acknowledges support
from the Alan Turing Institute under QUANT2-Contract-CID-381581.
G.B.W. acknowledges the generous support of Toby Shannon via theCharities Aid Foundation (CAF) of Canada and of the NSF under grant
no. PHY1838420. F.D., P.S. and C.R. acknowledge all members of MIT
Senseable City Lab consortium.

Author contributions

All the authors participated in the discussion and writing of the paper.

Competing interests

The authors declare no competing interests.

Additional information

Correspondence and requests for materials should be addressed to
Paolo Santi.

Q12

Perspective
Peer review information Nature Cities thanks Lewis Dijkstra, MarkMontgomery and the other, anonymous, reviewer(s) for theircontribution to the peer review of this work.

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