∎

11institutetext: Saleem, MA 22institutetext: School of Mathematics and
Computer Science, Institute of Business Administration, Karachi, Pakistan.
22email<EMAIL_ADDRESS>33institutetext: Zaidi, F 44institutetext:
School of Administrative Studies, York University, Canada and School of
Mathematics and Computer Science, Institute of Business Administration,
Karachi, Pakistan. 44email<EMAIL_ADDRESS>55institutetext: Rozenblat,
C 66institutetext: University of Lausanne, Institute of Geography and
Sustainability, Lausanne, Switzerland. 66email<EMAIL_ADDRESS>
# World City Networks and Multinational Firms: An Analysis of Economic Ties
Over a Decade

Mohammed Adil Saleem  Faraz Zaidi111Corresponding author: Faraz Zaidi,
<EMAIL_ADDRESS>Céline Rozenblat

(Received: date / Accepted: date)

###### Abstract

One perspective to view the economic development of cities is through the
presence of multinational firms; how subsidiaries of various organizations are
set up throughout the globe and how cities are connected to each other through
these networks of multinational firms. Analysis of these networks can reveal
interesting economical and spatial trends, as well as help us understand the
importance of cities in national and regional economic development. This paper
aims to study networks of cities formed due to the linkages of multinational
firms over a decade (from 2010 to 2019). More specifically we are interested
in analyzing the growth and stability of various cities in terms of the
connections they form with other cities over time. Our results can be
summarized into two key findings: First, we ascertain the central position of
several cities due to their economically stable connections; Second, we
successfully identify cities that have evolved over the past decade as the
presence of multinational firms has increased in these cities.

###### Keywords:

Complex Networks Multinational Firms Temporal Networks Social Network Analysis
Economic Networks

††journal: Networks and Spatial Economics

##  1 Introduction

Multinational firms play an essential role in the economic development of
cities. The presence of multinational firms ensures a prosperous ecosystem for
a city as it positively contributes towards tax revenue, employment rate,
economic activity, and improved gains for domestic firms
keller2009multinational ; melnyk2014impact ; abor2008foreign . Different
cities around the world are connected via their linkages through these
multinational firms, impacting economies at both domestic and international
levels. A city where numerous multinational firms are established can strongly
influence the region where it is situated. New York, for example, is a mega-
city housing headquarters of several multinational firms. It is highly
connected domestically as well as internationally. Economic changes in New
York not only impacts the US but other world regions that are connected to,
and dependent on the economic stability of New York.

Many researchers have studied the role of multinational firms in the
development of cities derudder03 ; derudder2011global ; belderbos2020firms ;
iammarino2018international . As new firms are established, or existing firms
are acquired by multinationals, city to city links also change. This change
can be studied over time to understand how urban and regional economies shape
as a function of multinational firms and their links with other cities
hussain19 ; rozenblat17 . Typically, we can classify the change as either
stable or changing. Cities that maintain their connections with other cities
over time can be called stable cities, whereas cities whose linkages vary over
time can be called changing cities. Economic stability of a city can be
directly associated with cities that are able to maintain economic ties with
other cities. For a city that changes its connections, we can say that the
city demonstrates economic growth (or contraction), as new linkages are
established (or previous ones are broken) fritsch2004effects .

In this paper, we study the networks of cities formed by multinational firms
as they change from the year 2010 to 2019. We used a metric called topological
overlap to determine stable and changing cities in these networks. Topological
overlap is a temporal measure that determines the similarity between two
networks by considering the changes in links between the nodes. Two key
findings from this analysis reveal the role of multinational firms in the
economic stability of cities as well as successfully identify cities that have
shown economic development in the context of multinational firms.

The paper is organized as follows: We discuss related work in Section 2,
followed by details regarding the dataset used in this study in Section 3. In
Section 4, we discuss the methodology used to analyze the networks. We commit
Section 5 to Results and Discussion and Section 6 to wrap up with Conclusion
and Future research prospects.

##  2 Related Work

The role of multinational firms in the context of networks of cities has been
studied extensively in various contexts to understand their impact on global
economies. Taylor and Derudder thoroughly assessed the overall connectivity of
city networks using multinational firmsTaylor2003WorldCN . Derudder also
explored the hierarchical tendencies and regional patterns formed within the
city networks through links of multinational firmsderudder03 . Joyez studied
the network of French multinational firms and the global value chains to
reveal the alignment between the two networksjoyez19 . Silva et al. used wire
transfers between different cities to show how the transfers are directly
proportional to their dependence on each other’s economy silva2020 . Using the
links for Advanced Producer Service firms with their Initial Public Offerings
clients from the Hong Kong stock exchange from 1999 to 2017, Pan et al.
highlighted the role of Chinese cities in reshaping the global economy network
pan2018 . Using service provisioned connections between Advanced Producer
Service firms and their clients, they also showed dominant cities in the
Chinese urban network pan2017mapping .

Analysis of networks of cities can help understand various economic phenomena.
Mahutga et al. analyzed the shift of power distribution using airline
passengers data and its implication on the connectivity of cities mahutga10 .
Blumenfeld-Lieberthal used the topology of a transportation network of various
cities to show a positive correlation of economic activity, and high
connectivity between two cities blumenfeld09 . Interdependence within the
network of cities arising from global and local processes has been thoroughly
examined by Sassen sassen07 . Sassen also analyzed the impact on the social
structures emerging from these relationships and pointed out the importance of
global cities sassen11 . Ducruet et al. analyzed cities through a maritime
network to show the relevance of cities in maritime networks considering both
network-specific and classical factors ducruet2018maritime . Using a sea-port
network of 91 countries, Munim and Schramm found a correlation between the
quality of port infrastructure with higher economic growth for developing and
developed countries, albeit a bit weaker for the latter munim2018impacts . By
studying the high-speed rail network, Diao found growth in fixed asset
investments for cities with high-speed rail service in China diao2018does .

Network of cities also provide a dimension to rank cities based on different
metrics. Cities were ranked based on diversity, centrality, and strength by
Hussain et al. to identify established and changing cities hussain19 . In the
context of climate change, Wang et al. ranked various cities using their
economic performance and mitigation of climate changes based on Data
Envelopment Analysis wang2020 . Wang also evaluated the performance of global
cities based on Data Envelopment Analysis and Malmquist index taking into
consideration various aspects such as economy, R&D, etc. wang19 .

Pan et al.pan2018world  study the networks created from the global financing
of Chinese firms using data from initial public offerings (IPO) on the Hong
Kong stock exchange. The authors draw interesting conclusions based on
economic activities to study city-to-city links. Similar to our dataset, we
analyze all economic linkages (not just as a result of IPO) to understand how
world city networks have shaped over the past decade. Zhao et al. zhao2020
study service firm networks and the resulting connections of cities to
identify core and peripheral cities in China. Interesting observations about
the provincial capitals is found and discussed in the context of developing
the Chinese economy.

Rozenblat rozenblat21  study the intercity and intracity networks of cities at
meso-level and macro-level. This is to understand the complex interplay of
spatial scale and power as different cities and regions demonstrate various
strategies to develop and strengthen local economy and compete internationally
through global expansion.

Temporal networks have traditionally proven to be helpful in studying change.
Temporal networks were broadly studied by Holme and Saramäki, where they
defined different types of temporal networks and introduced various measures
for the study of networks that change over time (equivalent to their static
counterpart) holme12 . They also stated other existing temporal network models
and ways to represent temporal data in the form of static graphs. Raimbault
studied the temporal behavior of networks to observe the co-evolution of the
French system of cities with the transportation network raimbault2021 . Bagan
and Yamagata presented an approach to monitor land-cover dynamics of 50 global
cities using their temporal Landsat data of 25 years bagan2014 .

Many metrics have been used with various temporal networks in analyzing
network properties. Zhao et al. used temporal centrality on a stock market
based network as a portfolio selection tool zhao2018stock . They emphasized
the importance of temporal attributes of the network for real-world
applications. Prado et. al determined the most relevant characters in a story
by using eigenvector centrality over a temporal network of literary text
prado2016temporal . Cunha et al. analyzed contact duration and inter-contact
times in vehicular networks to compare original and calibrated mobility traces
of GPS-equipped taxis cunha2016communication . Clauset and Eagle introduced
topological overlap as a similarity measure between two networks (the two
networks can be consecutive snapshots of the same network) clauset2012 .
Buttner et al. adapted the metric for edge cases and used it on a real-world
animal trade network buttner2016 . Navarro et al. used topological overlap to
measure embeddedness of a link to show correlation with tie
persistence.navarro2017 .

Utilizing the methodical information gained from the aforementioned studies,
we used a network of cities connected via linkages of multinational firms.
These linkages allow us to study stable and changing cities from the
perspective of economic growth. We use a temporal metric to examine networks
of cities from 2010 to 2019 and use this data to identify the top stable and
changing cities over the time period.

##  3 Dataset

For the study, we used networks of cities in the context of multinational
firms for the years 2010 and 2019. A link in this network represents a
connection between two cities for which there exist two firms belonging to the
same group of companies with a financial tie. A financial tie means that a
firm owns a share in the capital of another firm. A node in this network is
not exactly a city but large urban areas labeled with the same criteria
worldwide. We selected the top 3000 group of companies based on their annual
turnover and their 800,000 direct and indirect subsidiaries accumulating over
1.3 million links for the years 2010 and 2019. This data is provided by Bureau
van Dijk222Bureau van Dijk Electronic Publishing (http://www.bvdep.com/).
Subsequent data cleansing was done as a collaboration between Université de
Lausanne - CitaDyne research group and University of Paris - ERC GeoDiversity
research group333ORBIS 2010, 2013: BvD - Universite de Lausanne (CitaDyne
group) and University of Paris (ERC Geodiversity group). to correct erroneous
entries and fill in missing values. The network is similar to other datasets
used by researchers alderson04 ; wall11 ; kraetke14  in that they all
represent economic networks of cities. However, our dataset is comparatively
larger. Another necessary difference in the network is the removal of the
self-loop since we are primarily concerned with the linkages between the
cities rather than within them.

Figure 1 rozenblat17  demonstrates the construction of these networks. To show
the construction, we use three groups of companies as an example. Figure 1a
shows the three groups: Group 1, Group 2, and Group 3 colored Pink, Green, and
Dark Blue respectively. They are present in three different cities: City A,
City B and City C colored Yellow, Red, and Light Blue respectively. Figure 1b
shows how the cities are connected through the branches of the above-mentioned
companies spread across the cities. Figure 1c shows how a simple graph444A
simple graph has only one edge between two vertices with no self-loop is
created by aggregating links between the cities.

Mathematically, we can define the cities’ network as:

$G^{\prime}=(V^{\prime},E^{\prime})$ (1)
$G^{\prime\prime}=(V^{\prime\prime},E^{\prime\prime})$ (2)

where $G^{\prime}$ is the cities’ network for the year 2010, comprising of
nodes $V^{\prime}$ and edges $E^{\prime}$ and, $G^{\prime\prime}$ is the
cities’ network for the year 2019, comprising of nodes $V^{\prime\prime}$ and
edges $E^{\prime\prime}$ such that $V^{\prime}\subseteq V^{\prime\prime}$.

Table 1 shows a summary of standard network metrics for the two networks. The
networks are slightly different if we see their respective average path
lengths and transitivity. We also see a relatively significant difference in
the number of nodes, number of edges, the edge-node ratio, and the highest
degree between the two networks. This is due to the growth of the network over
the studied period, where new cities became part of the network, and current
cities further consolidated their presence in the network by forming new links
with other cities.

Figure 1: Economic Networks of Cities: (a) Hierarchical linking of Multinational Firms to their branches (b) Firms are Geographically Distributed and (c) Link aggregation to form connection between cities. Image Source: Originally constructed to explain how the multinational firms’ networks were built rozenblat17 . Table 1: Network Statistics: Comparison of the two networks. Structural similarity between the two networks is evident from global metrics.  Metric | 2010 | 2019
---|---|---
Nodes | 1210 | 1423
Edges | 32374 | 54048
Edge-Node Ratio | 26.75 | 37.98
Highest Degree | 737 | 873
Average Path Length | 2.29 | 2.24
Transitivity | 0.343 | 0.393

##  4 Methodology

Figure 2 outlines the methodology used to analyze the dataset. We first
compute degree centrality for each city and use that as a criterion to
shortlist important cities. Then, we calculate the topological overlap for the
shortlisted cities and sort the results in descending order. Cities with high
topological overlap are classified as stable cities, while those with low
topological overlap are identified as the cities with the most topological
change over the studied period.

Figure 2: Methodology for identifying stable and changing cities in the
network. Candidate cities are shortlisted using the degree centrality;
topological overlap is then computed for these cities to find stable and
changing cities.

Topological overlap clauset2012  is a similarity measure that we can use to
define similarity between the connections of a city over the next interval.
The topological overlap for node i between $t_{m}$ and $t_{m+1}$ is defined
as:

$C_{i}(t_{m},t_{m+1})=\dfrac{\sum_{j}a_{i,j}(t_{m})a_{i,j}(t_{m+1})}{\sqrt{\sum_{j}a_{i,j}(t_{m})\sum_{k}a_{i,k}(t_{m+1})}}$
(3)

subject to $\sum_{j}a_{i,j}(t_{m})>0$ and $\sum_{j}a_{i,j}(t_{m+1})>0$

Here, $C_{i}$ is the topological overlap of node $i$, $t_{m}$ and $t_{m+1}$
are the time intervals for which topological overlap is computed.
$a_{i,j}(t_{m})$ and $a_{i,j}(t_{m+1})$ are link’s weight for weighted graphs
(1 or 0 for unweighted graphs), corresponding to weighted presence or absence
of a link between node i and node j, determined through adjacency matrix of
the network for time $t_{m}$ and $t_{m+1}$ respectively.

Two important properties help us to understand how topological overlap works.
The first property is that the topological overlap of a node $i$ is $0$ if
there is no overlap between the links of node $i$ for the two time periods
$t_{m}$ and $t_{m+1}$. Second, the topological overlap is greater than $0$
when there is some overlap between the two graphs at time intervals $t_{m}$
and $t_{m+1}$. We show the proofs of these two properties below:

Property 1: $C_{i}(t_{m},t_{m+1})=0$, when there is no overlap

Proof: The numerator in equation (3) is a summation of the product of two
terms, $a_{i,j}(t_{m})$ and $a_{i,j}(t_{m+1})$. If any of the two terms is
zero, the respective term in the summation will be zero. If all terms in the
summation are zero, $C_{i}(t_{m},t_{m+1})$ will be zero.
In case when there is no overlap between $t_{m}$ and $t_{m+1}$ for node $i$,
then $a_{i,j}(t_{m})\cdot a_{i,j}(t_{m+1})$ will always be zero because, by
definition

$a_{i,j}(t_{m})=0$ if $a_{i,j}(t_{m+1})>0$,
$a_{i,j}(t_{m+1})=0$ if $a_{i,j}(t_{m})>0$

Hence, all the product terms in the summation will be zero and therefore,
$C_{i}(t_{m},t_{m+1})$ will be zero.

Property 2: $C_{i}(t_{m},t_{m+1})>0$, if there is overlap between graph
$t_{m}$ and $t_{m+1}$

Proof: In contrast to the statement in the above proof, if even a single term
in the summation of the numerator of equation (3) is greater than zero,
$C_{i}(t_{m},t_{m+1})$ will not be zero.
In case when there is overlap between $G^{\prime}$ and $G^{\prime\prime}$ for
node $i$ and node $j$, then $a_{i,j}(t_{m})\cdot a_{i,j}(t_{m+1})\forall j\in
V^{\prime\prime}$ will be greater than zero because, by definition

$a_{i,j}(t_{m})>0$ if $a_{i,j}(t_{m+1})>0$

Hence, at least one product term in the summation will be greater than 0 and
therefore, $C_{i}(t_{m},t_{m+1})$ will be greater than zero.

Topological overlap is generally used with binary links. The output
interpretation is relatively straightforward; if there is no change in the
link for a city over the next interval, topological overlap will be 1; for a
complete change of links, topological overlap will be 0. Partial changes will
then lie between 0 and 1. Weighted topological overlap has also been used in
the past to study networks where the links have a certain strength mumford2010
. The downside of this approach is that the values are no longer constrained
between 0 and 1, making it irrelevant for certain comparisons but still useful
in the absolute sense.

In this study, we have used weighted links to compute topological
overlapteneto2020 . The objective for this selection was to capture the effect
of high connectivity between the cities in the topological overlap value. The
weight of a link is determined by the number of financial ties between two
cities. Furthermore, we used directed links to compute topological overlap
taking into account the parent/subsidiary relationship between two cities.

To illustrate the point, take two cities with different connectivity patterns
that have maintained all their links over the next interval. In the case of
binary links, since the output is constrained between 0 and 1, the topological
overlap will be 1 for both cities. However, we will see that cities with
higher connectivity will have a proportionally higher topological overlap in
the weighted case.

Figure 3: Various cases for evolution of city’s connection over time

The connections of a city can evolve over time in the following manner (see
Figure 3):

  * •

No connections are retained

  * •

All connections are retained (a) with no new connections and (b) with new
connections

  * •

Some connections are retained (a) with no new connections and (b) with new
connections

To get meaningful insights from the topological overlap, we were required to
shortlist candidate cities. This step was not necessary for identifying stable
cities as weighted links amplify topological overlap values for them. However,
important changing cities could easily be mistaken due to the behavior of
topological overlap for maximum change, which will return zero. For example,
take two cities with degree centralities of 1 (City A) and 100 (City B),
respectively. Over the next time interval, City A does not retain any
connection, and City B retains 1 connection out of 100. The topological
overlap for City B, in this case, will be more significant than City A, which
is a misleading result. We used degree centrality as a centrality measure to
shortlist the top 250 cities filtering out all cities with low connectivity.

Before proceeding towards results and discussion, it would be interesting to
see whether topological overlap offers a different perspective to determine
changing cities or not. A simpler way to observe changing cities would be to
observe the change in the degree centrality of the cities from 2010 to 2019.
Table 2 compares the rank of top changing cities identified through degree
centrality and topological overlap. Two lists are presented (see Table 2), one
where top 25 cities based on Topological overlap (TO-Rank) are listed along
with their relative rank in terms of degree centrality (DC-Rank); the second
list is where the top 25 cities with respect to change in Degree centrality
(DC-Rank) from 2010 to 2019, and their respective ranking in terms of
topological overlap (TO-Rank) are identified. Considering the top 25 cities
that have changed over the studied period based on weighted degree centrality,
we can clearly see that cities from the US and China dominate the list.
Beijing, Shanghai, Hong Kong and Shenzen, all represent the strong developing
economy of China around these central cities where the presence of
multinational firms has increased their local as well as global ties. On the
other hand, cities such as Washington, Chicago, Los Angeles, Dallas,
Philadelphia, New York, Houston, San Francisco, Atlanta, Denver, Wilmington,
Nashville, Boston, Miami and Detroit represent the strong domination of
multinational firms headquartered in the US in the world economy. In terms of
topological overlap, top cities identified as changing cities are again
dominated by cities from the US and China. Cities from China include Urumqi,
Zhengzhou, Wenzhou, Jiujiang, Qingdao, Jinan, Hefei, Ganzhou, Chongqing and
cities from the US include Lafayette, Grrenville, Shreveport, Fort Myers,
Little Rock, Dayton, Knoxville and Flint. These cities are different than what
we see in the list based on degree centrality. This is because weighted degree
centrality is a good measure to capture absolute change in the number of
connections whereas topological overlap focuses on the change in terms of the
structure of connections and thus reveals a different set of cities
altogether. A detailed discussion and our findings on the cities that stand
out is given in section 5 below.

Table 2: List of Top Changing Cities Ranked using Topological Overlap and Degree Centrality for the year 2010 and 2019. TO-Rank represents the ranking of cities based on Topological Overlap and DC-Rank represents the ranking of cities based on Weighted Degree Centrality. City | TO-Rank | DC-Rank | City | TO-Rank | DC-Rank
---|---|---|---|---|---
Doha | 1 | 147 | Beijing | 192 | 1
Urumqi | 2 | 112 | Tokyo | 237 | 2
Zhengzhou | 3 | 72 | Washington DC | 191 | 3
Wenzhou | 4 | 95 | Chicago | 221 | 4
Lafayette | 5 | 140 | Los Angeles | 210 | 5
Greenville | 6 | 156 | Dallas | 201 | 6
Shreveport | 7 | 142 | Philadelphia | 222 | 7
Jiujiang | 8 | 164 | New York | 243 | 8
Abu Dhabi | 9 | 141 | London | 239 | 9
Fort Myers | 10 | 83 | Houston | 190 | 10
Qingdao | 11 | 114 | Shanghai | 184 | 11
Jinan | 12 | 64 | San Francisco | 225 | 12
Hefei | 13 | 99 | Atlanta | 188 | 13
Ganzhou | 14 | 93 | Dublin | 194 | 14
Little Rock | 15 | 130 | Singapore | 226 | 15
Boise | 16 | 135 | Denver | 148 | 16
Dayton | 17 | 175 | Wilmington | 213 | 17
Cork | 18 | 107 | Grand Cayman | 244 | 18
Limassol | 19 | 146 | Nashville | 173 | 19
Colombia | 20 | 133 | Hong Kong | 235 | 20
Chongqing | 21 | 76 | Shenzen | 122 | 21
Knoxville | 22 | 115 | Boston | 234 | 22
Flint | 23 | 118 | Luxembourg | 224 | 23
Changsha | 24 | 101 | Miami | 162 | 24
Madison | 25 | 132 | Detroit | 153 | 25

##  5 Results and Discussion

Following the steps mentioned earlier, we obtain a list of cities sorted by
decreasing topological overlap. At the top of this list are the cities that
retain their connections from 2010 to 2019; We call these cities, stable. In
contrast, at the bottom of the list are cities that changed most of their
connections from 2010 to 2019; and these are called changing cities.

Figure 4: The figure shows the selection of stable(blue) and changing
cities(orange) from the top 250 cities shortlisted using degree centrality.
log(DC) and log(TO) represent log of degree centrality and topological
overlap, respectively. Inner figure: Plot of linear degree centrality vs.
topological overlap; changing cities are not distinguished from other cities
due to low degree centrality and topological overlap.

###  5.1 Discussion for stable cities

Table 3 shows the list of stable cities identified through topological
overlap. At first glance, cities like New York, London, and Paris emerge; The
presence of these cities in this list reaffirms results from previous studies
about their economic importance in the world sassen01 ; zukin2005 ; hussain19
. These cities are global hubs555Global hubs are centers for many
multinational firms with very high degree centralities, bringing economic
stability to not only their countries but to their regions as well.

Apart from London and Paris, other cities of the Western European region also
make this list. Amongst theses is Edinburgh, which is at the top of the list
in the region (ahead of London and Paris), Madrid, Amsterdam, Birmingham,
Luxembourg, and Frankfurt. Edinburgh is considered amongst one of the
strongest economies in the region, with a strong financial services industry
as its backbone. Birmingham makes it to the list as a result of its
manufacturing industry and its strong inclination towards entrepreneurship.
Edinburgh and Birmingham’s high economic outputs contribute to maintaining a
steady economy for the UK. Madrid is the financial and industrial center for
Spain. Despite being an industrial hub, the services sector is the major
contributor to the Spanish economy. For the Netherlands, Amsterdam is the
financial hub housing major banking corporations. Being a port city, Amsterdam
also contributes to the country’s economy via national and international
trade. The city of Luxembourg is considered for its financial services, with
the financial sector being the largest contributor to its country’s economy.
Lastly, Frankfurt, one of Germany’s financial centers, has contributed over
the time period studied to the German economy via its banking sector
consisting of major banks. Frankfurt also has a strong aviation presence in
the world. Both these industries help Frankfurt provide economic stability to
Germany.

Figure 5: Top stable cities identified by region: a) North America b) Europe
c) Asia and d) Australia

In the Eastern European region, the top two cities of Russia, Moscow and St.
Petersburg, are identified amongst the stable cities in the list. Moscow is
the financial center for Russia and is home to many of Russia’s largest firms,
including its major tech companies. St. Petersburg is a port city and is
pivotal to the Russian economy. It also has a stable automotive industry. Both
the cities have been vital for Russia’s strong economy over the years.

Table 3: List of Top 25 Stable Cities Based on Topological Overlap for 2010 and 2019 Rank | City | Country | Region | Rank | City | Country | Region
---|---|---|---|---|---|---|---
1. | Grand Cayman | Cayman Islands | Carribean | 14. | Moscow | Russia | Eastern Europe
2. | New York | USA | North America | 15. | Amsterdam | Netherlands | Western Europe
3. | Bermuda Kindley | Bermuda | Caribbean | 16. | Birmingham | UK | Western Europe
4. | Edinburgh | UK | Western Europe | 17. | Toronto | Canada | North America
5. | Osaka | Japan | Eastern Asia | 18. | Barcelona | Spain | Western Europe
6. | London | UK | Western Europe | 19. | Singapore | Singapore | Eastern Asia
7. | Paris | France | Western Europe | 20. | San Francisco | USA | North America
8. | Tokyo | Japan | Eastern Asia | 21. | Luxembourg | Luxembourg | Western Europe
9. | Tortola | BVI | Caribbean | 22. | Frankfurt | Germany | Western Europe
10. | Hong Kong | Hong Kong | Eastern Asia | 23. | Philadelphia | USA | North America
11. | Boston | USA | North America | 24. | Chicago | USA | North America
12. | Sydney | Australia | Australia/Oceania | 25. | St. Petersburg | Russia | Eastern Europe
13. | Madrid | Spain | Western Europe |  |  |  |

In the North American region, Boston, Chicago, San Francisco, and Philadelphia
from the USA also make it into the list, along with Toronto from Canada.
Boston has one of the largest economies in the US and houses numerous tech
companies, a large number of these geared towards biotechnology. This is
primarily influenced by the schools and research centers in and around Boston
attracting investment. On the other hand, Chicago is one of the most important
financial centers of the world. Chicago also has a strong food and retail
industry with major firms headquartered in the city. San Francisco is another
financial center in the US and has a growing technology industry. Philadelphia
also has a strong biotechnology industry and contributes to the economy via
trade as a port city. Toronto has been a financial hub for Canada for many
years. Due to its start-up ecosystem, it has also grown as one of the largest
cities to host the tech industry in the North American region. Since all the
industries mentioned above have remained relevant throughout the past decade,
these cities have experienced stability in their linkages with other cities
and thus feature in the list of most stable cities.

Three cities from the Caribbean region, namely Grand Cayman, Bermuda Kindley,
and Tortola, are also listed as stable cities. Financial services provided by
these cities are responsible for a large part of their economy. These cities
are home to many offshore companies attracted by their lucrative tax policies.

Sydney is the only stable city identified in the Australia/Oceania region. It
is the leading financial center in the region, and at the national level, most
of the banks are based out of Sydney. Sydney also has the largest
manufacturing industry in Australia. We can also see three important cities of
the Eastern Asia region in the list: Tokyo and Osaka, from Japan, and
Singapore. These cities are again important financial centers of the world.
Japan also has one of the largest industry for electronics globally, which has
remained steady over the last decade, and so has Japan’s economy. Major
multinational electronics firms have their headquarters situated in Tokyo and
Osaka. Similarly, Singapore holds a significant share in the global
semiconductors market and has been important for its stable economy.

Stable cities have continued to maintain their existing connections to gain
economic stability. A majority of these cities are either financial centers or
providers of financial services worldwide. Some cities are manufacturing
giants, while others have relied on their strong technological foundations to
maintain stability.

Table 4: List of Top 25 Changing Cities Based on Topological Overlap for 2010 and 2019 Rank | City | Country | Region | Rank | City | Country | Region
---|---|---|---|---|---|---|---
1. | Doha | Qatar | Western Asia - Gulf | 14. | Ganzhou | China | Eastern Asia
2. | Urumqi | China | Eastern Asia | 15. | Little Rock | USA | North America
3. | Zhengzhou | China | Eastern Asia | 16. | Boise | USA | North America
4. | Wenzhou | China | Eastern Asia | 17. | Dayton | USA | North America
5. | Lafayette | USA | North America | 18. | Cork | UK | Western Europe
6. | Greenville | USA | North America | 19. | Limassol | Cyprus | Western Europe
7. | Shreveport | USA | North America | 20. | Columbia | USA | North America
8. | Jiujiang | China | Eastern Asia | 21. | Chongqing | China | Eastern Asia
9. | Abu Dhabi | UAE | Western Asia - Gulf | 22. | Knoxville | USA | North America
10. | Fort Myers | USA | North America | 23. | Flint | USA | North America
11. | Qingdao | China | Eastern Asia | 24. | Changsha | China | Eastern Asia
12. | Jinan | China | Eastern Asia | 25. | Madison | USA | North America
13. | Hefei | China | Eastern Asia |  |  |  |

###  5.2 Discussion for changing cities

Table 4 shows the list of cities where significant change can be observed
between the year 2010 and 2019. To reiterate, we are labeling a city as
changed if its connections are not similar over the studied time periods. It
can also be interpreted as if some, or all the links from the previous
timestamp are not retained thus resulting in being identified as changing
cities.

Doha (Qatar), is identified as the city with the most significant change on
this list. Doha’s economy is based on oil and gas industries, with many firms
headquartered in the city. It is also expected to host the 2022 FIFA World Cup
as Qatar spent heavily to develop infrastructure before the event. The
infrastructure changes include expanding airports and constructing new road
and rail networks. Doha’s most substantial ties are formed within the Middle
East with Bahrain and UAE. Outside the region, Doha is also strongly connected
with London and with tax havens, Grand Cayman, and Kwajalein. Abu Dhabi is
another Middle Eastern city on this list. To restrict its economic reliance on
oil, UAE has invested heavily to diversify its economy.

Many cities where change can be observed have been identified in China, with
ten cities making it to the list. These cities have grown exponentially, with
only a handful of connections in 2010 but hundreds of links by 2019. A
majority of the links for these cities are local, bringing economic stability
to different regions in the country. There also have been initiatives to
develop infrastructure, attracting foreign investments to connect them with
international cities. Geographically, the economic decentralization strategy
also comes into play since the cities are not concentrated in a single region.
Decentralization means less dependence on a few critical cities for economic
prosperity, providing better resilience to China. In this case, if an
important city suffers contraction, the economy will not crash for the whole
country and the damage will be limited to the respective region. Moreover, it
gives better chances to the affected city to recover quickly through the
support of other cities. Apart from this economic decentralization, geographic
decentralization can also be observed with cities emerging from different
regions.

Figure 6: Top changing cities identified by region: a) US b) China c) Europe
and d) Middle-East

For example Urumqi from the province of Xinjiang in the far northwestern
region of China is China’s attempt to access markets from Central Asia. Urumqi
has been identified as the city with the highest change in China. To promote
foreign trade, the construction of a free trade zone was started in 2015 in
Urumqi. It also hosted the 1st China-Eurasia Expo in 2011, an upgrade from its
regional trade fair. The expo was intended to encourage trade not only from
Central Asia but also from Europe and other Asian regions. To improve its
connectivity, both domestically and internationally, various modes of
transportation have also been upgraded for the city.

The city of Chongqing also appears in the list which has evolved as the
commercial capital of southwestern China. The city is one of four
municipalities under direct administration of central government (equivalent
to a province). Manufacturing industry is the backbone of its economy and it
is one of the largest vehicle manufacturers in China. The region is also rich
in natural resources and agriculture. Recent developments in infrastructure
has led to the arrival of many multinational corporations. It was identified
as one of the top-performing economies in the world by Brookings Institution
in 2018 brookings2018 .

Changsha is the largest city in the Hunan province from central China and is
the 17th most populous city in China. It is located on the banks of Xiang
River, which is 30 miles south of the Dongting Lake. This gives the city
access to water ways all across the southern and southwestern parts of Hunan.
The city is a major trade center with rice, cotton, timber and livestock being
traded here. It is also an important railway connection from Hankou to
Guangzhou and as a result, has attracted handsome investments and many
multinational firms to make it into the list. Rice milling, oil extraction,
tobacco, textile and agricultural chemicals and fertilizers are some of the
key industries boosting the city’s economy.

Apart from these three inland cities (Urumqi,Chongqing and Changsha), the
other cities that appear in the list are either port cities, or cities from
provinces neighboring port cities. Starting from the northeastern province of
Shandong, two cities Qingdao and Jinan appear in the list. Qingdao, a port
city is famous for its brewery industry and manufacturing white goods (large
home appliances) and electronics. Since it is a vital port, it has attracted a
lot of foreign investments in the past decade. Being a free trade zone, the
presence of industrial zones has also helped its economic growth. Another city
from the Shandong province is Jinan which is home to the top universities in
the country, and access to academic talent has been pivotal for attracting
foreign investments. Also, Jinan’s Innovation Zone has the highest economic
growth in the country zheng19 . Automobiles, information technology, and
materials are the key industries for Jinan.

Wenzhou from the province of Zhejiang is another port city from southeastern
part of China. The city is known for low-power electrical appliances and local
firms have collaborated with major players internationally. It is home to many
privately owned business involved in low-end manufacturing. The export of
these goods are responsible for significant boost to China’s economy. The
Wenzhou Economic and Technological Development Zone has also been established
which also offers high connectivity to other cities along with lenient
economic policies.

Zhengzhou is the capital city of Henan province and is also known as the
’iPhone City’. It is the most prominent smartphone manufacturing site
globally. Zhengzhou also has an Airport Economy Zone, started in 2013,
allowing businesses to connect with other firms quickly and smoothly. Other
economic and industrial zones were also established in the city to promote
industrial growth in IT, pharmaceutical and materials sectors. Zhengzhou is
also pivotal from logistics perspective as it is also one of the transport
hubs in China. The city lies in the northern part of Henan, where the railway
line accesses the Longhai line which connects the east to west. The province
itself has an agricultural economy with cotton, silk, tobacco and vegetable
oils as its primary produce.

Hefei is the largest city of the province of Anhui and like Jinan, an academic
center with numerous universities and research centers present in the city.
Hefei’s economy is based on its manufacturing industry, with the automobile,
information technology, materials, and chemicals being the key industries.
Hefei was amongst the fastest-growing metropolitan economy in the world in
2014 brookings2014 .

Jiujiang is another port city on this list and the only international trade
port city from the province. It has attracted sizable foreign investments,
boosting its economy significantly. Apart from its strong transport network,
Jiujiang is supported by its automotive, energy, materials, and electronic
industries within the Economic and Technological Development Zone.

Ganzhou, which was poverty-ridden, has seen significant development over the
past decade. A reliable high-speed rail network has been set up, connecting it
to its neighboring province, making it an important strategic location for the
One Belt One Road plan. Lenient tax policies have been introduced to encourage
the growth of industries in the city.

Chinese cities have focused on industries that have been relevant in the past
decade. These industries primarily belong to technology, automotive, and
manufacturing sectors zhang2021study ; techakanjanakit2012 ; wubbeke2016made .
They have invested in infrastructure and introduced favorable policies, and in
return, they have experienced positive economic growth. Many of the changing
cities have ports666Ports are either seaports or inland ports; inland ports
are similar to seaports but with smaller capacity and use inland waterways
such as rivers instead of the sea., facilitating ease of trade. Interestingly,
their focus has not only been on port cities but also on the landlocked cities
such as Urumqi, which is vital for trade with Central Asia and Europe
bird2020belt ; wen2019impacts .

Most cities with change have been identified from the USA. A majority of these
cities are in the eastern states of the USA, except for Boise (Idaho),
situated on the western coast. Lafayette is identified as the city with the
biggest change for the USA. Major oil, retail, and IT firms are situated in
the city. Oil and gas have been the key industry for Lafayette, but it has
been on the decline as of late. Other than Lafayette, Shreveport is another
city from Louisiana that has been identified for its change. Port of
Shreveport is a designated foreign trade zone, and with immediate access to
barge, motor freight, rail, and air transport facilities, it is lucrative for
businesses to invest in the city. Shreveport is also growing as an IT industry
and is part of the technology cluster forming along the I20 corridor. Fort
Myers and Little Rock also have foreign trade zones. Like Shreveport, Little
Rock also provides inter-modal logistic facilities for businesses. Greenville
has evolved from a textile-based economy to a diverse economy based on
automotive, energy, and manufacturing sectors. Many multinational companies
have a presence in Columbia from various sectors such as manufacturing, health
care, information technology, and energy. To increase investments, Dayton
introduced Opportunity Zones within the city which provides substantial tax
incentives to investors. Boise has been home to a few big technology
companies, but recently, there has been a surge of tech start-ups in the city.
As former technological hubs become competitive, entrepreneurs have approached
Boise, contributing to its growth. Madison is also growing steadily with the
boom in technology companies, inclined towards biotechnology, influenced by
academia’s collaboration with local businesses. Knoxville has shown growth due
to its energy and retail sector. Despite the declining automotive industry and
water, crisis pieper2017flint  in the city, Flint continues to maintain ties
both locally and internationally, suggesting its growth.

The economic growth of changing cities in the US can be attributed to its
entrepreneurial culture hafer2013entrepreneurship . Opportunities in the
technology sector have attracted many entrepreneurs to start new businesses,
assisted by the collaboration of academia to provide a skilled workforce.
Besides the technology industry, other sectors have also contributed to the
economic growth of these cities. As a result, the connections of these cities
have grown drastically. Like the Chinese cities, these changing cities have
most of their links within the country.

Two European cities were identified among the changing cities in the list.
Cork is one of the port cities of Ireland. Over the past decade, Cork has
evolved as an IT hub with major technological firms stationed there.
Pharmaceutical companies have also invested significantly in the city.
Limassol is the port city of Cyprus and is an essential source of revenue for
the country. Limassol is experiencing growth in the economy as low corporate
tax and port availability attracts investments from multinational firms.

Cities with the most change have been identified mainly in Asia and North
America, many of them found in China and the US, respectively. Their
connections are primarily local, providing stability to their regions. These
cities have focused mainly on technology and manufacturing for their economic
growth. The Middle East has focused on diversified economic growth and reduced
their reliance on oil and gas industry. A couple of European cities also
indicated growth in their connections, while cities from other regions showed
no significant change in their connections.

###  5.3 Summary of Results and Discussion

Based on the discussion, an analysis of the topological overlap allowed us to
reach some critical conclusions. Firstly, the stable cities identified in our
study align with previous studies related to important cities of the world.
These include New York, London, Paris, and Tokyo, which are home to many
multinational firms. Secondly, the identified changing cities in China hinted
towards a decentralized economic strategy as almost all the identified cities
belonged to different provinces. Most of these Chinese cities have ports
(either seaport or inland port) which are vital for trade ducruet10 . China’s
inclination towards international trade for economic growth is also
highlighted by the development of the landlocked city of Urumqi, which is
pivotal for its Belt and Road initiative. Lastly, the changing cities
identified in the US showed less inclination towards international trade as
only a few of them are port cities. Furthermore, a majority of their
connections were found within the US with the highly connected Interstate
Highway System facilitating domestic trade between cities
jaworski2018interstate . These factors suggest the US’ self-dependence on the
economic growth of its changing cities.

From a macroscopic point of view, analyzing the data set makes a strong case
of a relational economy bathelt11  where interactions among global companies
situated geographically around the world play an important role in the
economic development of not just cities, but regions and even countries to
some extent. The complex interconnected systems, inter-dependencies, global
exchanges, intertwined economies and, local and national policies all play a
vital role in shaping the economic landscape of the world we live in. This
study provides evidence that integrated relational economies result in
creating and adding value to the modern successes of fast growing cities and
countries.

##  6 Conclusions and Future Work

In this paper, we studied the network of cities formed through multinational
companies and their subsidiaries for 2010 and 2019. We used topological
overlap as a metric to identify stable and changing cities in this network.
The stable cities identified in this paper further strengthen previous studies
on the importance of cities like New York, London, Paris, and Tokyohussain19 ;
king2015global . Stable cities are home to many multinational firms, which
contribute to the economic stability of these cities. Analyzing the list of
changing cities, it is clear that most of them are in the US or China.
Changing cities in China are not concentrated in a single region implying
decentralization strategy for economic growth. Most of these cities are port
cities, indicating a higher focus on international trade for economic growth.
On the other hand, US cities showed more intent towards domestic trade as
these cities are densely connected within the country, and only a few of them
are port cities.

Coincidentally, all cities identified in the changing cities indicated growth.
Identifying declining cities can also provide interesting insights and can be
pursued in the future. This study has considered just two intervals separated
by a decade to identify important cities. Considering intermediate intervals,
we can get a deeper understanding of the development of cities. As it is
unnecessary for the change to be monotonous in each instance, we may observe
swings in the growth over the studied time intervals. We may also observe
cities exhibiting different growth rates and ending up with the same strength
of linkages in the end. Further research in this direction can aid in making
informed decisions and devising better policies to promote economic growth
resulting in urban and regional development.

##  7 Conflict of Interest Statement

All authors declare that they have no conflicts of interest.

##  8 Data Availability Statement

The data used in this study was made available by Bureau van Dijk (Bureau van
Dijk Electronic Publishing http://www.bvdep.com/). The data cannot be shared
publicly due to certain licensing restrictions.

##  9 Acknowledgments

The authors would like to thank the team members of CitaDyne research group at
Université de Lausanne, Switzerland and ERC GeoDiversity research group at
University of Paris, France to correct erroneous entries and fill in missing
data. The authors would also like to thank the anonymous reviewers for their
valuable feedback and comments that enabled us to improve the quality of this
manuscript by adding insightful discussions.

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