[1]Ghazal Kalhor

[1]School of Electrical and Computer Engineering, College of Engineering,
University of Tehran, Tehran, Iran

2]Tehran Institute for Advanced Studies, Tehran, Iran

# Understanding Trends, Patterns, and Dynamics in Global Acquisitions: A
Network Perspective

<EMAIL_ADDRESS>Behnam Bahrak<EMAIL_ADDRESS>*  [

###### Abstract

Studying acquisitions offers invaluable insights into startup trends, aiding
informed investment decisions for businesses. However, the scarcity of studies
in this domain prompts our focus on shedding light in this area. Employing
Crunchbase data, our study delves into the global network of company
acquisitions using diverse network analysis techniques. Our findings unveil an
acquisition network characterized by a primarily sparse structure comprising
localized dense connections. We reveal a prevalent tendency among
organizations to acquire companies within their own country and industry.
Furthermore, our temporal analysis indicates a growth in network communities
over time, accompanied by a trend toward a sparser network. Through centrality
metrics computation in the cross-city acquisition network, we identify New
York, London, and San Francisco as pivotal and central hubs in the global
economic landscape. Finally, we show that the United States, United Kingdom,
and Germany are predominant countries in international acquisitions.

###### keywords:

International acquisitions, Network analysis, Startup trends, Crunchbase data,
Economic hubs

##  1 Introduction

Today, a multitude of startups are emerging at a faster pace compared to
previous times [1]. This surge can be attributed, in part, to advancements in
technology, leading to the rapid establishment of a great number of IT-based
startups [2]. The abundance of startups presents venture capitalists and
investors with a wide array of options for investment or acquisition.
Therefore, it is crucial for these organizations to conduct thorough research
before making such decisions, aiming to enhance their prospects of success [3,
4]. On the other hand, being acquired by a larger and financially stronger
company is considered a measure of success and the ultimate goal for startups,
making it a critical step for the founders of these young firms [5, 6]. As a
result, offering a more profound understanding of global-level acquisitions
holds great importance for businesses in various sectors and geographic
regions, encompassing both large companies and startups at different stages of
evolution.

Crunchbase111https://www.crunchbase.com, PitchBook222https://pitchbook.com,
and VentureSource333https://www.venture-source.com are among the most popular
platforms providing extensive datasets, collecting information about global
firms and their transactions, making them valuable data sources for evaluating
acquisitions [7]. However, Crunchbase stands out as the most complete and
comprehensive database among them, covering the greatest number of entries and
features [8]. Additionally, this platform offers detailed information
regarding acquisitions, including type, date, and price, making it a useful
data source for analyzing various facets of these transactions. Therefore, we
leverage this insightful data for our research to provide a holistic view of
company acquisitions.

In this study, we construct and investigate the acquisition network of
companies, exploring its projections onto acquiring and acquired firms,
cities, and countries using Crunchbase data. We employ a network science
approach in our analyses and interpret various structural features of these
networks to gain a deeper understanding of dynamics and trends in acquisitions
over time.

Throughout this research work, our goal is to address the following questions:

  * •

What features influence the interconnections between organizations within the
acquisition network?

  * •

How has the structure of the acquisition network evolved over time?

  * •

Which cities or countries serve as global economic hubs in terms of
acquisitions?

Our contributions can be summarized as follows:

  1. 1.

We construct the company acquisition bipartite network and its projections on
acquirers and acquirees, providing their fundamental topological features.

  2. 2.

We calculate and interpret structural features such as transitivity, average
clustering coefficient, and the number of communities for these networks.

  3. 3.

We identify the most central companies within the acquisition network and its
projections by calculating various centrality measures to pinpoint influential
companies in acquisition transactions.

  4. 4.

We compute assortativity coefficients of different nodal attributes within the
networks to assess the tendency of companies in making connections with
similar companies.

  5. 5.

We build exponential random graph models (ERGM) for our networks to identify
which features cause connections between organizations within the networks.

  6. 6.

We calculate different structural features of the acquisition network over
time to provide a perspective on the evolution of the network.

  7. 7.

We build the cross-city acquisition network and the cross-border acquisition
network, calculating various centrality metrics to identify economic hubs
among cities and countries.

The rest of the paper is structured as follows. In the “Related work” section,
we explore previous studies based on Crunchbase data and juxtapose their scope
and perspectives with ours. In the ”Methods and materials” section, we provide
an explanation of our data and its features along with the definition of
metrics that we calculate in this study. In the ”Results and discussion”
section, we describe our analyses and findings and then interpret them.
Finally, we conclude the paper and provide directions for future work in the
”Conclusion” section.

##  2 Related work

Different economic and managerial studies have utilized Crunchbase data since
its foundation in 2007 to gain insights into company interactions, market
trends, and strategic behaviors [9, 10]. They have employed various
perspectives, focused on different sectors, geographic areas and time
brackets, and utilized a wide range of data analysis techniques to address
their research inquiries. We provide a general classification of these
research works below to offer a more comprehensive view of previous scholarly
work in this field.

###  2.1 Business success prediction

Several studies have utilized Crunchbase data to forecast firms’ success using
various methodologies. In [11], the authors constructed machine learning
models leveraging demographic, geographical, and fundamental company
information obtained from Crunchbase as predictors to gauge the success of
young companies, defined by their completion of a series B round, undergoing
an IPO, or being acquired. Their findings revealed that the gradient boosting
algorithm surpassed other classifiers in accuracy for this prediction task,
demonstrating its potential application in real-world scenarios. Te et al.
[12] enhanced Crunchbase data with information sourced from LinkedIn and
utilized gradient boosting models to predict the successful attainment of
Series A funding as a pivotal marker of startup success. Their research
demonstrated that integrating this additional data substantially improved
model performance, resulting in a higher AUC. In the study conducted by Kim et
al. [13], they investigated the influence of industry-specific features on
predicting startup success. Employing various machine learning models, they
highlighted the significance of these characteristics. Another group of
researchers employed a network-based approach to predict the future economic
success of young firms, emphasizing the pivotal role of startups’ positions
within their ecosystem [14].

###  2.2 Investment network analysis

Some studies employed network analysis techniques to examine investor behavior
utilizing Crunchbase data. Lian and Yuan constructed a social network
comprising individuals and companies using this dataset, calculating its
characteristics to forecast investors’ funding behavior. Their findings
revealed that proximity between investors and companies enhances the
likelihood of investment, whereas a higher count of shared connections
exhibits a negative impact [15]. The authors of [16] used network alignment
methods and proposed intersect proportions to distinguish between investor
commitments to startups and entrepreneurs. In [17], the authors introduce an
investment behavior prediction model by constructing heterogeneous networks
involving various entities within Crunchbase data. They demonstrated the
effectiveness of their model as a similarity measure between investors and
companies. Holicka and Vinodrai [18] concentrated on blockchain firms and
examined city-region level networks to evaluate investment interactions. Their
study unveiled that investments in tech startups primarily originate from a
select few global cities.

###  2.3 Industry-specific analysis

Some studies have concentrated on analyzing market trends within specific
industries using Crunchbase data. For instance, the authors of [19] explored
the evolution of software startup ecosystems. They scrutinized various stages
along this trajectory, elucidating the requisites and motives for each
developmental phase. Halminen et al. [20] investigated the factors influencing
the allocation of venture capital funding for healthcare AI companies using
Crunchbase data. Their findings indicated that the presence of research and
pharmaceutical organizations as clients positively correlates with increased
funding for these companies. In [21], researchers explored the origins of
manufacturing startups, examining features by integrating Crunchbase data on
experts and managers at these firms with information from their LinkedIn-
published CVs. Their findings highlighted the significance of prior experience
and academic or tech backgrounds among the teams within these young firms.
Eickhoff et al. [22] utilized Crunchbase data to classify FinTech business
models. Another group of scholars harnessed this database to assess investor
funding preferences specifically within cloud computing startups [23]. They
emphasized that investors in this domain show a preference for funding
startups offering services in crucial, emerging, and rapidly expanding IT
sectors.

###  2.4 Merger and acquisition analysis

Only a few studies have sought to examine merger and acquisition patterns
using Crunchbase data. In [24], the authors constructed temporal networks
representing international mergers and acquisitions from this dataset,
analyzing both the topological and geographical characteristics of these
networks. Additionally, they conducted a comparative analysis between these
networks and the international trade network, aiming to discern differences
and similarities, thus gaining valuable insights. Guo et al. [25] concentrated
on Chinese companies while investigating merger and acquisition networks. They
computed various centrality measures to scrutinize M&A behaviors and
constructed multiple linear regression models to evaluate the influence of
diverse structural features on merger and acquisition activities. In [26], Lee
and Geum classified merger and acquisition patterns among startups using data
analysis techniques like K-means clustering and visualization. They identified
five distinct clusters for M&A activities within the Crunchbase dataset. The
authors of [27] integrated Crunchbase data on mergers and acquisitions with
other sources such as Zephyr, predicting future acquisitions through the
application of machine learning and network algorithms.

To the best of our knowledge, our work is the first study on the network
perspective of acquisitions. Additionally, unlike prior studies, we do not
confine our focus to a specific time bracket, leading to a more holistic view
of the networks.

##  3 Methods and materials

In this section, we provide a descriptive explanation of the data and the
metrics that we utilized in this study.

###  3.1 Data

In this part, we investigate the dataset analyzed in this paper. Figure 1
illustrates a simplified entity relationship diagram showcasing the Crunchbase
data collected from the Crunchbase website by the end of July 2023. Crunchbase
is a company that provides information about acquisitions, investments, and
funding activities of startups. Within this comprehensive dataset, our focus
was on three specific tables: organizations, acquisitions, and organization
descriptions. These tables were merged based on their unique identifiers.

The organizations table contains various details about companies, including
geographic features such as country, region, city, and industry features like
category groups list, category list, and social network URLs such as Facebook,
Twitter, LinkedIn, along with founding dates. The acquisitions table holds
information related to acquisition transactions, encompassing details like
acquirer ID, acquiree ID, acquisition type, and acquisition date. Lastly, the
organization descriptions table provides information taken from the companies’
homepages on Crunchbase.

Figure 1: Entity relationship diagram of the data.

####  3.1.1 Data preprocessing

In this part, we outline the steps taken to prepare the data for our analyses.
First, we remove acquisitions where the date is unspecified or the type is not
labeled as an acquisition. Next, we eliminate duplicate acquisitions, ensuring
that only one acquisition remains for each pair of acquirer and acquiree on a
specific date. Subsequently, we exclude organizations from the acquisitions if
details such as their country, region, city, description, category groups
list, category list, or founding date are unspecified. To ensure features are
in a single-valued format, columns with list values are converted into
singular values. To achieve this, we preprocess the descriptions and
categories provided for each organization. We then calculate the cosine
similarity between the description and each category to identify the primary
category of that organization. The same process is applied to category groups.
It is important to note that the categories and category groups in the initial
data were sorted alphabetically, making it impossible to infer the primary
ones without utilizing NLP techniques. Finally, date columns are transformed
into the year-month format and then converted into numerical format for
comparison across different dates. After these steps, we acquired complete
data on 92,788 acquisitions, involving 119,263 organizations, out of the
initial 152,923 acquisitions present in the raw data. In essence, 39.32% of
the initial data was removed during the data cleansing stage.

####  3.1.2 Data exploration

In this part, we analyze the distribution of various features within our
dataset to gain deeper insights into their characteristics.

Figure 2 depicts the global distribution of companies across different
countries. The United States, United Kingdom, Canada, Germany, and France
stand out with the highest number of startups in comparison to other
countries. This finding corroborates earlier studies suggesting that Western
nations typically exhibit higher rates of entrepreneurial activity than others
[28]. Bürgel et al. [29] also highlight the substantial internationalization
of sales among British and German startups. Furthermore, Klapper [30] notes a
significant growth in the number of startups in France in 2009.

Figure 2: Representation of company distribution across countries on a world
map, with the size of each country (depicted as circles) proportional to its
frequency.

Figure 3 presents the distribution of companies across various cities
worldwide. As per this figure, London, New York, and San Francisco host the
highest number of startups, followed by Paris and Toronto in the fourth and
fifth positions, respectively. These observations are consistent with prior
studies highlighting London and Paris as significant European hubs [31],
alongside New York and San Francisco as prominent cities for building startups
[32, 33].

Figure 3: Representation of company distribution across cities on a world map,
with the size of each city (depicted as circles) proportional to its
frequency.

Figure 4 offers an overview of the primary categories within companies. Our
dataset comprises 698 unique primary categories, prompting us to employ a
bubble chart for visualization. This chart emphasizes categories with the
highest frequencies, with each bubble’s size directly proportional to its
frequency within companies. Notably, Software, Health Care, Manufacturing,
Financial Services, and Information Technology emerge as the categories with
the highest frequencies. This finding is in the line of prior work [26].

Figure 4: Bubble plot of companies’ primary categories.

Figure 5 presents the distribution of companies based on their founding years,
spanning from 1900. The distribution demonstrates a leftward skew, suggesting
a gradual rise in startups from 1900 to 1966, succeeded by a rapid increase
leading to its initial peak in 1999. This surge may be associated with the
dot-com boom in the late 1990s, contributing to a rise in technology-driven
startups [34]. Following this, there is a distinct decrease in 2002, succeeded
by a resurgence leading to a second peak in 2012. However, post-2014, there is
a discernible decline. The decrease in 2002 could be related to the aftermath
of the dot-com boom, which resulted in financial problems for internet-based
companies [35].

Figure 5: Distribution of companies across founding years.

Figure 6 illustrates the distribution of acquisitions across different years,
beginning from 1908 (the earliest transaction date in our dataset). The
distribution exhibits a left-skewed pattern, with a gradual increase in
acquisitions followed by a steep upward trend starting from 2000. This
increasing pattern could also be due to the dot-com crash. Ultimately, the
highest peak in 2021 can be linked to businesses recovering post the COVID-19
pandemic, resulting in a rise in both acquisitions and investments [36].

Figure 6: Distribution of acquisitions across different years.

###  3.2 Metrics

In this part, we provide the definitions of the metrics we calculate in
different parts of our analyses.

####  3.2.1 Transitivity

The transitivity of a network is calculated as the proportion of all potential
triangles existing within the network. The formula for transitivity is:

$\displaystyle\frac{(number\>of\>triangles\times
3)}{(number\>of\>connected\>triples)}$ (1)

as proved by [37]. We utilize this metric to assess the strength of the
community structures of the acquisition network and the common acquirer
network.

####  3.2.2 Average clustering coefficient

The average clustering coefficient of a network indicates the tendency of
nodes to cluster together. The formula for the average clustering coefficient
is as follows:

$\displaystyle C=\frac{1}{n}\sum_{v\in G}c_{v},$ (2)

where $n$ is the number of nodes in the network, and $c_{v}$ is the local
clustering coefficient of node $v$ [38]. We utilize this metric to assess the
level of interconnectedness and community structure within the acquisition
network and the common acquirer network.

####  3.2.3 Average shortest path length

The average shortest path length of a network is computed as the average
length of the shortest paths between all pairs of nodes in the network. The
formula for average shortest path length is as follows:

$\displaystyle S=\frac{\sum_{u,v}d(u,v)}{n\times(n-1)},$ (3)

where $d(v,u)$ is the length of shortest path between nodes $v$ and $u$, and
$n$ is the number of nodes in the network [37]. We calculate this metric for
the largest connected component of the acquisition network and the common
acquirer network to evaluate the mean distance between each pair of
organizations.

####  3.2.4 Assortativity

The assortativity coefficient of a network measures the proportion of
connections in the network that occur between nodes of the same type based on
a specific attribute [37]. We compute this metric for various node attributes
to identify which attributes are more influential in shaping the connections
within the acquisition network and the common acquirer network.

####  3.2.5 Betweenness centrality

The betweenness centrality calculates the extent to which a node lies on paths
between other nodes in a network. The formula for betweenness centrality is as
follows:

$\displaystyle B_{u}=\sum_{i,j}\frac{\sigma(i,u,j)}{\sigma(i,j)},$ (4)

where $\sigma(i,u,j)$ represents the number of shortest paths between nodes
$i$ and $j$ that pass through node or edge $u$, and $\sigma(i,j)$ is the total
number of shortest paths between $i$ and $j$. The sum is computed over all
pairs $i$, $j$ of distinct nodes in the network [37]. We calculate this
measure for the nodes in the cross-city acquisition network to determine which
cities are influential in terms of their control over acquisition transactions
between other cities.

####  3.2.6 Closeness centrality

The closeness centrality calculates the mean distance from a node to other
nodes in a network. The formula for closeness centrality is as follows:

$\displaystyle C_{u}=\frac{n-1}{\sum_{v=1}^{n-1}d(v,u)},$ (5)

where n indicates the count of nodes accessible from node $u$, and $d(v,u)$
represents the shortest distance between nodes $v$ and $u$ [37]. We calculate
this measure to determine which cities are closer to other cities in the
cross-city acquisition network.

####  3.2.7 Weighted degree centrality

The weighted degree centrality calculates the sum of the weights of the edges
connected to a node in a network. The formula for weighted degree centrality
is as follows:

$\displaystyle WD_{u}=\sum_{v}w(v,u),$ (6)

where node $v$ is a neighbor of node u, and $w(v,u)$ is the weight of the edge
between nodes $v$ and $u$ [37]. We calculate this metric to assess which
cities acquire a greater number of organizations from other cities in the
cross-city acquisition network.

####  3.2.8 PageRank centrality

The PageRank centrality calculates the ranking of a node within a network by
considering the incoming link structure. The formula for PageRank centrality
is as follows:

$\displaystyle x_{i}=\alpha\sum_{j}{A_{ij}\frac{x_{j}}{d_{j}^{out}}}+\beta,$
(7)

where $A_{ij}$ is an element of the adjacency matrix, $d_{j}^{out}$ denotes
the out-degree of node $j$, and $\alpha$ and $\beta$ are positive constants
[37]. We calculate this metric to identify influential cities in the cross-
city acquisition network in terms of their incoming link counts.

####  3.2.9 Eigenvector centrality

The eigenvector centrality calculates the centrality of a node considering the
centrality of its neighboring nodes. It is determined by solving the equation

$\displaystyle Ax=\lambda x,$ (8)

where $A$ represents the adjacency matrix of the network and $x$ is the
eigenvector. The eigenvalue associated with $A$ influences this calculation
[37]. We employ this metric to assess the transitive influence among cities in
the cross-city acquisition network.

####  3.2.10 Authority centrality

The authority centrality of a node within a network is derived from the
principal eigenvector of the matrix $A^{T}A$, where $A$ stands for the
network’s adjacency matrix [39]. We utilize this measure to assess the most
influential countries in the cross-border acquisition network.

##  4 Results and discussion

In this section, we provide a detailed description of the analyses performed
and our findings, along with their interpretations.

###  4.1 Acquisition network

In this part, we delineate the construction process of the acquisition network
using Crunchbase data. In this network, nodes represent organizations engaged
in acquisitions. We establish directed edges from organization $A$ to
organization $B$ if $A$ has acquired $B$, resulting in a directed network
comprising 119,263 nodes and 92,788 edges. Considering the network’s extensive
size, we selected a sample for visualization purposes. To accomplish this, we
displayed the four largest Louvain communities from the largest weakly
connected component of the network. Figure 7 illustrates this subgraph,
encompassing 1,445 nodes and 1,447 edges, highlighting four distinct
communities within the network.

Figure 7: A sampled subgraph of the acquisition network. Nodes are colored
based on their community detected via the Louvain algorithm [40].

###  4.2 Common acquirer network

In this part, we delve into the common acquirer network, which is a projection
of the acquisition network onto acquiree nodes. To construct this network, we
establish an edge between two organizations whenever a common entity has
acquired both of them. This results in an undirected weighted network, where
the weight of an edge signifies the number of shared acquirers between two
organizations. This network encompasses 68,297 nodes and 639,064 edges. Figure
8 depicts a sample of this network, showcasing the six largest Louvain
communities within the largest connected component of the network. The
resulting sample consists of 3,937 nodes and 44,340 edges. As illustrated in
Figure 8, each community within the network is highlighted with a specific
color. Companies within each community primarily originate from the United
States. Table 1 presents the percentage of the major industry category within
each community. As shown, most communities have Health Care or Manufacturing
as their primary industry category, aligning with our previous observation
indicating that these industries are the most common category groups among
startups.

Figure 8: A sampled subgraph of the common acquirer network. Nodes are colored based on their community detected via the Louvain algorithm. Table 1: Percentage of major industry categories within communities. Community | Industry category | Portion
---|---|---
0 | Health Care | 18.35%
1 | Manufacturing | 14.81%
2 | Manufacturing | 15.01%
3 | Manufacturing | 11.76%
4 | Manufacturing | 20.48%
5 | Food and Beverage | 12.40%

###  4.3 Common acquiree network

In this part, we describe the construction of the common acquiree network,
which is another projection of the acquisition network. To build this network,
we establish an undirected edge between two organizations if they have
acquired the same organization. The weight of these edges corresponds to the
number of shared acquirees between the two organizations. This process results
in a weighted network comprising 4,063 nodes and 3,115 edges when applied to
the entire dataset. To facilitate visualization, we have selected the eight
largest communities from within the largest connected component, creating a
sample network composed of 496 nodes and 593 edges. Figure 9 depicts this
visualization with communities detected using the Louvain algorithm. Each
community mainly comprises acquirer companies from the United States and the
Financial Services industry. Table 2 represents the most common regions within
each community, along with their respective percentages. According to this
table, New York and England are the major regions from which acquirer
companies originate, aligning with prior studies that highlight the prominence
of these regions in startup ecosystems [32, 41].

Figure 9: A sampled subgraph of the common acquiree network. Nodes are colored based on their community detected via the Louvain algorithm. Table 2: Percentage of major regions within communities. Community | Region | Portion
---|---|---
0 | New York | 10.23%
1 | California | 15.38%
2 | England | 12.50%
3 | Ontario | 11.29%
4 | New York | 8.47%
5 | New York | 14.81%
6 | New York | 12.24%
7 | England | 14.29%

###  4.4 Structural analysis

In this part, we present a summary of the structural properties of the
acquisition network, common acquirer network, and common acquiree network.
Based on the data in Table 3, it is evident that these networks have low
densities, suggesting the likelihood of organizations forming smaller,
distinct communities within these networks. The transitivity of the
acquisition network is remarkably low, while that of the common acquirer
network is close to 1. The common acquiree network exhibits a transitivity
that is relatively low, but it is higher compared to that of the acquisition
network. This outcome was anticipated since projection networks typically
manifest strong community structures, resulting in high transitivity [42].

We computed the average clustering coefficient and average shortest path
length within the largest weakly connected component of the acquisition
network. These metrics indicate that this network is not well-connected. The
low average clustering coefficient suggests the presence of weak ties, and on
average, it takes at least 14 steps to reach from one randomly selected
organization to another. Conversely, the common acquirer network exhibits a
contrasting scenario. It boasts a high average clustering coefficient and a
small average shortest path length. This pattern aligns with the network’s
configuration of well-connected clusters of organizations sharing common
acquirers, as anticipated. On the other hand, the common acquiree network has
a moderate average clustering coefficient and an average shortest path length
close to that of the common acquirer network.

For community detection, we employed the Infomap algorithm [43] to identify
communities within these networks. The substantial number of communities
implies acquisitions occurring among distinct subgroups of organizations.
Additionally, we calculated the sizes of the largest connected components
(both weakly and strongly connected for the acquisition network) in these
networks. Notably, the presence of a strongly connected component with a size
of three in the acquisition network indicates that at most three organizations
are mutually involved in acquisitions. Conversely, the substantial size of the
largest connected component (and the largest weakly connected component for
the acquisition network) underscores the robust and centralized structures
inherent in these networks.

Table 3: Structural properties of the acquisition network and its projections. Property | Measurement
---|---
Acquisition network |  Common acquirer network |  Common acquiree network
Density | $6.524\times 10^{-6}$ | $2.740\times 10^{-4}$ | $3.775\times 10^{-4}$
Transitivity | $6.024\times 10^{-5}$ | 0.993 | 0.081
Average clustering coefficient | 0.002 | 0.828 | 0.064
Average shortest path length | 14.344 | 7.242 | 6.825
Number of communities | 32250 | 12786 | 1366
Largest weakly connected component size | 25285 | - | -
Largest strongly connected component size | 3 | - | -
Largest connected component size | - | 10427 | 1098

We also identify the most central nodes within these networks to pinpoint hub
companies in acquisitions. Table 4 presents the most central companies in the
networks based on different centrality measures, providing a holistic view of
these economic hubs. According to our results, Gallagher, HUB International,
Napster, Solidscape, and Hume Brophy emerge as the most centric acquiring
firms in the acquisition network, most of which are from the United States and
have already been acquired at the present time. In the common acquirer
network, William H. Connolly & Co., Raet, Nets, and Webhelp stand out as the
most centric acquired firms. Most of them are located in European countries,
including the Netherlands, Denmark, and France, emphasizing the significance
of European startups in acquisition transactions [44]. In the common acquiree
network, Advent International has the highest values for all centrality
metrics, highlighting its dominant role as a private equity firm based in the
United States.

Table 4: The most central nodes within the acquisition network and its projections. Centrality metric | Most central nodes
---|---
Acquisition network |  Common acquirer network |  Common acquiree network
Degree centrality | Gallagher | William H. Connolly & Co. | Advent International
Betweenness centrality | HUB International | Raet | Advent International
Closeness centrality | Napster | Nets | Advent International
Eigenvector centrality | Solidscape | William H. Connolly & Co. | Advent International
PageRank centrality | Hume Brophy | Webhelp | Advent International

###  4.5 Assortativity analysis

In this part, we calculate and interpret assortativity coefficients for the
acquisition network, common acquirer network, and common acquiree network.
Table 5 provides an overview of these coefficients for different node
features. As shown, the acquisition network exhibits the highest assortativity
coefficient with respect to the country feature. This suggests that
organizations are more likely to pursue acquisitions within their own country,
consistent with previous studies that highlight a higher inclination among
companies to engage in domestic acquisitions [45]. Such acquisitions are known
to yield greater returns for acquirers [46]. The next feature with the highest
assortativity is the category group, indicating organizations’ preference for
acquiring those in the same industries as themselves, aligning with prior
studies [47, 26]. The third highest coefficient corresponds to the founding
date of the organizations, suggesting that organizations involved in
acquisitions tend to have close founding dates, consistent with previous
research [26]. Notably, all coefficients are positive, indicating a prevailing
inclination among organizations to acquire entities similar to themselves,
aligning with findings from prior studies [47].

In the common acquirer network, the highest assortativity is observed for the
node degree, as anticipated. This is due to the fact that 96.87% of acquiree
organizations, based on the indegree of nodes in the acquisition network, have
only one acquirer. Consequently, neighbors in the common acquirer network tend
to have similar node degrees. The second and third highest assortativity
values are linked to the category group and founding date, respectively.
Consistent with previous studies [48, 49], this finding suggests a propensity
among acquirers to target organizations within specific industries or age
brackets.

Similar to the acquisition network, the highest assortativity coefficients in
the common acquiree network belong to the country, category group, and
founding date, respectively. In essence, organizations from the same country,
industry, or age bracket are more inclined to acquire similar organizations.

Table 5: Assortativity coefficients of the acquisition network and its projections. Feature | Assortativity coefficient
---|---
Acquisition network |  Common acquirer network |  Common acquiree network
Country | 0.472 | 0.216 | 0.286
Region | 0.167 | 0.042 | 0.083
City | 0.088 | 0.013 | 0.054
Category group | 0.292 | 0.236 | 0.157
Category | 0.177 | 0.162 | 0.082
Founding date (year-month) | 0.248 | 0.228 | 0.097
Node degree | 0.019 | 0.986 | 0.088

###  4.6 ERGM analysis

In this part, we present the ERGMs calculated for the acquisition network,
common acquirer network, and common acquiree network. Our models utilize
similar sets of node features and “edges” as parameters. Table 6 provides a
summary of the ERGM statistics. According to the results, for these networks,
all predictors are statistically significant $(p<0.0001)$ with positive
estimates, except for the founding date, indicating that organizations with
similar values for each feature are more likely to be connected. For instance,
organizations within the same country are more likely to share the acquirer-
acquiree relationship. This aligns with prior research indicating that
companies tend to purchase firms located in closer geographic proximity [50].
Conversely, negative estimations regarding the founding date suggest that this
feature cannot be the cause of the connection between organizations within the
networks. Furthermore, both networks have positive estimates for “edges”,
indicating that they have higher densities than random networks with similar
numbers of nodes. In other words, nodes in both networks are more inclined to
be connected to each other [51]. The negative estimate for “edges” indicates
that the common acquiree network exhibits lower density in comparison to
random networks possessing similar topological features. The AIC values for
each model, as shown in Table 6, reveal that the ERGM of the common acquiree
network has a better fit (lower AIC value) compared to other networks.

Table 6: Estimates from the ERGMs of the acquisition network and its projections. Variable | Estimate (standard error)
---|---
Acquisition network |  Common acquirer network |  Common acquiree network
edges |  8.135*** $(2.005\times 10^{-1})$ |  9.803*** $(1.053\times 10^{-1})$ |  -4.634*** $(1.115)$
Country |  1.161*** $(7.342\times 10^{-3})$ |  0.721*** $(2.605\times 10^{-3})$ |  0.787*** $(3.840\times 10^{-2})$
Region |  1.117*** $(1.169\times 10^{-2})$ |  0.544*** $(5.706\times 10^{-3})$ |  0.503*** $(8.354\times 10^{-2})$
City |  1.373*** $(1.505\times 10^{-2})$ |  0.479*** $(1.107\times 10^{-2})$ |  0.693*** $(1.031\times 10^{-1})$
Category group |  1.794*** $(9.213\times 10^{-3})$ |  1.481*** $(3.856\times 10^{-3})$ |  1.193*** $(5.116\times 10^{-2})$
Category |  1.351*** $(1.104\times 10^{-2})$ |  1.553*** $(4.454\times 10^{-3})$ |  0.882*** $(7.056\times 10^{-2})$
Founding date (year-month) |  $-5.298\times 10^{-5}***$ $(5.048\times 10^{-7})$ |  $-4.678\times 10^{-5}***$ $(2.647\times 10^{-7})$ |  $-9.727\times 10^{-6}***$ $(2.819\times 10^{-6})$
AIC | 2226707 | 11085347 | 53343
$*p<0.05,**p<0.01,***p<0.001$ |  |  |

###  4.7 Temporal analysis

In this part, we investigate the evolution of the acquisition network over
time. We begin our analysis with the January 2000 network and subsequently
consider one-month intervals between consecutive time points, resulting in 283
time points up to the present data collection date. At each time point, we
compute various structural metrics for the corresponding acquisition network.

Figure 10 illustrates the temporal changes in network density. The visual
representation reveals a declining trend, suggesting that the network has
gradually become sparser over time. In essence, organizations within the
network have exhibited reduced connections over time. This trend could be
attributed to the increase in the number of investors and venture capitalists,
and the fact that we are no longer observing a dominant monopoly [52, 53].

Figure 10: Time series of the density of the acquisition network.

Figure 11 illustrates the average clustering coefficient of the network at
different time points. According to this figure, the network’s average
clustering coefficient remained at zero before 2012, indicating a lack of
connections between the organizations’ neighborhoods within the network.
However, starting from 2012, it shows an upward trend, reaching its peak in
2013. Subsequently, there is a decline observed until 2014, followed by a
general increasing trend with intermittent fluctuations. This pattern suggests
a gradual densification of local connections over time, even as the overall
connections have become sparser. It could be related to the European debt
crisis in the early 2010s, which might have prompted many companies to attempt
acquiring neighboring businesses as a strategic move to expand and overcome
economic challenges [54].

Figure 11: Time series of the average clustering coefficient of the
acquisition network.

Figure 12 illustrates the average shortest path length of the acquisition
network over time. The metric remains around 2 until 2007, after which it
steadily increases, reaching its initial peak in the same year. Subsequently,
from 2007 onward, it gradually ascends to its second peak in 2015. Following
this, it displays a gradual decrease and eventually fluctuates around 14.
Essentially, this suggests that in recent years, on average, organizations
required approximately 14 hops to reach another organization within the
network. This pattern could be related to the 2007–2008 financial crisis,
which might have resulted in the fragmentation of the acquisition network in
the subsequent years [55].

Figure 12: Time series of the average shortest path length of the acquisition
network.

Figure 13 displays the changes in the number of communities identified within
the acquisition network. As illustrated, it follows an increasing pattern,
indicating a rising level of segregation in the network. In other words,
organizations within the network have formed more distinct groups, resulting
in a more complex structure. This could be related to the increase in the
number of industries in which acquisitions occur, considering that
acquisitions mostly happen between companies within the same industry [56, 47,
26].

Figure 13: Time series of the number of communities identified within the
acquisition network.

Figure 14 represents the number of weakly connected components in the network
over time. Similar to the number of communities, the number of connected
components has also increased. In fact, the network has become more fragmented
and less cohesive, further highlighting the absence of a monopoly in
acquisition transactions in recent years [52, 53].

Figure 14: Time series of the number of weakly connected components within the
acquisition network.

Figure 15 represents the evolution of a sample of the acquisition network over
time. We can observe the aforementioned trends in these networks. For
instance, the average clustering coefficient of the network has increased,
while the density of the network has declined. Moreover, both the number of
communities and the number of connected components have increased.

Figure 15: Evolution of a sample of the acquisition network over time.

###  4.8 Cross-city acquisition network

In this part, we construct the cross-city acquisition network, where nodes
represent cities of organizations, and directed edges connect city A to city B
if an organization from city A has acquired an organization in city B. The
weight of each edge represents the number of acquisitions between the two
cities. Figure 16 displays a sample of the cross-city acquisition network,
including 50 cities with the highest numbers of connections (indegree +
outdegree) with other cities.

In the visualization, node colors indicate their respective Louvain
communities, and edge thickness is proportional to their weights.
Additionally, node sizes correspond to their betweenness centrality, and the
label sizes are proportional to their closeness centrality. According to our
analysis, the network reveals three distinct communities: the green community
represents cities in the United States, the golden community encompasses
cities in California, and the pink community predominantly consists of
Canadian and European cities, with a few Asian cities like Tokyo, Singapore,
and Mumbai.

Figure 16: A sample of the cross-city acquisition network. Nodes are colored
based on their community detected via the Louvain algorithm.

###  4.9 Centrality metrics

In this part, we calculate and discuss the centrality measures for the top ten
central cities in the cross-city acquisition network. Figure 17 provides a
detailed summary of centrality values for these cities. In terms of weighted
degree centrality, New York exhibits the highest values, aligning with
previous studies that assert New York’s predominant position in the global
economy [57]. Following New York, London and San Francisco have the second and
third highest weighted degrees, respectively. This observation coincides with
Budd and Whimster’s findings, highlighting London’s status as a global
financial center [58]. Additionally, Ester’s work suggests that San Francisco,
with its accelerators in Silicon Valley, plays a significant role in
attracting startups [59].

Regarding betweenness centrality, values remain relatively small due to direct
connections between most cities. The top three cities’ order mirrors that of
weighted degree centrality. This ranking indicates these cities’ influence in
controlling acquisition transactions among other cities.

Figure 17 depicts that New York, London, and San Francisco have the highest
PageRank values, signifying their active engagement in acquisitions with other
influential cities within the network. The top three nodes in eigenvector
centrality rankings align with PageRank, except for the first position, which
is held by London. This outcome further confirms the strong connections of
these cities to central hubs within the network.

In terms of closeness centrality, New York, London, and San Francisco each
have a maximum value of 1, signifying direct acquisition transactions with all
other cities in the network. Essentially, they have acquired at least one
organization from every other city in the network.

Figure 17: Side-by-side bar plot of centrality measures for the top ten
central cities within the cross-city acquisition network.

###  4.10 Cross-border acquisition network

In this part, we construct the cross-border acquisition network to explore
country relationships. We establish a directed edge from country A to country
B whenever an organization in A acquires an organization in B. This creates a
weighted directed network where edge weights signify the number of
acquisitions between countries. Figure 18 showcases a sample of this network,
featuring the top 60 countries based on their node degrees. Node size reflects
their authority centrality, while label size corresponds to their betweenness
centrality. Furthermore, nodes are color-coded according to their Louvain
community. According to the findings, the United States, United Kingdom, and
Germany exhibit the highest authority centralities respectively, indicating
their significant influence in the global economy. Additionally, they possess
the third-highest betweenness centralities, confirming their pivotal role in
facilitating acquisition transactions among other countries. These results
align with prior research, reinforcing the dominant position of the United
States in the global economy [60, 61]. Moreover, previous studies have
underscored the substantial contributions of the United Kingdom and Germany in
cross-border acquisitions [62, 63].

Figure 18: A sample of the cross-border acquisition network. Nodes are colored
based on their community detected via the Louvain algorithm.

Figure 19 illustrates the connections between countries in terms of
acquisitions on a world map. For visualization purposes, we utilized the
undirected version of the cross-border acquisition network involving 30
countries with the highest node degrees. The size of each node corresponds to
the number of incoming edges, and the size of its label corresponds to its
betweenness centrality. Additionally, the thickness of the edges is
proportional to their respective weights.

Figure 19: A sample of the cross-border acquisition network on the world map.

##  5 Conclusion

In this study, we analyzed global acquisitions with a network approach to gain
insights into trends, patterns, and dynamics in this realm. We constructed the
acquisition network and its projections on acquirers and acquirees to evaluate
interconnections between companies. Our findings revealed that these networks
have low densities and comprise a great number of small communities. By
calculating assortativity coefficients, we demonstrated a preference among
organizations to acquire companies from the same country, industry, or age
bracket as themselves. ERGMs coefficients indicated the significant impact of
different company features, such as country, region, city, and category, on
the formation of connections between organizations, while founding date did
not prove to be the cause of connections. Additionally, we conducted a
temporal analysis on the acquisition network, which indicated that the average
clustering coefficient has increased over time, while the network has become
sparser, comprising more communities. We computed different centrality metrics
for the cross-city acquisition network and found that New York, London, and
San Francisco are global economic hubs. Finally, the analysis of the cross-
border acquisition network revealed that the United States, United Kingdom,
and Germany are the dominant countries in international acquisitions.

Future work can utilize insights from this paper in designing models for
predicting future acquisitions. Additionally, researchers may focus on a
specific city or country based on the economic hubs detected in this study to
explore domestic acquisitions. Another avenue of research for future work is
to create and analyze the merger network and compare its features with those
of the acquisition network.

## Declarations

### Availability of data and materials

The data that support the findings of this study are available from Crunchbase
but restrictions apply to the availability of these data, which were used
under the Crunchbase research license for the current study, and so are not
publicly available. Data are however available from the authors upon
reasonable request and with the permission of Crunchbase.

### Competing interests

The authors declare that they have no competing interests.

### Funding

No funding was received for conducting this study.

### Authors’ contributions

GK: Data curation, Formal analysis, Methodology, Investigation, Validation,
Visualization, Writing- Original draft. BB: Conceptualization, Project
administration, Supervision, Writing- Reviewing and Editing. All authors read
and approved the final manuscript.

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