The Form and Evolution of International Migration Networks

1

The Form and Evolution of International Migration Networks, 1960-2015:

Implications for the Globalization of Migration Thesis

Guy J. Abel1,2 • Jack DeWaard3 • Jasmine Trang Ha3 • Zack W. Almquist3,4

_______________________________________________

1. Asian Demographic Research Institute, School of Sociology and Political Science, Shanghai University,

200444, China

2. Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/ÖAW, WU), Vienna Institute of

Demography (Austrian Academy of Sciences), Vienna 1020, Austria.

3. Department of Sociology, Minnesota Population Center, University of Minnesota, 909 Social Science Tower,

26 19th Ave. S., Minneapolis, MN 55455, USA.

4. School of Statistics, University of Minnesota, 313 Ford Hall, 224 Church St. S.E., Minneapolis, MN 55455,

USA.

2

Abstract We demonstrate the utility of community detection methods—specifically, the

Walktrap algorithm—for identifying the geographic boundaries of international migration

networks. In documenting the form and evolution of international migration networks over the

past half-century, our work opens up a unique opportunity to test the globalization of migration

thesis. Our results demonstrate a tendency toward Balkanization (versus consolidation) in the

number of international migration networks; however, we also document substantial changes

over time in the internal country compositions of these networks. We conclude by discussing the

policy relevance of our work for anticipating future migration and developing appropriate

responses.

Keywords International migration • Migration systems • Migration networks • Community

detection • Globalization of migration

3

Introduction

A longstanding and sometimes contentious issue in research on international migration

systems is how to specify the boundaries of the “identifiable geographic structure[s]” that

systems are ultimately manifested in (Massey et al. 1998:61; see also Bakewell 2014; Kritz and

Zlotnik 1992; Mabogunje 1970). Presently, aside from a generic set of guiding “general

principles” (Zlotnik 1992:20), there is no agreed upon data-driven approach for systematically

identifying these structures, or what Kritz and Zlotnik (1992:15) called migration “network[s]”

consisting of sets of countries that are connected to one another in regular ways by migration

flows. The first aim of this paper is therefore to introduce and demonstrate the utility of

community detection methods (Fortunato 2010)—and, in particular, the Walktrap algorithm

(Pons and Latapy 2006)—for determining the geographic boundaries of international migration

networks. Using a new set of estimates of country-to-country migration flows (Abel 2017), the

most geographically and temporally encompassing of their kind to date, we trace the form and

evolution of international migration networks over the past half-century.

Along the way, our work presents a unique opportunity to generate new insights on the

so-called “globalization of migration” thesis, which refers to the general “tendency for more and

more countries to be significantly affected by international migration” (Castles et al. 2014:16;

see also Czaika and de Haas 2015). Specifically, our work permits us to distinguish between two

very different migration globalization processes. The first process, which we call consolidation,

was originally suggested by Zlotnik (1992:19), and involves the absorption of countries into a

single, “all-encompassing” global migration network over time. Borrowing the term from Frey

(1996), the second process is one of Balkanization whereby multiple migration networks come to

coexist alongside one another. In the lead up to our analysis, we discuss how each process points

4

to a different set of potential causes and mechanisms. And, building on policy research on

international migration “corridors” (IOM 2013:55-60), we conclude by considering how

knowledge of the form and evolution (e.g., globalization) of international migration networks is

critical for anticipating future migration patterns and informing the development of appropriate

responses.

Migration Systems and the Geographic Boundaries of Migration Networks

Research on migration systems is often traced to Mabogunje’s (1970) work on rural-

urban migration in Africa (Bakewell 2014). Mabogunje (1970:3) defined a migration system as

“a complex of interacting elements, together with their attributes and relationships.” Unpacking

this definition, the elements comprising a migration system take many forms, ranging from

individuals and households to nation-states and international bodies like the United Nations.

Elements are characterized by unique sets of demographic, economic, geopolitical, and

sociocultural attributes, with recent studies also stressing the importance of environmental

characteristics (Curtis et al. 2015; Hunter et al. 2015). Finally, elements engage in relationships,

or exchanges, with one another. These take many forms, and might include, for example, flows

of ideas and information, financial capital, and goods and services (Fawcett 1989).

According to Massey et al. (1998:61), “[t]he end result is a set of relatively stable

exchanges of people between [places]…yielding an identifiable geographic structure that persists

across space and time.” In other words, while migration systems are “emergent social entities”

that are actively and continually created and sustained by unique sets of elements and exchanges

at different levels of scale (Bakewell 2014:301; see also Bakewell et al. 2016), they are

5

ultimately manifested in “network[s]” of places that are connected to one another by migration

flows (Kritz and Zlotnik 1992:15). As the focus of this paper is with international migration

networks, our concern going forward is with sets of countries that are connected to one another

by country-to-country migration flows.

A persistently thorny issue in research on international migration networks is how to

identify their geographic boundaries (Bakewell 2014; Mabogunje 1970; Zlotnik 1992). One a

priori approach is to do so based on consideration of why and how certain countries, and not

others, are “linked by large migration flows” (Kritz and Zlotnik 1992:3). For example, scholars

routinely reference a “European migration [network]” (Favell 2008:711), the origins of which

Massey et al. (1998) trace to the 1957 signing of the Treaty of Rome, which established the

European Economic Community. Similarly, Martin (2013) and others refer to a “North American

migration [network]” that revolves around immigration to Canada and the United States. On the

surface, there seems nothing problematic with these sorts of designations; however, upon closer

inspection, they lack a uniform set of criteria for making these assignments that can be applied

across cases.

This issue led Zlotnik (1992:20) to propose five “general principles” to guide empirical

efforts to identify international migration networks. To paraphrase, these principles include: 1)

focusing on “interacting nation-states,” 2) analyzing available migration data, 3) identifying

other relevant linkages (“comparable levels of development,” “cultural affinity,” etc.) shared by

migrant-sending and migrant-receiving countries, and 4-5) separately examining the

characteristics of migrant-sending countries and of migrant-receiving countries to see what those

in each group have in common (e.g., “coherence in policies”) (Ibid.). Zlotnik (1992) used these

principles to subsequently identify migration networks in the Americas and Western Europe.

6

More recently, DeWaard et al. (2012) applied these principles to identify three migration

networks in the European Union (EU) and Norway, followed by examining the key determinants

of migration flows therein (see also Nogle 1994).

The importance of Zlotnik’s (1992) work notwithstanding, as DeWaard et al. (2012)

noted at the conclusion of their paper, it is not exactly clear how to go about putting the

aforementioned five principles into practice. For example, in discussing her second principle,

Zlotnik (1992:20) suggested that migration networks might be identified by locating

“threshold[s]” in “matrices of inflows, outflows, and net flows between all countries as they

evolved through time.” However, little guidance is provided on exactly how to go about doing

this. Accordingly, as a place to start, DeWaard et al. (2012) used average linkage clustering to

partition nearly 4,000 annual migration flows among EU countries and Norway over a five-year

period between 2003 and 2007 into three migration networks.

In this paper, we build on and further systematize this work by introducing and

subsequently demonstrating the use of community detection methods for determining the

geographic boundaries of international migration networks. Community detection methods

provide a rich and growing set of tools for working with relational data that can be used to

understand the structure of complex networks (Fortunato 2010). In our case, we seek to identify

clusters, or communities, that take the form of networks of countries that are connected to one

another by migration flows. Because there are many community detection algorithms and the

number continues to grow (Gates et al. 2016; Yang et al. 2016), as a place to start, we apply the

Walktrap community structure algorithm (Pons and Latapy 2006) to trace the form and evolution

of international migration networks over the past half-century. We introduce and justify our

choice of the Walktrap algorithm after the next section.

7

The Globalization of Migration: Consolidation or Balkanization?

In the process of the work described above, our efforts open up a unique opportunity to

generate new insights on the “globalization of migration” thesis, which Castles et al. (2014:16)

broadly defined as “the tendency for more and more countries to be significantly affected by

international migration.” Czaika and de Haas (2015:292) recently elaborated on this idea, and

sought to clarify the pertinent “theoretical dimensions of migration globalisation.” These include,

among others, the intensity, or volume, of global migration, which has actually decreased in

recent years (Abel 2017). They also consider the spread, or diversity, of migration with respect to

which countries are (versus are not) connected to one another by migration. Using some of the

migration measures described by Bell et al. (2002), they showed that the spread of global

emigration and immigration has become less and more diverse over time, respectively.

Building on the work of Czaika and de Haas (2015), our efforts to trace the form and

evolution of international migration networks over the past half-century allow us to distinguish

between two very different processes of migration globalization. Zlotnik (1992:19) alluded to the

first process of, what we call, consolidation, which involves the emergence of a single, “all-

encompassing” global migration network over time. The origins of this idea can be found in

several globalization theories, especially world systems theory (Wallerstein 1974, 1980) and

world polity theory (Meyer et al. 1997; Thomas and Meyer 1984), which emphasize the long-run

historical progression of global capitalist expansion, exploitation, and inequality driven by

competition for [cheap] land, raw materials, and labor (Castles et al. 2014). In the process, trade,

transportation, and military linkages were established and expanded (Massey et al. 1998). This

8

has continued to the present day, as has the proliferation of ideas and identities aided in no small

part by media and communications technologies in an increasingly transnational world (Ali and

Hartmann 2015; Nobles 2013; Portes 2001; Schiller et al. 1995).

Borrowing the term from Frey (1996), the second process of migration globalization is

that of Balkanization whereby multiple migration networks come to coexist alongside one

another. This idea fits with Salt’s (2001:31) suggestion that international migration networks are

“geographically discrete”; however, geography and associated geopolitical linkages between

countries are not the only relevant factors. For example, a large body of literature on social

capital theory and the cumulative causation of migration shows that interpersonal ties to migrant

family members and friends help to lower the costs and increase the potential benefits of

migrating (Garip 2008; Massey 1990; Portes 1998). Importantly, encoded in these ties is

information (about the costs and dangers of migrating, of employment and wages, etc.) that is

specific to those migrant-receiving countries that have previously been accessed by migrant

family members and friends. As a result, migration flows are often highly “channelized” (Jones

1982:76) between specific pairs of migrant-sending and migrant-receiving countries, or what the

International Organization for Migration (IOM 2013:55-60) and others call migration

“corridors.” With respect to the globalization of migration, the implication, then, is that multiple

migration networks (versus a single all-encompassing one) emerge and crystalize over time.

The above dynamics of Balkanization are, in many cases, set into motion by historical

linkages and legacies of colonialism (e.g., Algeria and France) and military intervention (the

United States in Latin America and Southeast Asia). And they are reinforced by policies and

practices that are specific to particular places (the EU, the African Economic Community, etc.)

and populations (guestworkers, refugees fleeing communism after World War II, etc.). As a

9

result, multiple migration systems and subsystems are sustained over time, and, with respect to

the interests of this paper, are manifested in a corresponding set of largely Balkanized

international migration networks.

In light of the discussion above, the second aim of this paper is to determine which

migration globalization process—consolidation or Balkanization—has been primarily at play,

and when, over the past half-century. By focusing on international migration networks, our

efforts expand on the work of Czaika and de Haas (2015), who focused only on countries and

migration corridors. As Messias et al. (2016:1) recently argued, in going “from migration

corridors to clusters,” we stand to learn whether and to what extent the former are not

independent from one another. Knowledge of the latter can likewise help to open up new lines of

theoretical and empirical research, including on the need for better and more coordinated

migration data collection, processing, and reporting infrastructures (Willekens et al. 2016).

Finally, as a small but growing body of research on how migration networks and their underlying

migration systems change in response to environmental and climate shocks makes clear

(DeWaard et al. 2016; Hauer 2017; Suckall et al. 2015), there are important and unique

implications for policy makers and planners that follow from a better understanding of migration

networks. We discuss one of such implication in detail in the concluding section of this paper.

Data and Methods

In our analysis, we use a new set of estimates of country-to-country migration flows

(Abel 2017). Presently, these are the most geographically and temporally encompassing set of

their kind, and cover some 200 countries every five years from 1960-65 to 2010-15. The

10

methodology used to produce these estimates was recently developed by Abel (2013), and the

resulting estimates have received considerable attention in both scholarly and popular circles

(Abel and Sander 2014; Ali and Hartmann 2015; Mingels 2016; Sander et al. 2014; Sorrel 2016;

Stockton 2014).

The starting point for developing the above estimates is data on country-level migrant

stocks, disaggregated by country of birth, taken from national censuses and other administrative

sources and assembled by the World Bank (Özden et al. 2011) and the United Nations (2015).

Per the demographic balancing equation, any change in country-level migrant stocks between

two consecutive periods must be the product of component changes in fertility, mortality, and

migration. Thus, after accounting for fertility and mortality using data from the United Nations

(2015), Abel (2017) was able to estimate country-to-country migration flows every five years

over the past several decades. Given Abel’s (2013) estimation procedure, the resulting estimates

are minimum counts of country-to-country migration flows required to match the aforementioned

country-level migrant stock data. This is undoubtedly an important, but unavoidable, limitation

with these estimates.

Another issue with these estimates is that they make no attempt to reconcile the often

discrepant migration reports of migrant-sending and migrant-receiving countries. It is well-

documented that international migration data (e.g., those from Eurostat) suffer from problems of

availability, quality, and cross-national comparability due to different data collection, processing,

and reporting infrastructures, as well as the definitions (e.g., of “migrant”) and the timing criteria

(six months, one year, etc.) employed (Bilsborrow et al. 1997; Levine et al. 1986; Poulain et al.

2006; Willekens et al. 2016; Zlotnik 1987). Rather than tackling these issues (e.g., see Raymer et

al. 2013), Abel’s (2017) estimates can be viewed more pragmatically insofar as they effectively

11

force country-to-country migration flows to map onto each country’s [idiosyncratic] report of

migrant stocks.

The above said, as we show in Table 1, Abel’s (2017) estimates provide a new and rich

set of information on country-to-country migration flows among approximately 200 countries

(depending on the period) over the past half-century. In the first four periods (1960-65 to 1975-

80), these estimates include information on 173 countries and 29,756 country-to-country

migration flows (29,756 = 173 migrant-sending countries x 172 possible migrant-receiving

countries). As is evident in Table 1, the number of countries represented in these estimates

increased over time, with the final two columns in Table 1 reporting the number and names of

countries that were added or lost in each period. For example, during the 1995-00 period, 29

countries were added to the data and six countries were lost on account of both country boundary

changes (e.g., Namibia gained independence from South Africa in 1990) and the availability of

migrant stock data (e.g., in the cases of the Channel Islands and Taiwan) from the World Bank

(Özden et al. 2011) and the United Nations (2015).

---TABLE 1 ABOUT HERE---

We use Abel’s (2017) estimates of country-to-country migration flows, in conjunction

with community detection methods (Fortunato 2010), to determine the geographic boundaries of

international migration networks over the past 55 years. While there are many community

detection algorithms, and this number continues to grow, we focus on the Walktrap community

structure algorithm (Pons and Latapy 2006). We do so because several recent comparative

analyses of community detection algorithms showed that the Walktrap algorithm outperformed

other algorithms on a number of key metrics (identifying both large and small networks,

12

sensitivity to the total number of elements, or nodes, under consideration, etc.) (Gates et al. 2016

and Yang et al. 2016). The Walktrap algorithm is therefore a particularly strong jumping off

point for demonstrating the utility of community detection methods in efforts to identify the

geographic boundaries of international migration networks.

The Walktrap algorithm operates using random walks. The process begins in a starting

country, and then proceeds to move toward strongly related countries according to a set of

governing weights. In our case, these weights correspond to Abel’s (2017) counts of country-to-

country migration flows. Additionally, using population data from the United Nations (2015), we

also consider weights in the form probabilities of country-to-country migration. In both cases,

the random walks eventually get trapped in strongly weighted local communities, which, in this

paper, correspond to international migration networks. 1 The optimal number of networks is

determined by maximizing the modularity score, � � , across each partition � of potential

networks (Pons and Latapy 2006).

� � = ∑ ��∈� − ��2 (1)

The modularity score can be interpreted a measure of the strength of a given partition of

networks, where � is the fraction of edges (in our case, migration connections, or ties, between

countries) inside of community (or network) �, and � is the fraction of edges that are bound to �.

We use the maximum modularity score to identify the optimal number of international migration

1 We use the term “network” to be consistent with the use of this term in past and current research on international

migration systems as described in the previous section. However, we note that, from a purely methodological

perspective, what the Walktrap algorithm and others like ultimately do is find sub-components within a network.

These local clusters, or communities, are generally not given the label of “networks.”

13

networks in each five-year period in our data. We then compare these results across periods to

trace the form and evolution of international migration networks, as well as to determine which

migration globalization process—consolidation or Balkanization—has been primarily at work,

and when, over the past 55 years.

As a final caveat, although, as we noted earlier, the Walktrap algorithm outperforms other

community detection algorithms (Gates et al. 2016 and Yang et al. 2016), it is worth pointing out

that it identifies discrete (versus overlapping; see Devi and Poovammal 2016; Xie et al. 2013)

international migration networks. In our case, this feature is desirable for at least two reasons.

First, given the mechanics of the Walktrap algorithm described above, discrete is clearly not

synonymous with closed. As such, the Walktrap algorithm can be viewed as identifying the most

dominant network to which each country belongs, leaving open the possibility that a given

country (e.g., Mexico; see Martin 2013; Massey et al. 2002) might belong to multiple,

overlapping migration networks. Second, this feature of the Walktrap algorithm is consistent

with earlier ideas and prior research on international migration networks (DeWaard et al. 2012;

Salt 2001; Zlotnik 1992).

Results

We begin by displaying the distribution of modularity scores for each five-year period in

our data in Figures 1 and 2. The results in Figure 1 reflect the use of weights in the Walktrap

algorithm in the form of country-to-country migration counts. The results in Figure 2 reflect the

use of migration probabilities in an effort to account for different population sizes across

countries. For consistency, all subsequent figures in this section are ordered in exactly the same

14

way insofar as we present results that reflect our use of migration counts and then migration

probabilities as weights in the Walktrap algorithm.

---FIGURE 1 ABOUT HERE---


Focusing on the modularity scores displayed in Figure 1, the number of international

migration networks ranged from 7 to 26, with corresponding modularity scores of Q(1965-

70)=0.371 and Q(1995-00)=0.418, respectively. The modal number of international migration

networks was 10 during three consecutive five-year periods (1970-75, 1975-80, and 1980-85).

Over the next decade, the number of international migration networks remained roughly constant

at 9 and 12 networks, respectively. After increasing to 26 migration networks during the 1995-00

period, the number then decreased to 14 networks in the next two periods, followed by

increasing slightly to 16 networks in the most recent period, 2010-15.

As we show in Figure 2, when population size is taken into account in the Walktrap

algorithm, things become relatively more stable. With a few exceptions, the maximum modularly

scores in Figure 2 are higher than the corresponding maximum modularly scores in Figure 1. The

range of international migration networks is also smaller, with a minimum and maximum of 9

and 20 networks, and corresponding modularity scores of Q(1975-80)=0.417 and Q(1960-

65)=0.506, respectively. Finally, while the number of international migration networks oscillates

over time, there is a clear pattern of regression to the mean, which, across all periods, is just

under 15 networks.

In Figures 3 and 4, we go two steps further. Figures 3 and 4 contain Sankey diagrams

that, as we noted earlier, reflect our use of migration counts and migration probabilities as

15

weights in the Walktrap algorithm, respectively. These diagrams show 1) the size of international

migration networks with respect to the number of countries comprising each network in each

five-year period, and 2) the transitions of countries from one network to another between

consecutive five-year periods. Additionally, we note that the “Residual” category at the bottom

of Figures 3 and 4 is not an international migration network, but, rather, is simply a container

that we use to hold countries that were added or lost in each period, counts and names of which

were shown earlier in Table 1.



In Figure 3, focusing on the first five-year period, 1960-65, we identified 18 international

migration networks. Each of these 18 networks is displayed as a vertical black bar. The length of

each bar corresponds to the number of countries comprising the network in question, with

networks ordered from largest to smallest. As is evident, two international migration networks

were comparably larger than the other 16 networks during the 1960-65 period. The largest

network was comprised of 42 countries. The second largest network was comprised of 31

countries. Along with several countries from some of the smaller networks during this period, the

two largest networks combined to form an even larger migration network comprised of 86

countries during the 1965-70 period. Looking across the remaining five-year periods, there were

consistently 2-3 large international migration networks in each five-year period. The most

obvious exception was the 1990-95 period when a network comprised of 135 countries

temporarily materialized.

16

A similar story emerges in Figure 4 when population size is taken into account in the

Walktrap algorithm. In fact, the consistent presence of 2-3 large international migration

networks, including during the 1990-95 period, is even more apparent. In the most recent period,

2010-15, the three largest international migration networks were comprised of 65 countries, 48

countries, and 24 countries, respectively. Together, these three networks accounted for about

two-thirds of the countries in our data in this period. Accordingly, with respect to the substantive

aims of this paper, our results demonstrate a clear pattern of Balkanization (versus consolidation

into a single migration network) over the past half-century in the number of international

migration networks. Of course, as we later discuss, the internal country compositions of these

networks changed over time.

Before turning our attention to the changing internal country compositions of

international migration networks, as Figures 3 and 4 also evidence, there are a number of very

small international migration networks that are identified by the Walktrap algorithm. However,

upon closer inspection, these are not actually migration networks in the sense of the term as we

have used it in this paper and as it is used in prior research. These are, instead, isolate countries

and corridors. Due to space restrictions, in two supplemental figures provided in the appendix

(Figures A1 and A2), we lumped these isolates into the “Residual” category so that the

remaining international migration networks shown include only country triads or higher order

migration linkages (i.e., at least three countries connected to one another by migration flows). In

doing so, the number of international migration networks does not exceed 13 in any five-year

period in our data, regardless of whether migration counts or probabilities are used as weights in

the Walktrap algorithm. Clearly, our attempt to be more rigorous with respect to what qualifies

as a migration network does nothing to alter the main substantive finding that emerges from our

17

results, which is the tendency toward Balkanization (versus consolidation) in the number of

international migration networks over the past half-century.

As we transition to discussing changes in the internal country compositions of

international migration networks, it is natural to want to know exactly which countries are

transitioning from one network to another over time. Accordingly, in Figures 5 and 6, we display

tile plots in which we show the internal country compositions of international migration

networks in and across five-year periods, organized by world region. Three character ISO-3

country codes are provided.2 Numbers are used to distinguish international migration networks

from one another and to denote the rank of the network with respect to the number of countries

that comprise it (1 is largest, 2 is second largest, etc.) so that readers can locate each country in

the Sankey diagrams shown earlier in Figures 3 and 4 (and in Figures A1 and A2).



Examining the results in Figures 5 and 6, three clear patterns stand out. First, most

countries have transitioned between international migration networks of comparable rank over

time. For example, the United States (USA) has consistently fallen in the two largest migration

networks over the past 55 years. Importantly, note that Mexico (MEX) follows the exact same

pattern as the United States, which is consistent with previous research (Martin 2013; Massey et

al. 2002). Second, many international migration networks, especially those including African

countries, are largely regional, a finding that aligns with research by Bakewell et al. (2009) on

2 Country names corresponding to ISO-3 country codes are provided by the United Nations:

https://unstats.un.org/unsd/methodology/m49/.

https://unstats.un.org/unsd/methodology/m49/

18

the historical and contemporary evolution of South-South migration patterns. Third, the bulk of

the most pronounced transitions occur earlier (versus later) in the 55-year observation window,

which fits with idea that international migration systems have crystalized over time.

Of course, this general tendency toward Balkanization is accompanied by a number of

country outliers that transition between international migration networks of very different sizes

and ranks. In Table 2, we list those countries that experienced the greatest change in the rank of

the migration networks to which they belonged in consecutive five year periods. What is

especially interesting about these patterns is that these outliers largely, but not exclusively,

cluster along geographic lines. For example, using migration counts as weights in the Walktrap

algorithm, Bolivia, Paraguay, and Uruguay transitioned together from a migration network

comprised of four countries during the 1960-65 period, to a network comprised of 86 countries

during the 1965-70 period, to a network comprised of three countries during the 1970-75 period.

Similar geographic patterns are evident for groups of countries in other parts of the world, as

well as when migration probabilities are used as weights in the Walktrap algorithm.

--- TABLE 2 ABOUT HERE---

We conclude the results section of this paper by providing a map in Figure 7 that

summarizes international migration networks over the past half-century, versus in each five-year

period in our data. To create this map, we did the following: First, we developed a set of

crosswalks to convert the country boundaries in Abel’s (2017) migration data in each five-year

period to match the country boundaries in the most recent period, 2010-15, which are the

shapefiles that we used to create the map in Figure 7. Second, we constructed probability

matrices of country-to-country migration for each five-year period. Because the geographic

19

boundaries of these matrices are harmonized to match those for the 2010-15 period, we then

multiplied them together to arrive at a joint probability matrix of country-to-country migration

wherein each element denotes the probability of migrating from migrant-sending country i to

migrant-receiving country j over the 1960-2015 period. We then used these joint probabilities as

weights in the Walktrap algorithm. As is evident in Figure 7, over the 1960-2015 period, eight

international migration networks were detected. With the exception of the largest migration

network, the remaining seven networks are, for the most part, geographically clustered (Massey

et al. 1998; Salt 2001). Finally, and remarkably, there are no isolate countries or corridors.


Because community detection algorithms like Walktrap can sometimes be sensitive to the

number of, in our case, countries under consideration (Anderson et al. 1999), the harmonized

matrices of country-to-country migration, described and used above, permit us to assess the

sensitivity of the results shown earlier in this section. Due to space, these results, which use

harmonized probabilities of migration among a time-constant set of countries/country units as

weights in the Walktrap algorithm, are provided in the appendix (Figures A3, A4, A5, and A6).

The key takeaway from these results is that the changes in the number of countries in our data

over time do little to alter our earlier empirical results and nothing to change the substantive

conclusions about the Balkanization of migration in this paper.

Discussion

In this paper, we used a new set of estimates of country-to-country migration flows (Abel

2017) and community detection methods (Fortunato 2010)—specifically, the Walktrap

20

community structure algorithm (Pons and Latapy 2006)—to identify international migration

networks and trace their form and evolution over the past half-century. Along the way, we

generated new insights on the “globalization of migration” thesis (Castles et al. 2014:16; see also

Czaika and de Haas 2015) by documenting a clear pattern over time of Balkanization (versus

consolidation) in the number of international migration networks. As migration networks are

aggregate manifestations of underlying migration systems (Bakewell 2014; Kritz and Zlotnik

1992), our results point to a unique set of potential causes and mechanisms (e.g., interpersonal

ties to migrant family members and friends, and associated migration-specific social capital) that

ultimately permit and promote “identifiable” and differentiated “geographic structures” (Massey

et al. 1998:61). Although, as we noted earlier, the Walktrap algorithm yields a portrait of discrete

international migration networks, which is consistent with previous research (DeWaard et al.

2012; Salt 2001), our results should be viewed as summarizing the most dominant migration

network to which each country belongs, as opposed to seeing networks as closed. We further

showed that some countries experience substantial changes over time in the international

migration networks to which they belong.

Taking stock of our efforts, we make at least two important contributions to the literature.

First, building on longstanding interest in and problems with identifying the geographic

boundaries of international migration systems as they are manifested in networks of countries

connected to one another by migration flows (Bakewell 2014; Kritz and Zlotnik 1992;

Mabogunje 1970; Massey et al. 1998; Zlotnik 1992), we introduced community detection

methods and demonstrated the utility of the Walktrap algorithm as a potential way forward.

These methods can be used to develop an agreed upon data-driven approach for identifying and

analyzing international migration networks. More broadly, recognizing that community detection

21

methods are one set of tools in the toolkit that is network analysis (e.g., see Borgatti et al. 2009;

Wasserman and Faust 1994), our work can be viewed as promoting the application of network

methods in research on international migration systems and networks.

Second, our work suggests that the concept of migration globalization needs further

clarification. Recent efforts by Czaika and de Haas (2015) notwithstanding, their work is limited

for two reasons. First, as we noted earlier, their focus, both theoretically and empirically, is

limited to the experiences of specific countries and migration corridors, and thereby fails to

exhaust the ways that migration globalization plays out in international migration networks

(Messias et al. 2016). Second, Czaika and de Haas (2015) divide all aspects of theorizing and

empirical research into emigration and immigration camps. From the vantage points of countries

and of migration corridors, this makes sense; however, when the unit of interest is the migration

network, this distinction is less useful (Rogers 1990). The concept of migration globalization

therefore warrants further interrogation with respect to whether and how migration systems and

networks might be explicitly incorporated.

As for the limitations of this paper, there are many. First, as we noted earlier, Abel’s

(2017) estimates of country-to-country migration flows are the minimum counts required to

match country-level migrant stock data assembled by the World Bank (Özden et al. 2011) and

the United Nations (2015). This is an avoidable limitation with these estimates, and one that we

think is substantially outweighed by their temporal and geographic scope. Second, recalling

Zlotnik’s (1992:20) five “general principles” to guide empirical efforts to identify international

migration networks, there are other types of linkages (“comparable levels of development,”

“cultural affinity,” etc.) shared by migrant-sending and migrant-receiving countries that we did

not consider given the mechanics of the Walktrap algorithm that we sought to introduce here.

22

Third, as already noted, the Walktrap algorithm identifies discrete international migration

networks. Although there is precedent for this (DeWaard et al. 2012; Salt 2001), future research

might wish to consider the use of community detection algorithms that allow for the

identification of multiple, overlapping networks (Devi and Poovammal 2016; Xie et al. 2013).

Finally, as is the case with any research paper, especially those with such an expansive temporal

and geographic scope, a persistent challenge is to distill the information down in ways that are

digestible to diverse audiences.

This last limitation, as well as our attempt to mitigate it in this paper using a range of

innovative figures, is especially important given the unique implications of migration networks

and their underlying migration systems for informing the work of policy makers and planners.

International migration matters to policy makers and planners because it is a key input into

population estimates and projections, which afford countries and places therein the ability to

monitor population change (their size, density, composition, production and consumption, etc.)

(Kupiszewski 2013). However, going further than this, as several recent papers on how

migration networks and their underlying migration systems change in response to environmental

and climate shocks make clear (Curtis 2015; DeWaard et al. 2016; Hauer 2017; Suckall et al.

2015), countries have a vested interested in identifying and working collaboratively and

proactively with other countries with whom they have strong migration linkages to anticipate

future migration patterns and inform the development of appropriate responses. Going forward,

one framework might be useful here is that of “network governance” (Jones et al. 1997; Provan

and Kenis 2008), which, to our knowledge, has yet to explicitly consider the strong migration

linkages that exist between countries.

23

In summary, our work stands to inform theoretical and empirical research on

international migration networks and their underlying migration systems, as well as planning and

policy efforts to anticipate future migration and inform the development of appropriate

responses. Going forward, the insights and methods in this paper can and should be applied to

examine regional migration networks, both international and domestic. Future research might

also seek to take a more event-centered approach, and document the form and evolution of a

given migration network before, during, and after a specific shock or set of shocks (e.g., see Fix

et al. 2009; Fussell et al. 2014).

24

Acknowledgements

Abel and DeWaard contributed equally as lead authors. DeWaard, Ha, and Almquist

acknowledge support from NIH center grant #P2C HD041023 to the Minnesota Population

Center at the University of Minnesota from the Eunice Kennedy Shriver National Institute of

Child Health and Human Development. Earlier versions of this paper were presented at the

annual meetings of the British Society for Population Studies on September 14, 2016, and the

Population Association of America on April 2, 2016.

25

References

Abel, G. J. (2013). Estimating global migration flow tables using place of birth data.

Demographic Research, 28, 505-546.

Abel, G. J. (2017). Estimates of global bilateral migration flows by gender between 1960 and

2015. International Migration Review, forthcoming.

Abel, G. J. & Sander, N. (2014). Quantifying global international migration flows. Science, 343,

1520-1522.

Ali, S. & Hartmann, D. (2015). Migration, incorporation, and change in an interconnected

world. New York: Routledge.

Anderson, B. S., Butts, C., & Carley, K. (1999). The interaction of size and density with graph-

level indices. Social Networks, 21, 239-267.

Bakewell, O., de Haas, H., Castles, S., Vezzoli, S, & Jónsson, G. (2009). South-South migration

and human development: Reflections on African experiences. Research Paper 2009/07,

Human Development Reports, United Nations Development Programme, United Nations.

Bakewell, O. (2014). Relaunching Migration Systems. Migration Studies, 2, 300-318.

Bakewell, O., Engbersen G., Fonseca, M. L., & Horst, C. (2016). Beyond networks: Feedback in

international migration. Basingstoke, London: Macmillan Palgrave.

Bell, M., Blake, M., Boyle, P., Duke-Williams, O., Rees, P., Stillwell, J., & Hugo, G. (2002).

Cross-national comparison of internal migration: Issues and measures. Journal of the

Royal Statistical Society A, 165, 435-464.

26

Bilsborrow, R. E., Hugo, G., Oberai, A.S., & Zlotnik, H. (1997). International migration

statistics: Guidelines for improving data collection systems. Geneva: International

Labour Organization.

Borgatti, S. P., Mehra, A., Brass, D. J., & Labianca, G. (2009). Network analysis in the social

sciences. Science, 323, 892-895.

Castles, S., de Haas, H., & Miller, M. J. (2014). The age of migration: International population

movements in the modern world, 5th edition. New York and London: The Guilford Press.

Curtis, K. J., Fussell, E., & DeWaard, J. (2015). Recovery migration after Hurricanes Katrina

and Rita: Spatial concentration and intensification in the migration system. Demography,

52, 1269-1293.

Czaika, M. and de Haas, H. (2014). The globalization of migration: Has the world become more

migratory? International Migration Review, 48, 283-323.

Devi, J. C. & Poovammal, E. (2016). An analysis of overlapping community detection

algorithms in social networks. Procedia Computer Science, 89, 349-358.

DeWaard, J., Curtis, K. J., & Fussell, E. (2016). Population recovery in New Orleans after

Hurricane Katrina: Exploring the potential role of stage migration in migration systems.

Population and Environment, 37, 449-463.

DeWaard, J., Kim, K., & Raymer, J. (2012). Migration systems in Europe: Evidence from

harmonized flow data. Demography, 49, 1307-1333.

Favell, A. (2008). The new face of east-west migration in Europe. Journal of Ethnic and

Migration Studies, 34, 701-716.

27

Fawcett, J. T. (1989). Networks, linkages, and migration systems. International Migration

Review, 23, 671-680.

Fix, M., Papademetriou, D. G., Batalova, J., Terrazas, A., Lin, S. Y. L., & Mittelstadt, M. (2009).

Migration and the global recession: A report commissioned by the BBC World Service.

Washington D.C.: Migration Policy Institute.

Fortunanto, S. (2010). Community detection in graphs. Physics Reports, 486, 75-174.

Frey, W. H. (1996). Immigration, domestic migration, and demographic Balkanization in

America: New evidence for the 1990s. Population and Development Review, 22, 741-

763.

Fussell, E., Curtis, K. J., & DeWaard, J. (2014). Recovery migration to the City of New Orleans

after Hurricane Katrina: A migration systems approach.” Population and Environment,

35, 305-322.

Garip, F. (2008). Social capital and migration: How do similar resources lead to divergent

outcomes? Demography, 42, 591-617.

Gates, K. M., Henry, T., Steinley, D., & Fair, D. A. (2016). A Monte Carlo evaluation of

weighted community detection algorithms. Frontiers in Neuroinformatics, 10, 1-16.

Hauer, M. (2017). Migration induced by sea-level rise could reshape the US popualtion

landscape. Nature Climate Change, 7, 321-325.

Hunter, L. M., Luna, J. K., & Norton, R. M. (2015). Environmental dimensions of migration.

Annual Review of Sociology, 41, 377-397.

28

IOM. (2013). World Migration Report 2013. Geneva: International Organization for Migration.

Jones, C., Hesterly, W. S., Borgatti, S. P. (1997). A general theory of network governance:

Exchange conditions and social mechanisms. Academy of Management Review, 22, 911-

945.

Jones, R. C. (1982). Undocumented migration from Mexico: Some geographical questions.

Annals of the Association of American Geographers, 72, 77-87.

Kritz, M. M. & Zlotnik, H. (1992) Global interactions: Migration systems, processes, and

policies. In M. M. Kritz, L. L. Lim, & H. Zlotnik (Eds.), International migration systems:

A global approach (pp. 1–16). Oxford: Clarendon Press.

Kupiszewski, M. (2013). International migration and the future of populations and labour force

resources in Europe. New York: Springer.

Levine, D. B, Hill, K., & Warren, R. (1985). Immigration statistics: A story of neglect.

Washington D.C.: The National Academies Press.

Mabogunje, A. L. (1970). Systems approach to a theory of rural-urban migration. Geographical

Analysis, 2, 1-18.

Martin, P. (2013). The Global Challenge of Managing Migration. Population Bulletin, 68, 2-16.

Massey, D. S. (1990). The social and economic origins of immigration. The ANNALS of the

American Academy of Political and Social Science, 510, 60-72.

29

Massey, D. S., Arango, J., Hugo, G., Kouaouci, A., Pellegrino, A., & Taylor, J. E. (1998).

Worlds in motion: Understanding international migration at the end of the millennium.

Oxford: Clarendon Press.

Massey, D. S., Durand, J., & Malone, N. J. (2002). Beyond smoke and mirrors: Mexican

immigration in an era of economic integration. New York: Russell Sage Foundation.

Messias, J., Benevenuto, F., Weber, I., & Zagheni, E. (2016). From migration corridors to

clusters: The value of Google+ data for migration studies. IEEE/ACM International

Conference on Advances in Social Networks Analysis and Mining (ASONAM). August

18-21.

Meyer, J. W., Boli, J., Thomas, G. M., & Ramirez, F. O. (1997). World society and the nation-

state. American Journal of Sociology, 103, 144-181

Mingels, G. (2016). Global migration? Actually, the world is staying home. Spiegel Online, May

17.

Nobles J. (2013). Migration and father absence: shifting family structure in Mexico.

Demography, 50, 1303-1314.

Nogle, J. M. (1994). The systems approach to international migration: An application of network

analysis. International Migration, 32, 329-337.

Özden, Ç., Parsons, C. R., Schiff, M., & Walmsley, T. L. (2011). Where on Earth is everybody?

The evolution of global bilateral migration 1960–2000. The World Bank Economic

Review, 25, 12-56.

30

Pons, P. & Latapy, M. (2006). Computing communities in large networks using random walks.

Journal of Graph Algorithms and Applications, 10, 191-218.

Portes, A. (1998). Social capital: Its origins and applications in modern sociology. Annual

Review of Sociology, 24, 1-24.

Portes, A. (2001). The debates and significance of immigrant transnationalism. Global Networks,

1, 181-193.

Poulain, M., Perrin, N., & Singleton, A. (2006). THESIM: Towards harmonized European

statistics on international migration. Louvain-la-Neuve: UCL Presses Universitaires de

Louvain.

Provan, K. G. & Kenis, P. (2008). Modes of network governance: Structure, management, and

effectiveness. Journal of Public Administration Research and Theory, 18, 229-252.

Raymer, J., Wiśniowski, A., Forster, J.J., Smith, P.W.F. & Bijak, J. (2013). Integrated modeling

of European migration. Journal of the American Statistical Association, 108, 801-819.

Rogers, A. (1990). Requiem for the net migrant. Geographical Analysis, 22, 283-300.

Salt, J. (2001). Current trends in international migration in Europe. Report CDMG (2001) 33,

Council of Europe, Strasbourg.

Sander, N., Abel, G. J., Bauer, R., & Schmidt, J. (2014). Visualising migration flow data with

circular plots. Working Paper 02/2014, Vienna Institute of Demography, Vienna.

Schiller, N. G., Basch, L., & Blanc, C. S. (1995). From immigrant to transmigrant: Theorizing

transnational migration. Anthropological Quarterly, 68, 48-63.

31

Sorrel, C. (2016). Most conventional wisdom about refugees and immigration is wrong. Fast

Company, June 10.

Stockton, N. (2014). 20 years of global migration—in one chart. The Atlantic, April 10.

Suckall, N., Fraser, E., Forster, P., & Mkwambisi, D. (2015). Using a migration systems

approach to understand the link between climate change and urbanisation in Malawi.

Applied Geography, 63, 244-252.

Thomas, G.M. & Meyer, J. W. (1984). The expansion of the state. Annual Review of Sociology,

10, 461-482.

United Nations. (2015). World population prospects: The 2015 Revision. New York: United

Nations Population Division, Department of Economic and Social Affairs, United

Nations.

Wallerstein, I. (1974). The modern world system II: Mercantilism and the consolidation of the

European world-economy, 1600-1750. New York: Academic Press.

Wallerstein, I. (1980). The modern world system I: Capitalist agriculture and the origins of the

European world economy in the sixteenth century. New York: Academic Press.

Wasserman, S. & Faust, K. (1994). Social network analysis: Methods and applications.

Cambridge: Cambridge University Press.

Willekens, F., Massey, D. S., Raymer, J., & Beauchemin, C. (2016). International migration

under the microscope. Science, 352, 897–99.

32

Xie, J., Kelley, S., & Szymanski, B. K. (2013). Overlapping community detection in networks:

The state-of-the-art and comparative study. ACM Computing Surveys, 45, 1-37.

Yang, Z., Algesheimer, R., & Tessone, C. J. (2016). A comparative analysis of community

detection algorithms on artificial networks. Scientific Reports, 6, 1-16.

Zlotnik H. (1987). The concept of international migration as reflected in data collection systems.

International Migration Review, 21, 925-946.

Zlotnik, H. (1992). Empirical identification of international migration systems. In M. M. Kritz,

L. L. Lim, & H. Zlotnik (Eds.), International migration systems: A global approach (pp.

19-40). Oxford: Clarendon Press.

33

Table 1. Data description

Period

Countries

in Data

Countries Added in Period

Countries Lost in Period

1960-65 173 0 0

1965-70 173 0 0

1970-75 173 0 0

1975-80 173 0 0

1980-85 174 1 Taiwan 0

1985-90 174 0 0

1990-95

197

29

Channel Islands, Curaçao, Eritrea, Ethiopia, Namibia, South Africa, Western Sahara, 2 countries from former Czechoslovakia, 5 countries from former Yugoslavia, 15 countries from former Soviet Union

6

Czechoslovakia, Eritrea-Ethiopia, Namibia-South Africa, Soviet Union, Taiwan, Yugoslavia

1995-00 197 0 0

2000-05 198 0 Indonesia, Timor-Leste 0 Indonesia

2005-10 198 0 0

2010-15

200

4 Montenegro, Serbia, South Sudan, Sudan

2 Serbia and Montenegro, Sudan

Source: Authors’ calculations using data from Abel (2017).

34

Table 2. Countries experiencing largest change in rank of migration network to which they

belong: 1960-65 to 2010-15


Top countries and change in rank of network between periods

Period (weights = migration counts) (weights = migration probabilities)

1960-65 to 1965-70

Bolivia (-11), Cameroon (-11), Central African Republic (-11), Chad (-11), Chile (-11), Paraguay (-11), Uruguay (-11)

Malta (+7), Papua New Guinea (+7), Denmark (-6), Iceland (-6), Norway (-6), Vanuatu (-6)

1965-70 to 1970-75

Bolivia (+7), Paraguay (+7), Uruguay (+7)

Japan (+9), Fiji (-7), New Zealand (-7), Papua New Guinea (-7), Samoa (-7), Tonga (-7), Vanuatu (-7)

1970-75 to 1975-80

Bolivia (-7), Paraguay (-7), Uruguay (-7)

Japan (-9), Chile (-8), Uruguay (-8), China (+7), Mongolia (+7), South Korea (+7)

1975-80 to 1980-85

Philippines (+5); 12 countries (-4) Netherlands (+10), Spain (+10), Suriname (+10), Chile (+9), Uruguay (+9)

1980-85 to 1985-90

Democratic Republic of the Congo (+5), Mongolia (+4)

Chile (-9), Netherlands (-9), Spain (-9), Suriname (-9)

1985-90 to 1990-95

Central African Republic (-5), Kenya (-5)

Bolivia (-7), China (-7), Paraguay (-7), Uruguay (-7)

1990-95 to 1995-00

Central African Republic (+7), Chad (+7), Eritrea (+7), Ethiopia (+7)

Aruba (-6), French Guiana (-6), Suriname (-6), Bhutan (-5), Nepal (-5)

1995-00 to 2000-05

Laos (+9), Myanmar (+9), Cambodia (+7), Kenya (+7), Somalia (+7)

Myanmar (+11), Laos (+11), Cambodia (+11), Aruba (+10), Uganda (+9)

2000-05 to 2005-10

Cambodia (-9), Jordan (+9), Laos (-9), Lebanon (+9), Libya (+9), Palestine (+9), Syria (+9)

Cambodia (-11), Laos (-11), Myanmar (-9)

2005-10 to 2010-15

Sierra Leone (-10), Iraq (+9), Turkey (+9), Guinea (-7), Liberia (-7)

Guinea (-12), Liberia (-12), Sierra Leone (-11)

35

Figure 1. Modularity scores (weights = migration counts): 1960-65 to 2010-15


36

Figure 2. Modularity scores (weights = migration probabilities): 1960-65 to 2010-15


37

Figure 3. Migration networks (weights = migration counts): 1960-65 to 2010-15

Source: Authors’ calculations using data from Abel (2017). Notes:

a Residual includes countries added or lost in each period (see Table 1).

38

Figure 4. Migration networks (weights = migration probabilities): 1960-65 to 2010-15



39

Figure 5. Country composition and rank of migration networks (weights = migration counts): 1960-65 to 2010-15

Source: Authors’ calculations using data from Abel (2017). Notes: Country names corresponding to ISO-3 country codes are provided by the United Nations: https://unstats.un.org/unsd/methodology/m49/. Numbers are used to distinguish and denote the rank of (e.g., 1 = largest; no number = no migration data) international migration networks.


40

Figure 6. Country composition and rank of migration networks (weights = migration probabilities): 1960-65 to 2010-15



41

Figure 7. Migration networks (weights = joint migration probabilities): 1960-2015


42

Figure A1. Migration networks (weights = migration probabilities; residual also includes country/corridor isolates): 1960-65 to

2010-15


a Residual includes countries added or lost in each period (see Table 1), plus isolate countries and corridors.

43

Figure A2. Migration networks (weights = migration probabilities; residual also includes country/corridor isolates): 1960-65 to

2010-15



44

Figure A3. Modularity scores (weights = migration probabilities; constant number of

countries across periods): 1960-65 to 2010-15


45

Figure A4. Migration networks (weights = migration probabilities; constant number of countries across periods): 1960-65 to

2010-15



46

Figure A5. Migration networks (weights = migration probabilities; residual also includes country/corridor isolates; constant

number of countries across periods): 1960-65 to 2010-15



47

Figure A6. Country composition and rank of migration networks (weights = migration probabilities; constant number of

countries across periods): 1960-65 to 2010-15



Documents

The Form and Evolution of International Migration Networks