Patterns of dominant flows in the world trade web
Patterns of dominant flows in the world trade web
M. Ángeles Serrano,1 Marián Boguñá,2 and Alessandro Vespignani3, 4
1Institute of Theoretical Physics, LBS, FSB, EPFL, BSP 725 - Unil, 1015 Lausanne, Switzerland
2Departament de F́ısica Fonamental, Universitat de Barcelona,
Mart́ı i Franquès 1, 08028 Barcelona, Spain
3School of Informatics, Indiana University, Eigenmann Hall,
1900 East Tenth Street, Bloomington, IN 47406, USA
4Complex Network Lagrange Laboratory (CNLL),
Institute for Scientific Interchange (ISI), Torino 10133, Italy
(Dated: today)
The large-scale organization of the world economies is exhibiting increasingly levels of local het-
erogeneity and global interdependency. Understanding the relation between local and global features
calls for analytical tools able to uncover the global emerging organization of the international trade
network. Here we analyze the world network of bilateral trade imbalances and characterize its over-
all flux organization, unraveling local and global high-flux pathways that define the backbone of the
trade system. We develop a general procedure capable to progressively filter out in a consistent and
quantitative way the dominant trade channels. This procedure is completely general and can be
applied to any weighted network to detect the underlying structure of transport flows. The trade
fluxes properties of the world trade web determines a ranking of trade partnerships that highlights
global interdependencies, providing information not accessible by simple local analysis. The present
work provides new quantitative tools for a dynamical approach to the propagation of economic
crises.
I. INTRODUCTION
The term “globalization”, when applied to the inter-
national economic order, refers to the presence of an in-
tricate network of economic partnership among an in-
creasing number of countries [1]. In this context, the
International trade system, describing the fundamental
exchange of goods and services, plays a central role as
one of the most important interaction channels between
states [2]. For instance, it broadly defines the substrate
for the spreading of major economic crises [3, 4, 5], such
as the 1997 Asiatic crisis [5, 6, 7] which shows how eco-
nomic perturbations originated in a single country can
somehow propagate globally in the world. Moreover,
commercial trade flows are indeed highly correlated with
other types of cross-country economic interactions (flows
of services, financial assets, workers) and so stand as a
good indicator for more general economic relations [8].
The International trade system as an independent extract
of the world economy is therefore still a partial view of the
whole system; a complete description would consider the
feedback mechanisms that operate between international
trade imbalances and other economic variables such as
investment, debt, or currency prices. On the other hand,
the study of the International trade network in a system’s
perspective represents a necessary first step before pro-
ceeding with a subsequent more integrative investigation
and has proven to be successful in providing insight into
some of its global properties.
The large size and the entangled connectivity pattern
characterizing the international trade organization point
out to a complex system whose properties depend on its
global structure. In this perspective, it appears natu-
ral to analyze the world trade system at a global level,
every country being important regardless of its size or
wealth and fully considering all the trade relationships.
A convenient framework for the analysis of complex in-
terconnected systems is network analysis [9, 10]. Within
this approach, countries are represented as nodes and
trade relationships among them as links. Such visual-
izations of bilateral trade relations have been used in
recent years to help analyze gravity models [11, 12], of-
ten proposed to account for the world trade patterns and
their evolution [13]. While the first attempts to study the
trade system as a complex network have successfully re-
vealed a hierarchical organization [14, 15, 16], these stud-
ies focused on topological aspects neglecting fundamental
components, such as the heterogeneity in the magnitude
of the different bilateral trade relations and their asym-
metry. These are essential issues in the understanding of
the interplay between the underlying structure and the
principles that rule the functional organization of the sys-
Here we tackle the quantitative study of the world
trade network by implementing the trade flux analysis
at a global scale. To this end, we construct the weighted
directed network of merchandize trade imbalances be-
tween world countries. In this representation, each coun-
try appears as a node and a directed link is drawn among
any pair whenever a bilateral trade imbalance exists,
i.e., whenever bilateral imports does not balance exports.
The direction of the arrow follows that of the net flow of
money and it is weighted according to the magnitude of
the imbalance between the two countries. More precisely,
we define the elements Eij that measure the exports of
country i to country j and the elements Iij that measure
the imports of country i from country j. The trade im-
balance matrix is therefore defined as Tij = Eij−Iij and
Pajek 
A B A B
A B A B
EAB = IBA
IAB = EBA
TBA  =  - TAB < 0   FBA   
EAB = IBA
IAB = EBA
TAB  =   - TBA < 0   FAB    
Totally inhomogeneous
Fit kY(k) = k
FIG. 1: Measuring local inhomogeneity in fluxes. a, concep-
tual representation of the link construction process. b and c,
local inhomogeneity for incoming (b) and outgoing (c) con-
nections measured by kY (k) as compared to the null model.
The diagonal line corresponds to the maximum possible in-
homogeneity, with only one connection carrying all the flux.
The line kY (k) = 1 is the maximum homogeneity, with all
the fluxes equally distributed among the connections. The
area depicted in grey corresponds to the average of kY (k) un-
der the null model plus two standard deviations. The solid
lines are the best fit estimates which give kinY (kin) ∼ k0.6in
and koutY (kout) ∼ k0.5out. The inset in (c) sketches a pathway
through a country arising from strong local inhomogeneity in
incoming and outgoing connections.
measures the net money flow from country j to country
i due to trade exchanges. Since Eij = Iji and Iij = Eji,
T is an antisymmetric matrix with Tij = −Tji, and a di-
rected network can be easily constructed by assuming a
directed edge pointing to the country with positive bal-
ance. The network of the net trade flows is therefore
defined in terms of a weighted adjacency matrix F with
Fij =| Tij |=| Tji | for all i, j with Tij < 0, and Fij = 0
for all i, j with Tij ≥ 0 (see Fig. 1a for a pictorial de-
scription).
By using the above procedure we constructed the net-
work of trade imbalances by using the data set which
reports the annual merchandize trade activity between
independent states in the world during the period 1948-
2000, together with the annual values of their Gross Do-
mestic Product per capita and population figures (1950–
2000) [17],[25]. The time span of the data set allows us
to study the change of trade flow networks with yearly
snapshots characterizing the time evolution of the trade
system. The most basic topological characterization of
each country within the network is given by the number
of incoming and outgoing links, kin and kout respectively,
which inform us about the number of neighboring coun-
tries that contribute positively and negatively to the net
trade imbalance of the country under consideration. A
precise assessment of the country trade balance cannot
however neglect the magnitude of the fluxes carried by
each trade relation. This information can be retrieved
summing up all the weights of the incoming or outgo-
ing links, which give us the total flux of money due to
trade entering to or leaving from the country of inter-
est. In the network literature, these two variables are
called incoming and outgoing strength and are denoted
by sinj =
i Fij and s
i Fji, respectively [18].
The total trade imbalance of a country can then be com-
puted as ∆sj = sinj − s
j . Depending on ∆sj , countries
can be then defined as net consumers and net produc-
ers. Net producers export more than they import, the
total outcome being a trade surplus which corresponds
to ∆sj > 0, whereas net consumers export less than they
import, the total outcome being a trade deficit which is
indicated by ∆sj < 0. Since one incoming link for a given
country is always an outgoing link for another, the sum
of all the countries’ trade imbalances in the network must
be zero. While the local balance is not conserved, we are
therefore dealing with a closed system which is globally
balanced (the total flux is conserved). Merchandizes, or
equivalently money, flows in the system from country to
country with the peculiarity that there is a global flow of
money from consumer countries to producer ones.
II. LOCAL HETEROGENEITY AND
BACKBONE EXTRACTION
The obtained networks show a high density of connec-
tions and heterogeneity of the respective fluxes among
countries. Indeed, as the number of countries increases,
so does the average number of trade partners, as well as
the total flux of the system, which is seen to grow pro-
portional to the aggregated world Gross Domestic Prod-
uct [19]. The overall flux organization at the global scale
can be characterized by the study of the flux distribution.
A first indicator of the system heterogeneity is provided
by the probability distribution P (Fij) denoting the prob-
ability that any given link is carrying a flux Fij . The
observed distribution is heavy-tailed and spans approx-
imately four orders of magnitude [19]. Such a feature
implies that only a small percentage of all the connec-
tions in the network carry most of its total flow F and
that there is no characteristic flux in the system, with
most of the fluxes below the average and some of them
with a much higher value. This is however not totally
TABLE I: Sizes of the backbones. Percentage of the original
total weight F , number of nodes N and links E in the 1960
and 2000 imbalance networks that remain in the backbone as
a function of the significance level α.
1960 2000
α %F %N %E %F %N %E
0.2 88 100 25 92 98 25
0.1 83 100 19 87 98 19
0.05 79 99 15 84 97 15
0.01 69 92 9 75 96 10
unexpected since a large scale heterogeneity is a typical
feature of large-scale networks. In addition, the global
heterogeneity could just be due to differences in the sizes
of the countries, in their population and in their respec-
tive Gross Domestic Product. More interesting is there-
fore the characterization of the local heterogeneity; i.e.
given all the connections associated to each given coun-
try, how is the flux distribution for each of them.
A local heterogeneity implies that only a few links
carry the biggest proportion of the country’s total in-flow
or out-flow. Interestingly, such a heterogeneity would de-
fine specific pathways within the network that accumu-
late most of the total flux. In order to asses the effect
of inhomogeneities at the local level, for each country
i with k incoming or outgoing trade partners we calcu-
late [20, 21]
kYi(k) = k
p2ij , (1)
where k can be either kin or kout in order to discern be-
tween inhomogeneities in incoming and outgoing fluxes,
and where the normalized fluxes of node i with its neigh-
bors are calculated as pij = Fji/sini for incoming con-
nections and as pij = Fij/souti for the outgoing ones.
The function Yi(k) is extensively used in economics as a
standard indicator of market concentration, referred as
the Herfindahl-Hirschman Index or HHI [22, 23], and it
was also introduced in the complex networks literature
as the disparity measure [24]. In all cases, Yi(k) char-
acterizes the level of local heterogeneity. If all fluxes
emanating from or arriving to a certain country are of
the same magnitude, kYi(k) scales as 1 independently
of k, whereas this quantity depends linearly on k if the
local flux is heterogeneously organized with a few main
directions. Increasing deviations from the constant be-
havior are therefore indicating heterogeneous situations
in which fluxes leaving or entering each country are pro-
gressively peaked on a small number of links with the
remaining connections carrying just a small fraction of
the total trade flow. On the other hand, the deviations
from the constant behavior have to be expected for low
values of k and it is important to compare the obtained
results with the deviations simply produced by statistical
fluctuations. To this end, we introduce a null model for
the distribution of flows among a given number of neigh-
bors in order to assess, in a case by case basis, whether
the observed inhomogeneity can just be due to fluctua-
tions or it is really significant.
The null model with the maximum random homogene-
ity corresponds to the process of throwing k − 1 points
in a [0, 1] interval, so that the interval ends up divided in
k sections of different lengths representing the different
values assigned to the k variables pij in the random case.
It can be analytically proved that the probability that
one of these variables takes a particular value x depends
on k and is
Prob{x < pij < x+ dx} = (k − 1)(1− x)k−2dx. (2)
This probability density function can be used to calculate
the statistics of kYNM (k) for the null model. Both the
average and the standard deviation are found to depend
on k:
〈kYNM (k)〉 = k〈YNM (k)〉 =
k + 1
σ2 (kYNM (k)) = k
20 + 4k
(k + 1)(k + 2)(k + 3)
(k + 1)2
so that each node in the network with a certain in or
out degree should be compared to the corresponding null
model depending on the appropriate k.
In Fig. 1, we show the empirical measures along with
the region defined by the average value of the same quan-
tity kY (k) plus two standard deviations as given by the
null model (shadowed area in grey). For a homogeneously
random assignment of weights, this quantity converges to
a constant value for large k, which is clearly different from
the observed empirical behavior. Most empirical values
lie out of the null model domain, which proves that the
observed heterogeneity is due to a well definite ordering
principle and not to random fluctuations.
The direct fit of the data indicates that both in and out
fluxes follow the scaling law kYi(k) ∝ kβ with βin = 0.6
for the incoming connections and βout = 0.5 for the out-
going ones (see Fig. 1). This scaling represents and in-
termediate behavior between the two extreme cases of
perfect homogeneity or heterogeneity but clearly points
out the existence of strong local inhomogeneities. The
emerging picture is therefore consistent with the exis-
tence of major pathways of trade flux imbalances (thus
money) that enters the country using its major incom-
ing links and leaves it through its most inhomogeneous
outgoing trade channels (see inset in Fig. 1c).
The analysis of the local inhomogeneities in the trade
fluxes prompts to the presence of high-flux backbones,
sparse subnetworks of connected trade fluxes carrying
most of the total flux in the network. This backbone
is necessarily encoding a wealth of information being the
dominating structure of the trade system. It is also worth
remarking that the local heterogeneity is not just encoded
Canada
Dominican R Mexico
El Salvador
Nicaragua Costa Rica
Panama
Venezuela
Ecuador
Brazil
Bolivia
Argentina
Uruguay
United Kingdom
Netherlands Belgium
Luxemburg
France
Switzerland
Spain
German FR
German DR
Poland
Austria
Hungary
Czechoslovakia
Italy
Yugoslavia
Cyprus
Bulgaria
Russia
Finland
SwedenNorwayDenmark
Ghana
Zaire
Ethiopia
Malagasy R
Morocco
Tunisia
Turkey
Egypt
Israel
Afghanistan
China
R of China
South Korea
Japan
India
Pakistan
Burma
R of Vietnam
Indonesia
Australia
New Zealand
Canada
Haiti
Jamaica
Trinidad and Tobago
Barbados
Dominica
Grenada
St Lucia
St Vincent and G
Antigua and Barbuda
St Kitts-Nevis
Mexico
Belize
Guatemala
Honduras
Nicaragua
Panama
Colombia
Venezuela
Guyana
Ecuador
Brazil
ChileArgentina
Uruguay
United Kingdom
Ireland
Netherlands
Belgium
LuxemburgFrance
Switzerland
Spain
Portugal Germany
Poland
Austria
Hungary
Czechoslovakia
Slovakia
Italy
Malta
Croatia
Yugoslavia
Bosnia-
Herzegovina
Slovenia
Greece
Cyprus
Bulgaria
Rumania
Russia
Estonia
Latvia
Ukraine
Belarus
Georgia
Finland
Sweden
Norway
Denmark
Iceland
Cape Verde
Guinea-Bissau
Equatorial 
Guinea
Gambia
Senegal
Benin
Niger
Ivory Coast Liberia
Sierra Leone
Ghana
CamerounNigeria
Gabon
Central African R
Congo
Zaire
Uganda
Kenya
Mozambique
Zambia
Zimbabwe
Malawi
South Africa
Lesotho
Botswana
Malagasy R
Comoros
Mauritius
Seychelles
Morocco
Algeria Tunisia
TurkeyEgypt
Jordan
Israel
Saudi Arabia
Yemen
Bahrain
Qatar
U Arab Emirates
China
R of China
North Korea
South Korea
Japan
India
Pakistan
Bangladesh
Sri Lanka
Nepal
Thailand
Cambodia Laos
Malaysia
Singapore
Philippines
Indonesia
Australia
Papua 
New Guinea
New Zealand
Vanuatu
Lithuania
FIG. 2: Backbone of the world trade system. Snapshots of the α = 10−3 backbone of the world trade imbalance web for the
years 1960 and 2000. Notice that the most central economies are depicted at fixed positions to make both graphs more easily
comparable.
in high flux links in terms of their absolute intensities, but
also takes into account the local heterogeneity by com-
paring the strength of the fluxes associated to a given
country with its total strength. It is then interesting to
filter out this special links and provide snapshots of the
trade system backbone. This can be achieved by com-
paring the link fluxes with the null model used for the
calculation of the disparity in a pure random case. The
same approach allows us the calculation for each connec-
tion of a country i of the probability αij that its normal-
ized flux value pij is due to chance. Along these lines, we
can identify highly inhomogeneous fluxes as those which
satisfy
αij = 1− (k − 1)
∫ pij
(1− x)k−2dx < α, (5)
where α is a fixed significance level. Notice that this ex-
pression depends on the number of connections of each
country, k. By choosing a global threshold for all coun-
tries we obtain a homogeneous criteria that allows us
to compare inhomogeneities in countries with different
number of connections and filter out links that carry
fluxes which can be considered not compatible with a
random distribution with an increasing statistical confi-
dence. The backbone is then obtained by preserving all
the links which beat the threshold for at least one of the
two countries at the ends of the link while discounting
the rest. By changing the significance level we can fil-
ter out the links focusing on progressively more relevant
heterogeneities and backbones.
An important aspect of this new filtering algorithm is
that it does not belittle small countries and then, it offers
a systematic procedure to reduce the number of connec-
tions without diminishing the number of countries and
choosing the backbone according to the amount of trade
flow we intend to characterize. It provides a quantitative
and consistent way to progressively identify the relevant
flow backbone once the level of statistical confidence with
respect to the null case is fixed, or instead the total flow
we want to represent in the system. Indeed, it is re-
markable that when looking at the network of the year
2000 one finds that the α = 0.05 backbone contains only
15% of the original links yet accounting for 84% of the
total trade imbalance. Most of the backbones form a
giant connected component containing most of the coun-
tries in the network, and only for very high values of
the confidence level, defining a sort of super-backbones,
some disconnected components appear and the number
of countries starts to drop. In this respect, the α = 0.01
backbone seems to offer the best trade-off since it keeps
nearly all countries, 75% of the total trade imbalances,
and one order of magnitude less connections than in the
original network (see Table 1).
The backbone reduction is extremely effective in sort-
ing out the most relevant part of the network and can
be conveniently used for visualization purposes. For the
sake of space and reproduction clarity, we report the
backbones corresponding to α = 10−3, still accounting
for approximately 50% of the total flux of the system.
Fig. 2 shows two snapshots of such backbones for 1960
and 2000. These high-flux backbones evidence geographi-
cal, political and historical relationships among countries
which affect the observed trade patterns. For instance,
the trade of US with its geographically closer neighbors
and also continental neighbors, the case of Russia and the
former Soviet republics, or France and its former colonies,
the lack of strong trade relations between the two blocks
in the cold war, more evident in 1960. In general terms, a
recurrent motif present in all years is the star-like struc-
ture, formed by a central powerful economy surrounded
by small dependent economies. The USA appears as one
of those powerful hubs during all this period. However,
other countries has gradually lost this role in favor of
others. This is the case of the UK, which was the only
star-like counterpart of the USA in 1948; since then its
direct area of influence has been narrowing. On the con-
trary, other countries have arisen for different reasons as
new hub economies. This is the case of some European
countries, Japan, and most recently, China.
III. DIFFUSION ON COMPLEX NETWORKS
AND THE DOLLAR EXPERIMENT
The picture emerging from our analysis has intriguing
similarities with other directed flow networks, such as
metabolic networks [21], that transport information, en-
ergy or matter. Indeed, the trade imbalances network can
be seen as a directed flow network that transport money.
In other words, we can imagine that net consumer coun-
tries are injecting money in the system. Money flows
along the edges of the network to finally reach producer
countries. Producer countries, however, do not absorb
completely the incoming flux, redistributing part of it
through the outgoing links. The network is therefore
characterizing a complex dynamical process in which the
net balance of incoming and outgoing money is the out-
come of a global diffusion process. The realization of
such a non-local dynamics in the flow of money due to
the trade imbalances spurs the issue of what impact this
feature might have on the effect that one economy can
have on another. In order to tackle this issue we per-
form a simple numerical study, defined as the “dollar ex-
periment”. The “experiment” considers running on the
networks two symmetric random walk processes. Since
we are limited by the yearly frequency of the empirical
data, we assume at first approximation that the time
scale of the changes in the structure of the underlying
trade imbalances network is bigger than the characteris-
tic diffusion time of the random walk processes. In the
first case we imagine that a consumer country (∆s < 0)
is injecting one dollar from its net debit into the system.
The dollar at this point travels through the network fol-
lowing fluxes chosen with a probability proportional to
their intensity, and has as well a certain probability of
being trapped in producer countries (∆s > 0) with a
probability Pabs = ∆ssin . More precisely, if we consider a
consumer country, such as the USA, the traveling dollar
goes from country to country always following outgoing
fluxes chosen with a probability proportional to their in-
tensity. If in its way it finds another source it just crosses
it, whereas if it finds a producer country j it has a prob-
ability Pabs(j) of being absorbed. Mathematically, this
process is a random walk on a directed network with
heterogeneous diffusion probability and in the presence
of sinks. By repeating this process many times it is possi-
ble to obtain the probability eij that the traveling dollar
originated in the source i is finally absorbed in the sink
j. In other words, for each dollar that a source country i
adds to the system, eij represents the fraction of that dol-
lar that is retained in country j. The symmetric process
considers that each producer country is receiving a dol-
lar and the traveler dollar goes from country to country
always following incoming links backward chosen with a
probability proportional to their intensity. If in its way
it finds another sink it just crosses it, whereas if it finds
a source j it has a probability Pabs(j) =
of remain-
ing in that country. The iteration of this process gives
the probability gij that yields the fraction originated in
the source country j of each dollar that a sink country
retains. Consequently, these two quantities are related
by the detailed balance condition
|∆si|eij = ∆sjgji. (6)
The matrices eij and gji are normalized probability dis-
tributions and, therefore, they satisfy that
j;sink eij =
1 and
i;source gji = 1. Using this property in the de-
TABLE II: Rankings from the Dollar experiment. Top: effect of two major source countries, USA and Switzerland, on the
rest of the world. The first list is a top ten ranking of countries according to eij , where the index i stands for the analyzed
source. The second list is the top ten ranking of direct bilateral trade measured as the percentage of flux from the source
country, that is, elocalij = Fij/s
i . Bottom: major contributors to two major sink countries, Japan and Russia. The first list is
a top ten ranking of countries according to gij , i standing for the analyzed sink. The second list is the top ten ranking due to
direct trade. In this case, the direct contribution is glocalij = Fji/s
i . Countries in boldface have no direct connection with the
analyzed country. The values for eij and gij are obtained from the simulation of the dollar experiment described in the text
using 106 different realizations for each country, for the year 2000.
Net Consumers - Sources
USA Switzerland
Dollar experiment Bilateral trade Dollar experiment Bilateral trade
Japan 19.5% Japan 17.2% France 27.3% France 75.0%
Canada 9.9% China 16.7% Germany 10.0% Germany 9.5%
China 9.3% Canada 15.6% Russia 9.7% Russia 4.1%
Saudi Arabia 6.1% Mexico 5.1% Japan 8.5% Netherlands 2.6%
Russia 5.4% Germany 4.8% Ireland 6.9% Ireland 2.3%
Germany 4.5% R of China 3.1% Norway 6.0% Belgium 1.7%
Indonesia 4.3% Italy 3.0% Saudi Arabia 4.2% Italy 1.2%
Malaysia 3.9% Venezuela 2.8% China 3.4% Austria 1.1%
Ireland 2.7% South Korea 2.4% Indonesia 2.3% Libya 0.4%
South Korea 2.7% Malaysia 2.4% Malaysia 1.9% Nigeria 0.4%
Net Producers - Sinks
Japan Russia
Dollar experiment Bilateral trade Dollar experiment Bilateral trade
USA 62.6% USA 40.2% USA 33.3% Germany 9.0%
UK 7.3% R of China 9.3% UK 7.2% Italy 8.1%
Spain 3.8% Singapore 7.0% Switzerland 7.1% USA 7.7%
Switzerland 3.3% South Korea 5.6% Poland 7.0% China 5.9%
Singapore 2.4% Germany 5.1% Turkey 6.9% Poland 5.4%
Turkey 2.1% UK 4.8% Spain 5.1% Japan 4.4%
Panama 2.1% Netherlands 4.8% Greece 3.5% Turkey 4.3%
Greece 1.9% China 3.9% Egypt 2.2% Switzerland 4.0%
Portugal 1.5% Mexico 2.1% Lithuania 2.0% Netherlands 4.0%
Egypt 1.5% Thailand 2.1% Portugal 1.9% UK 3.6%
tailed balance condition, we can write
∆sj =
i:source
eij |∆si| and |∆si| =
j:sink
gji∆sj .
Then, the total trade imbalance of a sink or source coun-
try can be written as a linear combination of the trade
imbalances of the rest of the source or sink countries,
respectively. Therefore, by measuring eij , it is possible
to discriminate the effect that one economy has on an-
other or, with gij , to find out which consumer country is
contributing the most to a producer one, in both cases
taking into account the whole topology of the network
and the inhomogeneities of the fluxes. The advantage of
this approach lies on its simplicity and the lack of tun-
able parameters. Indeed, all the information is contained
in the network itself, without assuming any kind of mod-
eling on the influences among countries.
By using this experiment it is possible to evaluate for
a consumer country where the money spent is finally go-
ing. For each dollar spent we know which percentage is
going to any other producer country and we can rank
those accordingly. It is important to remark that in this
case countries might not be directly connected since the
money flows along all possible paths, sometimes through
intermediate countries. This kind of ranking is there-
fore different from the customarily considered list of the
first neighbors ranked by magnitude of fluxes. The anal-
ysis indeed shows unexpected results and, as it has been
already pointed out in other works [5] applying other
methodologies, a country can have a large impact on
other countries despite being a minor or undirect trad-
ing partner, see Table 2. Similarly, producer countries
may have a share of the expenditure of non directly con-
nected countries resulting in a very different ranking of
their creditors. As an example, for each net dollar that
the USA inject into the system, only 9.3% is retained in
China although the direct connection imbalance between
these countries is 16.7%. Very interestingly, we find that
Switzerland spend a large share of his trade imbalance
in countries which do not have appreciable trade with it
and are therefore not directly connected such as Japan,
Indonesia, and Malaysia. The Swiss dollars go to these
countries after a long path of trade exchanges mediated
by other countries. By focusing on producer countries
we find other striking evidence. While the first importer
from Russia by looking locally at the ranking of trade im-
balances is Germany, the global analysis shows that one
third of all the money Russia gains from trade is coming
directly or undirectly from the USA. In Table 2, we re-
port other interesting anomalies detected by the global
analysis.
IV. CONCLUSIONS
In summary, we have introduced a novel quantitative
approach applicable to any dense weighted complex net-
work which filters out the dominant backbones while pre-
serving most of the nodes in the original connected com-
ponent. We have also discussed the behavior of a coupled
dynamical process, the dollar experiment, which unveils
the global properties of economic and trade partnerships.
In a globalized economy, we face ever increasing problems
in disentangling the complex set of relations and causality
that might lead to crisis or increased stability. Focusing
on just the bilateral relations among country economies
is a reductionist approach that cannot work in a highly
interconnected complex systems. We have proposed the
use of the trade network representation and mathemati-
cal tools that allow to uncover some basic ordering emerg-
ing from the global behavior and the inclusion of non-
local effects in the analysis of trade interdependencies.
Future work on this grounds might help in the assess-
ment of world trade relations and the understanding of
the global dynamics underlying major economic crises.
Acknowledgments
We thank F. Vega-Redondo for useful comments. M.
B. acknowledges financial support by DGES grant No.
FIS2004-05923-CO2-02 and Generalitat de Catalunya
grant No. SGR00889. A.V. is partially supported by
the NSF award IIS-0513650.
[1] M. A. Centeno, A. Cooke, and S. R. Curran,
NetMap Combined Studies, Mapping Globalization
Project (Princeton University and University of Wash-
ington, 2006).
[2] P. R. Krugman, Brookings Papers on Economic Activity
1995, 327 (1995).
[3] R. Glick and A. Rose, J. of Intl. Money and Finance 18,
603 (1999).
[4] K. Forbes, in In Sebastian Edwards and Jeffrey Frankel
(eds.), Preventing Currency Crises in Emerging Markets
(University of Chicago Press, Chicago, 2002), pp. 77–124.
[5] T. Abeysinghe and K. Forbes, Rev. of Intl. Econ. 13, 356
(2005).
[6] M. Goldstein, The Asian Financial Crisis: Causes,
Cures and Systemic Implications (International Institute
for Economics, Washington, D. C., 1998).
[7] M. Noland, L.-G. Liu, S. Robinson, and Z. Wang,
Global Economics Effects of the Asian Currency Devalu-
ations (International Institute for Economics, Washing-
ton, D. C., 1998).
[8] P. R. Krugman and M. Obstfeld, International Eco-
nomics: Theory and Policy, Seventh Edition (Addison-
Wesley, Lebanon, Indiana, U.S.A., 2005).
[9] R. Albert and A.-L. Barabási, Reviews of Modern
Physics 74, 47 74, 47 (2002).
[10] S. N. Dorogovtsev and J. F. F. Mendes, Evolution of
networks: From biological nets to the Internet and WWW
(Oxford University Press, Oxford, 2003).
[11] L. Krempel and T. Plümper, J. of World-Systems Re-
search 5, 487 (1999).
[12] L. Krempel and T. Plümper, J. of Social Structures 4, 1
(2003).
[13] J. H. Bergstrand, The Review of Economics and Statis-
tics 67, 474 (1985).
[14] M. A. Serrano and M. Boguñá, Phys. Rev. E 68,
015101(R) (2003).
[15] D. Garlaschelli and M. I. Loffredo, Phys. Rev. Lett. 93,
188701 (2004).
[16] D. Garlaschelli and M. I. Loffredo, Physica A 355,
138144 (2005).
[17] K. S. Gleditsch, J. Conflict Resolut. 46, 712724 (2002).
[18] A. Barrat, M. Barthélemy, R. Pastor-Satorras, and
A. Vespignani, Proc. Natl. Acad. Sci. USA 101, 3747
(2004).
[19] M. A. Serrano, J. Stat. Mech. p. L01002 (2007).
[20] M. Barthélemy, B. Gondran, and E. Guichard, Physica
A 319, 633 (2003).
[21] E. Almaas, B. Kovács, T. Vicsek, Z. N. Oltvai, and A.-L.
Barabási, Nature 427, 839 (2004).
[22] O. C. Herfindahl, Copper Costs and Prices: 1870-1957
(John Hopkins University Press, Baltimore, MD, USA,
1959).
[23] A. O. Hirschman, American Economic Review 54, 761
(1964).
[24] B. Derrida and H. Flyvbjerg, J. Phys. A 20, 5273 (1987).
[25] (version (4.1),
http://weber.ucsd.edu/∼kgledits/exptradegdp.html)
The following issues should be considered: i) This
expanded trade database includes additional estimates
for missing values. ii) The definition of state in the
international system is as defined by the Correlates of
War Project (http://www.correlatesofwar.org/). iii) The
http://weber.ucsd.edu/~kgledits/exptradegdp.html
http://www.correlatesofwar.org/
figures for trade flows are in millions of current-year
US dollars. iv) The import/export values correspond to
exchanges of merchandizes.
	Introduction
	Local heterogeneity and backbone extraction
	Diffusion on complex networks and the Dollar experiment
	Conclusions
	Acknowledgments
	References
