The EU public debt synchronization: A complex networks approach

Gka zoglou, Fo ios; So ianos, Emmanouil; Ba bie -Gaucha d, Amélie
A icle
The EU public deb synch oniza ion: A complex ne wo ks
app oach
Economies
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Sugges ed Ci a ion: Gka zoglou, Fo ios; So ianos, Emmanouil; Ba bie -Gaucha d, Amélie (2025) : The
EU public deb synch oniza ion: A complex ne wo ks app oach, Economies, ISSN 2227-7099, MDPI,
Basel, Vol. 13, Iss. 7, pp. 1-23,
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Ci a ion: Gka zoglou, F., So ianos, E.,
& Ba bie -Gaucha d, A. (2025). The EU
Public Deb Synch oniza ion: A
Complex Ne wo ks App oach.
Economies,13(7), 186. h ps://doi.o g/
10.3390/economies13070186
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A icle
The EU Public Deb Synch oniza ion: A Complex
Ne wo ks App oach
Fo ios Gka zoglou 1, Emmanouil So ianos 2,* and Amélie Ba bie -Gaucha d 2
1
Depa men o Economics, Democ i us Uni e si y o Th ace, 69100 Komo ini, G eece; [email p o ec ed]
2Bu eau d’Economie Théo ique e Appliquée (BETA), Uni e si y o S asbou g, 67000 S asbou g, F ance;
[email p o ec ed]
*Co espondence: [email p o ec ed]
Abs ac
This s udy examines he e olu ion o public deb among he 27 EU membe s a es using
G aph Theo y ools; he Th eshold Weigh ed–Minimum Domina ing Se (TW–MDS) and
he k-co e decomposi ion me hod, alongside a s anda d ne wo k quan i a i e me ic, he
densi y. By sepa a ing he da a in o h ee dis inc pe iods, p e-c isis (2000–2007), Eu opean
so e eign deb c isis (2008–2015), and pos -c isis (2016–2023), we examine he po en ial syn-
ch oniza ion o he deb a ios among EU coun ies h ough c oss-co ela ions o he public
deb s. The indings e eal ha public deb co ela ion was a i s highes le el du ing he
2008–2015 pe iod, e lec ing he uni e sal impac o he c isis and he subsequen synch o-
nized iscal and mone a y policy measu es aken wi hin EU. A signi ican ly lowe ne wo k
densi y is obse ed in bo h he p e- and pos -c isis pe iods. These esul s con ibu e o he
o e all deba e on iscal s abili y and policy coo dina ion by showing how EU coun ies end
o align hei iscal beha io s du ing pe iods o c isis while beha ing mo e independen ly
du ing s able imes. In addi ion, we yield a deepe insigh in o how economic shocks
eo ganize public deb in e connec ions wi hin he c isis pe iod. Finally, his analysis
highligh s o wha ex en Eu opean economic in eg a ion s eng hens connec ions be ween
he iscal posi ions ( h ough public deb ) o he Eu opean Union membe coun ies.
Keywo ds: public deb ; Eu opean in eg a ion; complex ne wo ks; co ela ion; synch oniza ion;
g aph heo y
JEL Classi ica ion: H63; O52; E62; C63
1. In oduc ion
The o ma ion o he Eu o A ea in 1999 was a signi ican miles one o he economic
in eg a ion o he pa icipa ing Eu opean Union na ions. The in oduc ion o he common
cu ency was in ended o p omo e s abili y and s imula e economic g ow h. I was a
necessa y—bu no su icien —condi ion o mo e om he heo e ical owa ds a eal
Op imal Cu ency A ea (OCA) by Robe Mundell s anda ds (Mundell,1961). Howe e ,
he Eu opean so e eign deb c isis ha mani es ed in he 2010s exposed undamen al
weaknesses in eal economic in eg a ion, go e nance, and policy coo dina ion among he
membe s a es. This c isis unde sco ed he need o imp o ed mechanisms o moni o and
manage mac oeconomic imbalances ha could h ea en he o e all s abili y o he egion
(Al es e al.,2020).
The e olu ion o he EU has been shaped by bo h economic and policy-d i en chal-
lenges. The Maas ich T ea y, app o ed in 1992, laid he ounda ion o a mone a y union
Economies 2025,13, 186 h ps://doi.o g/10.3390/economies13070186
Economies 2025,13, 186 2 o 23
by se ing con e gence c i e ia ha coun ies mus mee o adop he eu o. These c i e ia
include limi s on budge de ici s, public deb le els, in la ion, long- e m in e es a es, and
exchange a e s abili y.
The in oduc ion o he eu o in 1999 ma ked he beginning o a new mone a y e a,
wi h he Eu opean Cen al Bank (ECB) assuming esponsibili y o he uni ied mone a y
policy. Following he es ablishmen o he Eu ozone, he S abili y and G ow h Pac (SGP)
became he iscal ule o coun ies belonging o he mone a y union. The pac seeks o
balance iscal discipline wi h go e nmen lexibili y. The ac ha hese iscal ules ha e
been e o med se e al imes highligh s ha public deb emains a pe sis en challenge,
especially unde heigh ened sc u iny om inancial ma ke s. The la es e o m, adop ed in
2024, ea i ms he 3% GDP de ici limi and he 60% GDP deb h eshold and in oduces
lexible adjus men pa hways. Due o he geopoli ical con ex , including he wa in Uk aine,
which s a ed in 2022, and poli ical ins abili y in he Uni ed S a es since ea ly 2025, his
new ule has al eady been elaxed. This measu e allows coun ies o exclude de ense
spending om he c i e ia assessed unde he excessi e de ici p ocedu es o a pe iod o
ou yea s. Ne e heless, unce ain y in he ma ke s ega ding he sus ainabili y o public
deb emains, in luencing c edi a ings and economic s abili y wi hin he egion.
The inancial c isis o 2008 and he ollowing Eu opean so e eign deb c isis (which
occu ed in 2010) u he exposed he weaknesses o a mone a y union wi hou a com-
mon iscal policy. The c isis, igge ed in pa by he e ela ion o unde epo ed budge
de ici s in ce ain Eu ozone coun ies, led o a loss o ma ke con idence and a sha p ise in
bo owing cos s. In esponse, eme gency measu es such as he Eu opean S abili y Mech-
anism (ESM) we e implemen ed o p o ide inancial assis ance o s uggling economies.
In addi ion o hese empo a y measu es, pe manen e o ms we e aken o add ess he
d awbacks associa ed wi h he lack o a cen alized iscal au ho i y. One o he mos signi i-
can was he Eu opean Semes e , es ablished in 2010, which se es as a key ins umen o
ensu ing economic policy alignmen and coo dina ion wi hin he Eu o A ea. I in eg a es
he S abili y and G ow h Pac (SGP), he B oad Economic Policy Guidelines (BEPGs), he
Eu opean Employmen S a egy (EES), he Lisbon S a egy, and he Social Open Me hod
o Coo dina ion (OMC), c i ical amewo ks designed o main ain iscal discipline and
economic s abili y (Ve dun & Zei lin,2017). Unde his sys em, he Eu opean Commission
assesses na ional economic policies, issues coun y-speci ic ecommenda ions, and moni-
o s mac oeconomic imbalances, including labo ma ke and c edi de elopmen s. These
measu es aim o synch onize economic cycles ac oss membe s a es and mi iga e he isks
o u u e inancial c ises (Papadopoulos & Pia oni,2019).
In addi ion, he implemen a ion and he second e o m o he S abili y and G ow h
Pac ( h ough he Six Pack (2011) and he Two Pack (2013)) s eng hened he coo dina ion
o iscal policies and imp o ed he moni o ing o membe s a es’ iscal posi ions.
Simila measu es we e aken ollowing he 2020 pandemic c isis o he whole EU wi h
he Nex Gene a ion EU, he Eu opean eco e y plan (a 30-yea bond launched o enable
Eu opean coun ies o add ess bo h sho - e m eme gencies and long- e m challenges), and
he hi d e o m o he S abili y and G ow h Pac adop ed in 2024 o EMU coun ies.
Thus, since he ad en o he Eu ozone in 1999, nume ous measu es, bo h empo a y
(implemen ed only du ing economic c ises) and pe manen ( e o ms o iscal ules), ha e
been aken o ensu e a g ea e con e gence o he iscal posi ions, hus s eng hening
Eu opean economic in eg a ion.
This s udy examines he economic ne wo k o he 27 EU coun ies, ocusing on public
deb le els o e h ee dis inc pe iods: 2000–2007 (Pe iod 1), 2008–2015 (Pe iod 2), and
2016–2023
(Pe iod 3). By analyzing c oss-co ela ions among membe s a es, i seeks
o iden i y he pa e ns o synch oniza ion in public deb dynamics. The indings will
Economies 2025,13, 186 3 o 23
con ibu e o a deepe unde s anding o he EU’s iscal landscape and in o m u u e policy
decisions ha p omo e economic esilience and in eg a ion (Mundell,1961;McKinnon,
1963;Kenen,1969). This s udy also con ibu es o he assessmen o iscal in eg a ion in
he EU by examining he synch oniza ion and in e connec ions o public deb ajec o ies
among membe s a es.
The o iginali y o his esea ch lies in i s applica ion o complex ne wo k analysis o
measu e bo h he ne wo k’s in ensi y as well as he numbe o in e connec ed coun ies
wi hin he Eu opean Union, as al eady employed by Papadimi iou e al. (2022). The
membe s a es cons i u e a union in which hey adhe e o sha ed ules ega ding deb a ios.
I he a ios mo e in di e en di ec ions, implemen ing a uni ied policy ac oss all coun ies
becomes qui e challenging.
In ligh o his, he s udy aims o examine he ollowing: (a) how he deb a ios o he
Eu opean economies ha e e ol ed o e ime and whe he hei ajec o ies ha e ollowed
he same di ec ion; (b) he ex en o which coun ies a e in e connec ed in e ms o deb
e olu ion (speci ically, whe he hey o m g oups exhibi ing simila beha io ); and (c) how
he deb a io synch oniza ion was a ec ed by e en s ha had a global e ec —p incipally
he 2007–2008 inancial c isis, ollowed by he COVID-19 pandemic in 2020 and he ou b eak
o he Russo-Uk ainian wa in 2022. Unde s anding whe he public deb ajec o ies a e
in e empo ally linked ac oss coun ies is essen ial o assessing he deg ee o which EU
membe s a es a e mo ing in a common iscal di ec ion.
The es o he pape is s uc u ed as ollows: In Sec ion 2, we p esen he ela ed
li e a u e, in Sec ions 3and 4, we p esen he da ase and he me hodology, espec i ely,
and in Sec ion 5, we analyze he esul s, while Sec ion 6concludes he pape .
2. Li e a u e Re iew
As he EU con inues o na iga e he challenges o iscal sus ainabili y, pa icula ly in
he a e ma h o ecen c ises, i has become inc easingly impo an o unde s and how
i s iscal ules in luence public deb . Recen esea ch sheds ligh on he e ec i eness o
EU-le el mechanisms and na ional iscal amewo ks, aising impo an ques ions abou
wha wo ks, wha does no , and whe e e o ms a e needed.
The s udy o K aeme and Leh imäki (2023) examines how EU-le el iscal ins i u ions
and na ional iscal ules ha e in luenced public deb dynamics ac oss EU membe s a es
om 1990 o 2019. Using a panel da a app oach wi h ixed e ec s, he au ho s ind ha
he S abili y and G ow h Pac (SGP) signi ican ly educed go e nmen deb , especially
a e i s es ablishmen . Howe e , la e e o ms o he SGP showed mixed e ec i eness.
Na ional iscal ules had a ying impac s depending on he ule ype and sec o , wi h
gene al go e nmen balance and deb ules showing mo e consis en deb - educing e ec s.
In e es ingly, some ules a he cen al go e nmen le el we e linked o ising deb . The
esul s highligh ha EU and na ional ules a e la gely complemen a y, bu hei design
and coo dina ion a e c i ical o e ec i e iscal go e nance.
In a ollow-up s udy K aeme and Leh imäki (2024), assess he impac o Eu opean
in eg a ion and he EU’s iscal amewo k on public deb le els ac oss he membe s a es.
Using he Syn he ic Con ol Me hod, he au ho s cons uc coun e ac ual scena ios o
es ima e wha deb ajec o ies migh ha e looked like wi hou EU membe ship o he
SGP. Thei indings e eal ha , o mos EU coun ies, ac ual go e nmen deb le els
we e signi ican ly lowe han hose in he syn he ic al e na i es, sugges ing a clea deb -
es aining e ec . This e ec pe sis s e en in cases o limi ed ule compliance, highligh ing
he ancho ing in luence o EU iscal s uc u es. Howe e , impo an he e ogenei ies a e
also unde sco ed, pa icula ly a e he global inancial c isis.
Economies 2025,13, 186 4 o 23
In a complemen a y pe spec i e, A nold e al. (2022) a gue ha he Eu opean Union’s
cu en iscal ules ha e allen sho in ensu ing deb sus ainabili y and mac oeconomic
s abiliza ion. The au ho s p opose a isk-based amewo k linking iscal a ge s o deb
sus ainabili y analysis, while main aining he 3% de ici and 60% deb - o-GDP h esholds.
A s eng hened ole o na ional iscal ins i u ions and medium- e m amewo ks is em-
phasized, alongside he c ea ion o a cen al EU iscal capaci y o suppo public goods
and coun e ac asymme ic shocks. The pape calls o ins i u ional e o ms, including an
independen Eu opean Fiscal Council and mo e obus na ional iscal councils. The goal
is o design ules ha a e bo h e ec i e and ealis ically implemen able, especially in a
high-deb , pos -c isis con ex .
Beyond iscal ules, he b oade ques ions o economic in eg a ion and con e gence
emain cen al o he iabili y o he Eu ozone. F om a heo e ical s andpoin , he concep
o economic synch oniza ion has been widely discussed in he li e a u e, pa icula ly in
ela ion o he Op imum Cu ency A ea (OCA) heo y (Mundell,1961;McKinnon,1963;
Kenen,1969). The OCA amewo k posi s ha egions adop ing a common cu ency
should exhibi synch onized business cycles and economic homogenei y o ensu e e ec i e
mone a y policy ansmission. Howe e , empi ical s udies sugges ha pe sis en s uc u al
dispa i ies among Eu ozone economies pose challenges o achie ing ull con e gence
(F ankel & Rose,1998;Rogo ,1985).
Recen empi ical s udies ha e con inued o unco e pe sis en s uc u al dispa i ies
among he Eu ozone economies. Fo ins ance, Cou inho and Tu ini (2020) analyzed how
economies in he Eu o A ea ha e been con e ging compa ed o o he EU and non-EU
coun ies. They ound ha , o e all, he pa e ns a e simila ac oss g oups. Howe e , he
coun ies ha ini ially adop ed he eu o ha e shown weake con e gence—a end ha
seems o ha e s a ed e en be o e he inancial c isis, likely due o he pe sis en di e ences
in p oduc i i y le els.
Simila ly, F anks e al. (2018) examined he economic con e gence among Eu o A ea
coun ies and concluded ha while nominal con e gence occu ed in a eas such as in la ion
and in e es a es, he eal con e gence o pe capi a income le els has no been achie ed
among o iginal Eu o A ea membe s ollowing he in oduc ion o he common cu ency.
Me hodologically, ne wo k analysis has gained signi ican ac ion in ecen yea s, as
i p o ides a obus amewo k o e alua ing economic linkages and o e ing aluable
insigh s in o economic synch oniza ion. P e ious s udies ha e applied his app oach o
e alua e inancial con agion, ade dependencies, and so e eign deb isks (Dellas & Ta las,
2009). One such s udy is ha o Papadimi iou e al. (2014), which ocuses on analyzing
inancial s abili y and economic con e gence. The au ho s p esen wo empi ical examples:
one based on a banking ne wo k o 200 US banks and ano he based on GDP g ow h a es
among 22 Eu opean coun ies. Thei indings emphasize he e ec i eness o he T-MDS
me hodology in analyzing complex economic sys ems. By le e aging echniques om
complex ne wo ks, esea che s can iden i y synch oniza ion pa e ns ha signi ican ly
con ibu e o s abili y. Wi hin he amewo k o ou esea ch, policy coo dina ion is mos
e ec i e when synch oniza ion is widesp ead and encompasses he maximum possible
numbe o membe s a es.
In ano he s udy, Papadimi iou e al. (2016) highligh he u ili y o ne wo k-based
app oaches in assessing economic cohesion wi hin he Eu ozone. The esea ch examines
he synch oniza ion o economic cycles h ough complex ne wo k me ics, demons a ing
how cen al and pe iphe al coun ies in e ac wi hin he Eu o A ea’s inancial amewo k.
The indings sugges ha while ce ain co e economies exhibi s ong in e connec ions,
pe iphe al na ions o en display g ea e ola ili y and weake ies o he ne wo k cen e ,
impac ing o e all economic s abili y.

Economies 2025,13, 186 5 o 23
Fu he , Dias (2012) examines he so e eign deb c isis in he Eu opean Union, em-
ploying minimum spanning ees wi hin a olling window amewo k. The s udy uses da a
om 19 EU coun ies conce ning daily 10-yea go e nmen bond yield a es, spanning
om Ap il 2007 o Oc obe 2010. The esul s highligh a lack o synch oniza ion be ween
he ou mos impac ed coun ies—G eece, I eland, Po ugal, and Spain—and he mo e
esilien na ions in he Eu o A ea, such as Ge many and he Ne he lands.
Kan a e al. (2014) examine he ela ionships be ween Eu opean coun ies by con-
s uc ing ne wo ks based on deb - o-GDP a ios. To analyze he opological p ope ies o e
he pe iod o 2000–2011, hey de elop hie a chical and minimum spanning ees. Thei
s udy co e s bo h he en i e pe iod (2000–2011) and wo speci ic sub-pe iods (
2000–2004
and
2005–2011
). The analysis e eals dis inc clus e s o coun ies g ouped by hei
deb le els.
Ma esanz and O ega (2015) examine he e ol ing ne wo k dynamics o qua e ly
public deb - o-GDP a ios ac oss 29 Eu opean coun ies om 2000 o 2014. U ilizing a olling
window app oach, hey cons uc hie a chical ees and minimum spanning ees while
e alua ing a ious s anda d me ics associa ed wi h complex ne wo ks. Thei indings
e eal ha he pe iod o he inancial c isis exhibi s he highes le el o connec i i y among
coun ies wi hin he ne wo k.
Papadimi iou e al. (2022) explo e he synch oniza ion le els o a ange o mac oeco-
nomic a iables in Eu ope, including he gene al go e nmen deb - o-GDP a io. Using
co ela ion-based ne wo ks and G aph Theo y me ics, hei analysis spans h ee dis inc
pe iods: 1999–2004, 2005–2010, and 2011–2019. Thei indings e eal signi ican synch o-
niza ion o he deb - o-GDP a io du ing he 2005–2010 pe iod, a end ha is dis up ed in
he subsequen in e al.
The p esen s udy builds on his li e a u e by examining public deb dynamics in
he EU o e h ee dis inc pe iods. By analyzing he e ol ing s uc u e o he ne wo k,
his esea ch aims o con ibu e o he ongoing discou se on iscal s abili y and policy
coo dina ion wi hin he Eu opean mone a y union. Fu he mo e, om a me hodological
s andpoin , he po en ial o k-co e analysis emains la gely unexplo ed in his con ex .
3. The Da ase
The da ase consis s o go e nmen consolida ed g oss deb o he gene al go e nmen
sec o , exp essed as a pe cen age o GDP
1
, in qua e ly equency (Figu e 1), spanning om
2000Q1 o 2023Q4
2
. I conce ns he 27 coun ies (Table 1) ha a e cu en ly EU membe
s a es, o which 18 also belong o he Eu o A ea and use he common cu ency. Figu e 1
illus a es he p og ession o deb - o-GDP a ios o he 27 EU membe s a es om he
i s qua e o 2000 o he i s qua e o 2024. The igu e highligh s subs an ial a ia ion
among coun ies, wi h a ios spanning a wide ange om low o high le els. Desc ip i e
s a is ics o each coun y and each pe iod a e p esen ed in Table A1 in Appendix A.
Table 1. The 27 membe s a es o he Eu opean Union in he da ase (alphabe ical o de ).
1 Aus ia 15 I aly
2 Belgium 16 La ia
3 Bulga ia 17 Li huania
4 C oa ia 18 Luxembou g
5 Cyp us 19 Mal a
6 Czechia 20 Ne he lands
7 Denma k 21 Poland
8 Es onia 22 Po ugal
Economies 2025,13, 186 6 o 23
Table 1. Con .
9 Finland 23 Romania
10 F ance 24 Slo akia
11 Ge many 25 Slo enia
12 G eece 26 Spain
13 Hunga y 27 Sweden
14 I eland

Figu e 1. E olu ion o he 27 EU membe s a es deb - o-GDP a io om 2000Q1 o 2024Q1. A ound
2008Q2 and 2020Q2, a sub le line appea s o be o ming, indica ing a ise in he a ios. Da a
sou ce: Eu os a .
The GDP o each coun y, exp essed in cu en p ices (millions o eu os), is u ilized
o assign a co esponding weigh o ha coun y ( he speci ic de ails a e ho oughly ex-
plained in Sec ion 4). The da a sou ce o go e nmen deb and GDP is Eu os a , ensu ing
consis ency and compa abili y ac oss all EU membe s a es.
The objec i e o his esea ch, as p e iously s a ed, is o examine he empo al e o-
lu ion o he deb - o-GDP a io among he membe s a es o he Eu opean Union and o
e alua e he ex en o which hei mo emen s align o e ime, sugges ing possible synch o-
niza ion. To achie e his and unco e possible s uc u al shi s in public deb dynamics, we
di ide he ini ial 2000–2023 da ase in o h ee consecu i e in e als: 2000–2007, 2008–2015,
and 2016–2023. The pa i ioning is based on signi ican mac oeconomic e en s ha shaped
iscal policy and deb dynamics in he EU. Mo e speci ically, he in e als a e he ollowing:
•2000–2007 (Pe iod 1): A p e-c isis pe iod cha ac e ized by ela i e economic s abili y,
wi h no majo economic shocks. Mo eo e , he la ges expansion occu ed du ing his
pe iod, wi h en coun ies joining he EU in 2004 (Czech Republic, Es onia, Cyp us,
La ia, Li huania, Hunga y, Mal a, Poland, Slo akia, and Slo enia), ollowed by wo
mo e in 2007 (Bulga ia and Romania). This b ough he o al numbe o membe s a es
o 27 (EU27).
Economies 2025,13, 186 7 o 23
•
2008–2015 (Pe iod 2): The pe iod encompassing he global inancial c isis and he
subsequen Eu opean so e eign deb c isis, along wi h he iscal measu es and policy
esponses implemen ed o s abilize EU economies o bo h c ises.
•
2016–2023 (Pe iod 3): A pos -c isis pe iod ma ked by wo majo ex e nal shocks: he
COVID-19 pandemic and he wa in Uk aine, bo h o which had signi ican mac oeco-
nomic epe cussions, including ene gy p ice luc ua ions and in la iona y p essu es.
The empo al pa i ioning o ime pe iods enables he ne wo k analysis echniques o
assess he e ol ing in e connec ions, in e ms o go e nmen deb le els. By segmen ing he
da a, we aim o cap u e shi s in he iscal ela ionships ac oss EU membe s a es, iden i ying
key s uc u al changes in deb dynamics be o e, du ing, and a e economic c ises.
4. Me hodology
The analysis is conduc ed sepa a ely o each de ined ime pe iod, yielding h ee
successi e ne wo ks ha e lec he empo al e olu ion o in e -coun y ela ionships. Each
node ep esen s an EU coun y o a o al o 27 nodes. The edges ha connec he nodes
deno e he ela ionship be ween each pai o coun ies in e ms o he selec ed a iable. In
ou empi ical analysis, he a iable selec ed is he Pea son co ela ion o he deb - o-GDP
a io o each pai o coun ies. The Pea son co ela ion coe icien i,jis de ined as
i,j≜COVZi,Zj
qVAR (Zi)VARZj(1)
whe e
Zi
,
Zj
a e pai s o obse a ions o he a iable unde examina ion o membe s a es
iand j. The co ela ion coe icien alue, in he ange o [
−
1, 1], quan i ies he s eng h and
di ec ion o he linea ela ionship be ween he wo coun ies. Values close o he uppe
and lowe bounds indica e a s ong ela ionship; when nea +1, i signi ies a s ong posi i e
ela ionship, while alues close o
−
1 indica e a s ong nega i e ela ionship. Values nea
ze o sugges no linea associa ion be ween coun ies iand j.
The ollowing pa in oduces some key concep s o ne wo k analysis used in he
empi ical pa o his pape , aiming o p o ide a clea e unde s anding o he concep .
G aph/ne wo k: A g aph G= (V,E) consis s o a se o nodes Vand a se o edges E
h ough which he nodes a e connec ed (i.e., an edge e
i,j ∈
Elinks he nodes iand j
∈
V).
Each edge e
i,j ∈
Econnec ing he nodes iand jca ies a alue which is calcula ed by he
Pea son’s co ela ion coe icien
i,j
(Figu e 2a). This pa ame e measu es he empo al
simila i y be ween he nodes iand j. In addi ion, he se o nodes associa ed wi h node iis
de ined as he neighbo hood Bio node i, i.e., Bi=j∈V:∃eij ∈E.
Isola ed node: A node i
∈
Vis conside ed isola ed when he e a e no edges connec ing
i o any o he es nodes o he ne wo k.
In e connec ed node: A node i
∈
Vis e med in e connec ed when i is connec ed o
a leas one o he node in he ne wo k ia an edge. In i s ini ial a angemen , he ne wo k
o he p esen esea ch is comple e, meaning ha he e is an edge connec ing e e y single
pai o nodes, and hence no isola ed nodes exis .
Domina ing Se : A Domina ing Se DS
⊆
Vis a subse o he in e connec ed
nodes in he ne wo k, cha ac e ized by he ollowing p ope y: e e y node i ha is
no pa o he DS is connec ed o a leas one DS node j h ough an edge e
i,j
i.e.,
∀i/∈DS,∃j∈DS :eij ∈E(Figu e 2b).
Economies 2025,13, 186 8 o 23

(a)(b)

(c)(d)
Figu e 2. (a) P esen a ion o a g aph pa adigm whe e each edge’s alue is measu ed by he Pea son’s
co ela ion coe icien
i,j
; (b) a Domina ing Se o he ne wo k ( ed nodes); (c) a Minimum Domina ing
Se o he ne wo k ( ed nodes); (d) a Th eshold Minimum Domina ing Se o he ne wo k ( ed nodes—
a h eshold o 0.8 was implemen ed). The edges po ayed wi h dashed lines did no su i e he
h esholding s ep.
Fo each o he nnodes o he ne wo k, a bina y pa ame e x
i
,i= 1, 2,
. . .
nis conside ed
o symbolize i s DS membe ship s a us, such ha
xi=(0, i i /∈DS
1, i i ∈DS (2)
Fo mula (3) ma hema ically displays he DS concep :
xi+∑
j∈Bi
xj≥1, i=1, 2, . . . n(3)
An in e connec ed node ihas o be ei he a node o he DS o adjacen (i.e., connec ed)
o a leas one such node. Howe e , his is no a mu ually exclusi e ela ionship; he e may
be nodes ha mee bo h condi ions (Figu e 2b). When he edges in a ne wo k e lec high
simila i y, as is he case he e, he dominance a ibu e p oduces an in iguing e ec : he
beha io o he en i e ne wo k can be e ec i ely ep esen ed by he beha io o he DS.
Minimum Domina ing Se : The Minimum Domina ing Se (MDS) is he DS wi h he
smalles ca dinali y.
min n
∑
i=1
xi!(4)
The Minimum Domina ing Se (MDS) is iden i ied by applying condi ion (4) while
complying wi h he cons ain s ou lined in condi ion (3) (Figu e 2c).
Since he co e ocus o he cu en esea ch is he empo al simila i y be ween nodes,
he s anda d Minimum Domina ing Se (MDS) algo i hm is no well-sui ed o his pu pose
due o an inhe en limi a ion. In a co ela ion-based ne wo k, such as he one examined
he e, edges do no necessa ily indica e simila i y. Gi en ha co ela ion alues ange om
Economies 2025,13, 186 15 o 23
is p obably he esul o he heigh ened deb o almos all EU coun ies and coo dina ed
policy measu es such as he ESM. The p esence o a la ge, densely connec ed co e con i ms
ha public deb dynamics we e closely in e ela ed ac oss membe s a es.
In con as , he ini ial (2000–2007) and las (2016–2023) pe iods display signi ican ly
lowe le els o connec i i y and, hus, synch oniza ion. Pe iod 1 ea u es a ne wo k o
weake in e connec ions be ween EU membe s a es. Howe e , despi e lowe o e all
densi y, he p esence o a highly connec ed co e du ing his pe iod (a 9-co e wi h a densi y
o 1 and a 7-co e wi h a densi y o 0.97 o 0.7 and 0.8, espec i ely) indica es he exis ence
o a subne wo k o coun ies exhibi ing highly simila beha io . The ne wo k in Pe iod 3,
e en wi h sligh ly g ea e densi y han in Pe iod 1, is composed di e en ly. The absence o
isola ed nodes sugges s highe synch oniza ion ac oss he ne wo k, and i is likely o be a
sign o he in luence o he EU-le el coo dina ion o policies due o ex e nal p essu es such
as he COVID-19 pandemic, he wa in Uk aine, and he p oac i e policy o he 2008 c isis.
Se e al ac o s can con ibu e o pos -c isis di e gence. The d i e s o di e gence
s em om s uc u al he e ogenei ies linked o s uc u al di e ences in an economic, de-
mog aphic, ins i u ional, and poli ical na u e ha exis in Eu ope. Such s uc u al he e o-
genei ies help explain why Eu opean economies espond di e en ly o economic shocks
(see Gue ini e al.,2018;Campos e al.,2020). Di e ences in p oduc i e specializa ion
emain signi ican wi hin he EU and con ibu e o a ying eac ions o economic shocks,
as each economy elies o di e en ex en s on ce ain sec o s, sec o s ha hemsel es
espond di e en ly o changes in demand, p ice luc ua ions, supply shocks, e c. The socio-
demog aphic cha ac e is ics o coun ies (e.g., he p opo ion o o e -65s in he popula ion
and exposu e o he isk o po e y o social exclusion) and ins i u ional di e si y (e.g.,
pa liamen a y s. semi-p esiden ial sys ems), as highligh ed by Lopez-Gomez (2024), also
play an impo an ole.
A quali a i e examina ion o he ne wo ks (Tables A2 and A3 in Appendix B) unco e s
se e al no ewo hy indings. While he TW-MDS algo i hm ends o a o coun ies wi h
highe GDPs when iden i ying dominan nodes, his is no consis en ly he case. Fo
ins ance, in he case o he 0.7 h eshold, Ge many—despi e ha ing he highes GDP in he
EU—is no iden i ied as a dominan node in any pe iod excep o Pe iod 3. In e es ingly,
e en du ing Pe iod 2, when ne wo k connec i i y is high, Ge many does no eme ge
as dominan . Addi ionally, Ge many is absen om he maximum k-co e in all h ee
pe iods. Summa izing he beha io o he EU’s h ee la ges economies, F ance appea s
as a dominan node in Pe iods 1 and 3, while I aly consis en ly holds a dominan s a us
ac oss all pe iods. Unde he s ic e 0.8 h eshold, Ge many is iden i ied as dominan in
Pe iods 1 and 3, F ance does no appea as dominan in any pe iod, and I aly is iden i ied
as dominan only in Pe iod 3. No ably, Ge many emains excluded om he maximum
k-co e h oughou all pe iods, ega dless o he h eshold.
I is wo h no ing ha Ge many no only emains ou side he maximum k-co e bu
also main ains signi ican ly ewe connec ions han he coun ies included in ha co e
ac oss all pe iods. This disc epancy is especially e iden unde he 0.8 h eshold: in Pe iod
1, Ge many is pa o he 3-co e while he maximum one is he 7-co e; in Pe iod 2, i
belongs o he 6-co e, whe eas he maximum is he 14-co e and includes a ound 60% o he
coun ies; and in Pe iod 3, Ge many is again in he 3-co e, compa ed o he maximum o
he 6-co e (Table A4 in Appendix B). These indings sugges ha Ge many, despi e being
he EU’s la ges economy, occupies a pe iphe al posi ion wi hin he ne wo k in e ms o i s
deb a io e olu ion. This has impo an implica ions, po en ially complica ing he policy
coo dina ion e o s ela ed o iscal s abili y.
Ano he inding is ha he beha io o he coun ies appea s o be independen o
hei Eu o A ea membe ship s a us. No clea pa e ns eme ge in e ms o clus e ing in o

Economies 2025,13, 186 16 o 23
neighbo hoods o co es o he iden i ica ion o isola ed s a us based on whe he a coun y
is pa o he common cu ency a ea. Fu he mo e, he synch oniza ion obse ed du ing
he 2008–2015 pe iod does no seem o be limi ed o Eu o A ea membe s. Finally, he e is
no indica ion o geog aphical di isions, such as a no h–sou h spli . Tables A2 and A3 in
Appendix Bp o ide ela i e in o ma ion o he 0.7 and 0.8 h esholds, espec i ely.
The indings p esen ed sugges ha big c ises ha e a conside able impac on iscal
in e ela ions be ween he EU membe s a es. Du ing ela i ely anquil pe iods, coun ies
end o beha e mo e independen ly, e lec ing a a he dissimila beha io in hei ac ions.
In con as , e en s ha igge global inancial unce ain y—along wi h he esul ing policy
in e en ions (such as he ESM)— o ce coun ies o ac in a mo e coo dina ed manne ,
ollowing a simila ajec o y.
This a icle highligh s he impac o p og ess made since 2008 in e ms o iscal in e-
g a ion on he synch oniza ion o na ional public deb . Indeed, he ad hoc in e en ion
mechanisms implemen ed since he 2008 inancial c isis (Eu opean S abili y Mechanism,
Eu opean Semes e , Six Pack, Two Pack, Nex Gene a ion EU, e c.) appea o ha e bo ne
ui by p e en ing excessi e na ional di e gence in public inance.
These esul s con i m ha when s abiliza ion mechanisms o economic shocks ha
a ec coun ies di e en ly (i.e., asymme ic shocks, o symme ic shocks wi h asymme ic
e ec s) a e implemen ed a he EU le el, he ul ima e impac on na ional public deb is
educed, and synch oniza ion is s eng hened. In such cases, an EU-le el s abiliza ion
mechanism s eps in o cushion economic shocks, elie ing p essu e on na ional budge s.
This sugges s ha he op imali y o he Eu ozone may be an endogenous p ocess,
d i en by he g adual implemen a ion o ools o s abilizing economic shocks wi hin he
Eu ozone, bu i will also ha e an impac on non-Eu ozone coun ies.
Looking ahead, he key challenge is o ensu e he sus ainabili y o hese al e na i e
economic s abiliza ion mechanisms, which ha e so a been implemen ed only empo a ily,
o ease he cons ain s on na ional budge s. The c ea ion o a Eu opean iscal capaci y could
ul ill his ole o abso bing symme ic shocks (wi h asymme ic e ec s due o s uc u al
he e ogenei ies) on na ional economies (see Bu iel e al.,2020), ul ima ely s abilizing public
deb ajec o ies, as al eady occu s in he Uni ed S a es, Canada, and Aus alia.
This would allow na ional budge s o ocus p ima ily on deli e ing public goods and
se ices (such as educa ion, heal h, social p o ec ion, secu i y, and anspo ) while being
subjec o igo ous o e sigh unde he e o med S abili y and G ow h Pac (2024), exclud-
ing na ional de ense expendi u e. Meanwhile, cyclical s abiliza ion would be handled
h ough a Eu opean iscal capaci y.
6. Conclusions
In his pape , we explo e how iscal beha io and in e connec ions among EU coun ies
e ol ed o e ime, especially in esponse o majo economic shocks, based on public deb .
By using G aph Theo y ools, we examined public deb dynamics ac oss h ee dis inc
pe iods: Pe iod 1, he yea s be o e he global inancial c isis (2000–2007), Pe iod 2, he
u bulen yea s o c isis and esponse (2008–2015), and Pe iod 3, he pos -c isis pe iod
shaped by new global dis up ions (2016–2023). I is impo an o no e ha his s udy is
limi ed o he pe iod ollowing he yea 2000 due o da a cons ain s. While analyzing
he ne wo k o coun ies p io o 2000 could po en ially yield aluable insigh s in o he
ea ly s ages o he union, such an analysis is un o una ely no easible gi en he lack o
a ailable da a.
The indings show a clea pa e n: when ex e nal p essu es ise, so does he iscal
synch oniza ion ac oss membe s a es. Pe iod 2 p esen s he highes le el o connec i i y
among coun ies, wi h ewe isola ed nodes and a la ge, dense co e. This sugges s ha he
Economies 2025,13, 186 17 o 23
inancial and so e eign deb c ises, combined wi h policy esponses like he ESM, b ough
EU coun ies close oge he in e ms o iscal beha io .
In con as , in mo e s able pe iods, such as he yea s p eceding he c isis and he mos
ecen in e al, he o e all ne wo k densi y ends o dec ease. S ill, he e is nuance he e.
E en in hose less u bulen pe iods, we disco e ed igh ly connec ed subne wo ks, poin -
ing o smalle g oups o coun ies wi h simila deb dynamics. In e es ingly, he ne wo k
in Pe iod 3, while no as synch onized as in he c isis yea s, shows some imp o emen
o e he p e-c isis e a. The absence o isola ed coun ies and a sligh ly g ea e densi y
sugges ha pas expe iences and EU-wide coo dina ion mechanisms migh ha e laid he
g oundwo k o close iscal alignmen , e en in he ace o new shocks like he pandemic
o he wa in Uk aine.
Thus, ou esul s highligh he impac ha he a ious measu es implemen ed o
suppo EU coun ies du ing he a ious economic c ises ha e had on he in ensi y o
connec ions in e ms o he ajec o ies o public deb . By aking cha ge o pa o he
cushioning o he cyclical shocks linked i s o he inancial c isis (Pe iod 2) and hen o he
pandemic c isis (Pe iod 3), he Eu opean mechanisms implemen ed ha e a o ed he be e
synch oniza ion o public deb s, an in ensi ica ion o he connec ions be ween na ional
public deb s, and also he disappea ance o he isola ed coun ies.
To conclude, he esul s highligh he impo ance o sha ed challenges in shaping
how EU membe s a es manage hei public inances. Du ing pe iods o s abili y, na ional
s a egies end o di e ge, e lec ing local p io i ies and poli ical con ex s. Howe e , in imes
o c isis, he e is a clea shi owa d con e gence, likely d i en by he need o coo dina ed
esponses and sha ed ools. This has implica ions no only o in e p e ing pas beha io
bu also o how EU policymake s may app oach he design o u u e iscal amewo ks.
Thus, a be e synch oniza ion o na ional public deb s in he EU ep esen s a eal
oppo uni y o ensu e he las ing mone a y and inancial s abili y o he mone a y union
and could appea as he solu ion o he challenge posed by he su eillance o na ional
public inances. Mo e synch onized na ional public deb s would make i possible o
es ablish e ec i e common Eu opean ools o suppo he cushioning o economic shocks.
Looking ahead, main aining deb synch oniza ion may equi e o malizing some o
he s abiliza ion ools in oduced since 2008. A pe manen Eu opean iscal capaci y could
help abso b economic shocks mo e e enly, educing he p essu e on na ional budge s and
allowing hem o ocus on p o iding public goods and se ices o ci izens. O e ime,
his could suppo s onge iscal alignmen ac oss he EU and ein o ce he goals o he
e o med S abili y and G ow h Pac .
Au ho Con ibu ions: Concep ualiza ion, F.G., E.S. and A.B.-G.; me hodology, F.G., E.S. and A.B.-G.;
so wa e, F.G., E.S. and A.B.-G.; alida ion, F.G., E.S. and A.B.-G.; o mal analysis, F.G., E.S. and
A.B.-G.; in es iga ion, F.G., E.S. and A.B.-G.; esou ces, F.G., E.S. and A.B.-G.; da a cu a ion, F.G., E.S.
and A.B.-G.; w i ing—o iginal d a p epa a ion, F.G., E.S. and A.B.-G.; w i ing— e iew and edi ing,
F.G., E.S. and A.B.-G.; isualiza ion, F.G., E.S. and A.B.-G.; supe ision, F.G., E.S. and A.B.-G.; p ojec
adminis a ion, F.G., E.S. and A.B.-G.; unding acquisi ion, E.S. All au ho s ha e ead and ag eed o
he published e sion o he manusc ip .
Funding: Emmanouil So ianos would like o acknowledge ha his wo k is pa o he In e disci-
plina y Thema ic Ins i u e MAKE S o he ITI 2021-2028 p og am o he Uni e si y o S asbou g,
CNRS and INSERM. I has ecei ed inancial suppo om he IdEx Unis a (ANR-10-IDEX-0002),
and om he P og amme In es issemen d’A eni ” as pa o he SFRI-STRAT’US p ojec (s) (ANR-20-
SFRI-0012).
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Economies 2025,13, 186 18 o 23
Da a A ailabili y S a emen : The o iginal da a p esen ed in he s udy a e openly a ailable in Eu os a
a h ps://ec.eu opa.eu/eu os a /web/main/da a/da abase (accessed on 18 June 2025).
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Appendix A
Table A1. Desc ip i e s a is ics (mean, s anda d de ia ion, minimum, and maximum) by coun y
and pe iod.
Mean S d Min Max
Coun y 2000–
2007
2008–
2015
2016–
2023
2000–
2007
2008–
2015
2016–
2023
2000–
2007
2008–
2015
2016–
2023
2000–
2007
2008–
2015
2016–
2023
Ge many 62.86 74.38 65.06 3.36 5.10 3.39 57.60 64.00 58.70 67.30 81.00 70.90
F ance 64.14 87.95 105.92 3.40 9.48 7.14 58.80 67.00 98.10 68.20 98.30 117.60
I aly 108.40 123.29 140.11 2.14 10.41 7.07 103.50 104.40 133.70 112.70 138.10 157.60
Spain 47.91 74.30 107.28 7.06 25.09 7.41 35.70 34.90 97.70 59.70 104.50 124.20
Ne he lands 50.00 60.71 52.31 3.40 6.95 5.14 42.80 43.60 44.40 59.60 68.20 63.40
Sweden 47.94 39.47 37.75 3.98 3.11 3.65 39.20 35.00 30.30 57.40 45.70 43.50
Belgium 103.35 103.84 106.32 7.93 5.92 4.02 87.30 89.70 97.70 117.40 111.00 116.00
Aus ia 70.51 80.38 79.58 2.90 5.87 4.47 65.40 66.70 70.70 76.10 86.10 86.90
Poland 43.72 51.93 51.60 4.18 4.15 3.32 35.70 42.70 45.70 49.10 57.90 58.60
Denma k 46.37 45.08 39.77 8.59 6.60 3.83 29.50 26.40 33.60 58.20 52.60 46.40
G eece 104.31 151.74 187.98 1.89 26.03 12.62 99.90 103.70 167.50 107.80 182.30 215.90
Finland 42.25 52.14 70.33 3.27 11.14 4.13 34.80 30.70 64.80 48.60 68.80 77.10
Po ugal 63.97 110.53 123.52 7.00 22.82 9.26 54.00 71.40 97.90 73.80 134.70 137.50
I eland 30.61 87.54 59.25 5.19 29.28 10.41 23.60 26.40 42.40 45.20 123.10 75.90
Czechia 25.27 37.81 37.72 4.56 5.78 4.24 15.20 26.00 29.60 30.60 44.90 43.50
Hunga y 59.53 77.77 73.27 4.74 4.75 3.91 52.20 64.40 65.00 66.80 83.80 79.70
Romania 19.57 29.33 41.01 4.76 9.61 6.27 11.60 10.50 33.50 25.90 39.10 49.70
C oa ia 38.00 62.80 75.75 2.53 16.33 6.45 31.40 35.60 61.80 41.70 85.20 88.50
Luxembou g 7.58 18.85 23.26 0.40 4.37 2.47 6.80 8.30 19.60 8.30 26.80 28.30
Slo akia 42.15 44.58 54.47 7.58 10.19 4.10 29.60 26.60 48.00 51.70 57.50 60.20
Slo enia 26.58 51.32 75.52 1.32 20.89 5.36 22.90 21.90 66.00 28.60 84.70 85.50
Bulga ia 44.25 17.21 23.67 19.89 4.83 2.86 16.30 12.70 20.00 77.40 28.70 29.30
Li huania 20.41 33.30 38.68 3.21 9.41 3.62 14.60 13.30 32.60 24.50 42.40 45.90
Cyp us 61.16 79.32 98.83 4.14 24.25 11.97 53.10 46.00 73.60 68.10 114.70 117.50
La ia 12.94 38.10 41.77 1.84 11.50 2.86 8.60 10.40 37.70 15.30 48.80 46.50
Es onia 4.97 8.76 13.82 0.62 2.52 4.82 3.60 4.10 8.30 5.80 11.70 20.20
Mal a 65.78 64.60 47.74 3.35 3.60 4.73 60.80 55.00 39.20 71.20 69.70 56.20
Appendix B
Table A2. Iden i y o he dominan nodes (wi h he co esponding ca dinali y o he neighbo hood
hey ep esen ), he isola ed nodes, and he en i ies ha compose he max k-co e subg aph in pe iods
2000–2007, 2008–2015, and 2016–2023 o he 0.7 h eshold le el.
2000–2007 2008–2015 2016–2023
TW-MDS
Dominan
nodes
Neighbo hood
ca dinali y
Dominan
nodes
Neighbo hood
ca dinali y
Dominan
nodes
Neighbo hood
ca dinali y
F ance 6 I aly 21 Ge many 8
I aly 3 Ne he lands 23 F ance 10
Sweden 12 I aly 7
Cyp us 2 Sweden 7
Isola ed nodes Isola ed nodes Isola ed nodes
Aus ia Mal a No isola ed
G eece
Luxembou g
Slo enia
Economies 2025,13, 186 19 o 23
Table A2. Con .
2000–2007 2008–2015 2016–2023
k-co e
decomposi ion
(max k-co e)
Spain
Sweden
Belgium
Denma k
Finland
I eland
Romania
Slo akia
Bulga ia
Li huania
F ance
I aly
Spain
Ne he lands
Belgium
Aus ia
Denma k
G eece
Finland
Po ugal
I eland
Czechia
Romania
C oa ia
Luxembou g
Slo akia
Slo enia
Li huania
Es onia
F ance
Spain
Finland
Czechia
Romania
Luxembou g
Slo akia
La ia
Es onia
Table A3. Iden i y o he dominan nodes (wi h he co esponding ca dinali y o he neighbo hood
hey ep esen ), he isola ed nodes, and he en i ies ha compose he max k-co e subg aph in pe iods
2000–2007, 2008–2015, and 2016–2023 o he 0.8 h eshold le el.
2000–2007 2008–2015 2016–2023
TW-MDS
Dominan
nodes
Neighbo hood
ca dinali y
Dominan
nodes
Neighbo hood
ca dinali y
Dominan
nodes
Neighbo hood
ca dinali y
Ge many 4 Denma k 14 Ge many 6
Spain 10 Slo enia 15 I aly 3
Poland 4 Ne he lands 4
Cyp us 1 Denma k 3
La ia 1 Finland 8
Isola ed nodes Isola ed nodes Isola ed nodes
I aly Mal a No isola ed
Aus ia
G eece
C oa ia
Luxembou g
Slo enia
k-co e
decomposi ion
(max k-co e)
Spain
Sweden
Belgium
Denma k
I eland
Romania
Slo akia
Bulga ia
Li huania
F ance
I aly
Spain
Ne he lands
Belgium
Aus ia
G eece
Finland
Po ugal
Czechia
Romania
C oa ia
Luxembou g
Slo akia
Li huania
Es onia
F ance
Finland
Romania
Luxembou g
Slo akia
La ia
Es onia
Economies 2025,13, 186 20 o 23
Table A4. The highes k-co e o which each EU membe s a e belongs ac oss all h ee ime pe iods,
unde bo h he 0.7 and 0.8 h eshold le els.
2000–2007 2008–2015 2016–2023
coun y
h eshold 0.7 0.8 0.7 0.8 0.7 0.8
highes k-co e
Ge many 4 3 12 6 6 3
F ance 4 3 16 14 7 6
I aly 3 0 16 14 6 2
Spain 9 7 16 14 7 5
Ne he lands 8 6 16 14 5 2
Sweden 9 7 7 3 5 2
Belgium 9 7 16 14 6 3
Aus ia 0 0 16 14 6 3
Poland 4 3 12 7 6 3
Denma k 9 7 16 10 5 3
G eece 0 0 16 14 3 1
Finland 9 6 16 14 7 6
Po ugal 4 3 16 14 5 3
I eland 9 7 16 12 4 2
Czechia 3 1 16 14 7 3
Hunga y 4 3 6 2 6 3
Romania 9 7 16 14 7 6
C oa ia 2 0 16 14 5 3
Luxembou g 0 0 16 14 7 6
Slo akia 9 7 16 14 7 6
Slo enia 0 0 16 13 6 3
Bulga ia 9 7 7 3 5 1
Li huania 9 7 16 14 6 3
Cyp us 2 1 15 13 5 3
La ia 4 1 12 7 7 6
Es onia 8 3 16 14 7 6
Mal a 2 1 0 0 5 3
Appendix C
The igu es below
6
illus a e he ne wo k opology as de i ed om he TW-MDS
echnique, showcasing i s ans o ma ion ac oss he h ee pe iods unde examina ion
(applying a 0.7 h eshold). Nodes in g een highligh he dominan en i ies, while ed
ma ks hose ha emain isola ed. G ay nodes signi y hose ha a e in e connec ed bu no
dominan . All connec ions o a dominan node a e colo ed g een, whe eas links be ween
non-dominan in e connec ed nodes appea in g ay.

Economies 2025,13, 186 21 o 23

Figu e A1. The 2000–2007 EU ne wo k ( h eshold le el o 0.7).
Figu e A2. The 2008–2015 EU ne wo k ( h eshold le el o 0.7).
Economies 2025,13, 186 22 o 23

Figu e A3. The 2016–2023 EU ne wo k ( h eshold le el o 0.7).
No es
1
Ge many’s da a in Eu os a da a base is ma ked as “p” (p o isional, indica ing alues ha a e subjec o e ision) o he pe iod
om 2018Q1 o 2023Q4, while o he Ne he lands, his p o isional s a us applies om 2023Q1 o 2023Q4. Acco ding o Eu os a ’s
e ision calenda , he mos ecen upda e o hese da a was on 22 Ap il 2025.
2
A he s a o he examined pe iod (2000Q1), 15 coun ies we e pa o he Eu opean Union, and 11 o hem had adop ed he
common cu ency.
3
The densi y calcula ion is di ec ly a ec ed by he h eshold le el. Al hough in i s ini ial se up he ne wo k o he cu en s udy is
comple e, a e he h eshold imposi ion on he edge’s alues, se e al edges a e emo ed om he ne wo k. Thus, E coun s he
edges ha su i ed he h esholding s ep.
4Being awa e o he k-co e sub ne wo k s uc u e o any k, i is possible o calcula e he densi y o he subg aph.
5
Fo ins ance, se ing a h eshold o 0.7 allows he su i al o co ela ions anging be ween 0.7 and 1. As a esul , wo nodes con-
nec ed o he dominan node wi h co ela ion alues o 0.71 and 0.99, espec i ely, may o may no sha e common cha ac e is ics
wi h each o he .
6The g aphs we e c ea ed using he Open G aph Viz Pla o m Gephi, Ve sion 0.10.0.
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