High-skilled labor mobility in Europe before and after the 2004 enlargement

Alexander M. Petersena,1 and Michelangelo Puliga1

1Laboratory for the Analysis of Complex Economic Systems,IMT Lucca School for Advanced Studies, Lucca 55100, Italy

The extent to which international high-skilled mobility channels are forming is a question of great importancein an increasingly global knowledge-based economy. Together with underlying globalization trends, the stan-dardization of certifiable degrees meriting international recognition has facilitated the growth of high-skilled la-bor markets. Here we analyze an extensive high-skilled mobility database over the period 1997-2014 comprisingroughly 382,000 individuals from 5 broad professions (Medical, Education, Technical, Science & Engineering,and Business & Legal), using the 13-country expansion of the European Union (EU) to provide insight into theintegration of labor markets. Our analysis comparing the periods before and after the 2004 enlargement, showthe emergence of a new East-West migration channel between the 13 mostly eastern EU entrants (E) and therest of the western European countries (W). From a traditional brain-drain perspective, we indeed observe a netdirectional loss of human capital from E →W , representing 29% of the total mobility after 2004. Nevertheless,over the same period the counter-migration from W → E is 7% of the total mobility, signaling the emergenceof brain circulation within the EU. Our network analysis also identifies the distinct roles of the United Kingdomand Germany: the former being the central mobility hub for the community of western countries, whereas thelatter is the mobility hub for the more eastern countries. As such, our in-depth network analysis of the country-country mobility networks and the country-profession bipartite networks provides timely quantitative evidencefor the integration and convergence of the EU. Moreover, our results also contribute to the ‘Brexit’ debate con-cerning the ramifications of the United Kingdom leaving the EU concerning its access to Europe’s large stocksof high-skilled labor.

Human migration is a topic of increasing interest as dataquality and coverage is increasing in our digital age. The dig-ital traces, arising from a wide range of electronic recordingsof everyday activities provide new avenues to study move-ments over various scales, from microscopic daily mobilitypatterns of individuals [1], to mesoscopic patterns accountingfor socioeconomic factors [2, 3], to macroscopic pattens oflong-term international migration [4–9].

Here we provide a contribution to the macro-scale literatureconcerning cross-border migration, in the particular context ofthe integration of European labor markets. While the growthand evolution of the European Union (EU) has been ongo-ing for decades, only recently has data become available tomeasure the impact of EU “free movement” open-border poli-cies on mobility rates within Europe, between and within theEU member and non-EU members countries. A better under-standing of intra-European migration is key to modeling thesupply and demand for high-skilled labor in European labormarkets, for measuring the distribution of human and intel-lectual capital and its geographic convergence over time, forevaluating European labor market policies.

Europe is among the global leaders in the production ofhigh-skilled labor, in particular scientists. However, develop-ing a competitive labor market that keeps the best talent withinEurope remains a challenge [10]. This is particularly prob-lematic, as mounting empirical evidence indicates that localeconomic spillovers are generated by the regional agglomera-tion of activities – both in innovation-driven industries as wellas other service industries that follow high-tech [11]. Thus, inorder to establish and maintain international competitiveness

[a] Send correspondence to: petersen.xander@gmail.com

[12], the retention and subsequent leveraging of human intel-lectual capital is of fundamental importance for knowledge-based economies.

Traditionally, the analysis of high-skilled labor mobility hasfocused on zero-sum perspectives – i.e. brain-drain versusbrain-gain [13–18]. Here we proceed with European unityas our broad focus by measuring the emergence of Europeanbrain circulation – a dynamic cross-border configuration withlong-term benefits for individuals and institutions across Eu-rope [19].

One of the resounding achievements of the European Union(EU) is the freedom of movement between member states.Aside from being convenient for European and internationaltravelers alike, open borders are the starting point for com-petitive labor markets, providing access to a wealth of careeropportunities for jobseekers across the EU. As such, cross-border activity, in particular the mobility of high-skilled labor,is an especially insightful indicator of European unity.

Scientists are likely aware of the long-standing tradition ofEuropean initiatives aimed at fostering both cross-border mo-bility (e.g. Marie Curie actions which fund short-term re-search fellowships) and cross-border activity (e.g. the Eu-ropean Cooperation in Science and Technology (COST) pro-gram which provides funding to gather researchers across Eu-rope for short-term conferences, schools, and missions).

Moreover, in order to improve the openness and compet-itiveness of the entire high-skilled labor market, the EU hasalso implemented the “Free movement of professionals” pro-gram, which provides individuals the opportunity to have theirprofessional credentials certified in other EU countries. In thisway, open borders have made an impact far beyond academia,affecting hundreds of thousands of career-minded individualsfrom a wide range of professions – from teachers, to doctors,lawyers, architects, electricians, and so on.

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FIG. 1: High-skilled mobility – by profession and geographic region – before and after the 2004 EU expansion. (a) Rank-distribution ofthe top-100 high-skilled professions over the entire period of analysis, 1997–2014. The color of each datapoint corresponds to its classificationwithin the 5 broad profession groups. Dividing any given value by the total number of observations (381,757) gives the frequency, i.e. thetop two professions are “Doctor of Medicine” and “Nurse,” accounting for 20% and 17% of the total observations, respectively. The top-100professions shown account for 97% of the total observations. (b) Distribution of the observations by profession group – before and afterthe 2004 EU expansion. Totals within each profession group and within each period are shown. (c) Comparison of the mobility within andbetween Eastern and Western Europe before (inner ring) and after (outer ring) the 2004 EU expansion. Listed in the center of each ring chartare the total mobility before (top) and after (bottom) 2004. (d). Disaggregation of the East-West mobility flow by year and profession group.Note that the y-axis is shown on logarithmic scale.

Recent studies [20, 21] have addressed the motivations andprogress towards the development of a unified R&D innova-tion system in Europe [22–24] using intra-European networksof collaboration and mobility as the unit of analysis. Herewe contribute to this research stream by performing a large-

scale analysis of the dyadic (country-country) and bipartite(country-profession) mobility networks for Europe over theperiod 1997-2014.

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FIG. 2: High-skilled mobility network: 2005–2014. Each country is represented on the circumference with an arc-length that is proportionalto the total incoming and outgoing mobility of each country after the 2004 EU enlargement. The mobility of each country can be summarizedby 3 histograms shown: the outer-most arc represents the total distribution of mobility by all partner countries, the middle arc represents thedistribution of incoming mobility by source country, and the inner arc represents the distribution of outgoing mobility by destination country.For example, roughly 80% of mobility for UK is incoming; of the remaining 20% of outgoing mobility, almost 10% is going to IE. Shown areonly the links representing more than 1% of the total flow into or out of a given country; the links shown account for 93% of the total mobility.

Data & Methods

We analyzed extensive records from the official EU Com-mission “Professionals moving abroad (Establishment)” pro-gram as documented in “The EU Single Market Regulatedprofessionals” database [25]. More specifically, this databaseaggregates records for (high-skilled) professionals who ap-plied for official recognition of their professional certifica-tion in a particular host country (destination country) froma given country of qualification (source country). 32 Eu-ropean countries are included in the database over the 18-year period 1997-2014: Austria (AT), Belgium (BE), Bul-garia (BG∗∗), Croatia (HR∗∗∗), Cyprus (CY∗), Czech Repub-lic (CZ∗), Denmark (DK), Estonia (EE∗), Finland (FI), France

(FR), Germany (DE), Greece (GR), Hungary (HU∗), Iceland(IS), Ireland (IE), Italy (IT), Latvia (LV∗), Liechtenstein (LI),Lithuania (LT∗), Luxembourg (LU), Malta (MT∗), Nether-lands (NL), Norway (NO), Poland (PL∗), Portugal (PT), Ro-mania (RO∗∗), Slovakia (SK∗), Slovenia (SI∗), Spain (ES),Sweden (SE), Switzerland (CH), United Kingdom (UK). Theasterisks indicate the entry year for the new EU memberstates: ∗2004,∗∗2007, ∗∗∗2013. The three countries that arenot members of the EU are CH, IS, and NO, however theyeach maintain close economic agreements; for Iceland andNorway through the European Economic Area (EEA), Euro-pean Free Trade Association (EFTA) agreements, and bothhave accepted the Schengen Agreement affording “Free ofMovement of Persons” to EU member citizens.

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The database covers a variety of certification “Recogni-tion Regime” categories (e.g. the top-5 mobile professionsfrom 1997–2014 are “Doctor of Medicine” (Nobs = 75, 567),“Nurse” (Nobs = 64, 945), “Secondary school teacher”(Nobs = 43, 479),“Physiotherapist” (Nobs = 18, 184), “Sec-ond level nurse” (Nobs = 13, 949); the number of observa-tions are provided in the parenthesis). We categorized theprofessions into 5 groups: Medical, Education, Technical,Science & Engineering and Business & Legal. Figure 1(a,b)show the frequency of each profession and profession groupin our dataset, which is dominated by the Medical and Educa-tion profession groups.

The EU data are grouped into 13 periods indexed hereby t = 1...13 corresponding to 1997/1998, 1999/2000,2001/2002, 2003/2004, 2005/2006, 2007, 2008, 2009, 2010,2011, 2012, 2013, 2014. For each period indexed by t werecorded Mij,t, the total number of high-skilled migrations(“Total positive decisions”) from country i (“Country of qual-ification”) to country j (“Host country”). In in addition toanalyzing the annual mobility matrices Mij,t, we also aggre-gated the final 9 periods in order to study the net mobility pat-terns after the 2004 expansion. In all, the total mobility (headcounts) for a given aggregate time period Mt =

∑ij Mij,t/2

are 381,757 (1997–2014), 43,010 (1997–2004), and 338,747(2005–2014). In all, comparing the period before and after2004, these numbers indicate a 530% increase in the per-yearmobility of high-skilled labor in Europe. Figure 2 provides avisualization of the mobility network after the 2004 enlarge-ment, with substantial cross-linking in all directions indicatingthe substantial progress towards European labor-market inte-gration.

ResultsRegional brain-circulation by profession group. This intra-EU mobility data provides a wealth of new insights into the re-organization of high-skilled labor following the 2004 EU en-largement. In addition to a sharp increase in the total amountof high-skilled mobility, the 2004 EU expansion facilitateda new mode of high-skilled mobility: East to West (E→W)and West to East (W→E). Here we define “East” as the groupof thirteen 2004/2007/2013 EU entrant countries, and “West”as the complementary set of European countries (includingcurrent non-EU members NO, IS and CH). While the withinregion mobility E→E and W→W was dominant before 2004,after the expansion, 29% of the total mobility was from E→Wand 6.8% was from W→E. Figure 1(c) shows the breakdownof mobility within and across East-West borders, before andafter the 2004 expansion and by profession group. Interest-ingly, within the Education, Sci&Eng, and Business & Legalprofession groups, there was a substantial W→E mobility af-ter 2004.

Figure 1(d) shows the dynamics of the intra- and inter-regional mobility flow. The juxtaposition of the Medicalprofession and the Sci&Eng profession illustrates the non-uniform patterns of mobility. While in the Medical professionthe E→W mode has stabilized since 2004 around 30% of

the net flow, for Sci&Eng this mode has actually decreasedsince 2004, from around 26% to roughly 6%. Interestingly,for Sci&Eng there has been a significant shift of mobilitytowards the E→E mode. The Education profession groupalso mimics this pattern, although less substantially. Overall,the Medical, Technical, and Business&Legal exhibit commondynamic patterns, with the E→W mode being substantial,while Education and Sci&Eng form a second group whereinE→E has been growing over time.

Relative comparative advantage in the import/export ofhigh-skilled labor. In order to measure each country’s rela-tive strength as an exporter and importer of high-skilled laborby profession group, we calculated the revealed comparativeadvantage (RCA) [26, 27]. Here the scalar quantity RCAi,p

measures to what extent the share of the total export (imports)by country i of profession group p is above or below the globalshare of the same profession.

First some basic definitions. At the aggregate country levelthe total incoming and outgoing mobility, Ii,t =

∑j,t|iMji,t

and Oi,t =∑

j,t|iMij,t, are net measures of ‘brain drain’and ‘brain gain’, respectively. The relative brain drain is thengiven by Bi,t = (Oi,t − Ii,t)/(Oi,t + Ii,t) ∈ [−1, 1].

Using these conventions, it is then straightforward to calcu-late each RCAi,p as

RCAouti,p =

(Oi,p/Oi)

(Op/Ototal)and RCAin

i,p =(Ii,p/Ii)

(Ip/Itotal). (1)

In other words, for exported mobility, the within-countryshare is given by (Oi,p/Oi), and this share is normal-ized by the net share of mobility in p across all countries,(Op/Ototal). As such, the threshold for being above or be-low the global baseline is RCAi,p = 1 . By definition, thenet export and import shares by profession group are equal,Sp ≡ (Op/Ototal) = (Ip/Itotal).

Figure 3(a) shows Sp separated into three sub-periods:the pre-enlargement period 1997–2004, the pre-crisis period2005-2007 and the post–crisis period 2008–2014. Figure 3(b)shows the export and import RCAi,p for these same three sub-periods. Since RCAi,p is principally a within-country com-parisons, by construction a country can have a relatively largeRCAi,p in at most just one or two different p. Whereas, con-versely, it is possible that several countries have large RCAi,p

for the same p group.By way of example, Poland (PO) appears as significant

exporter of Technical professions and Spain (ES) a significantexporter of Education and a significant importer of Sci&Engin each sub-period. Germany (DE) is closer to baselinelevels in all categories during each sub-period. The principalexport profession for the United Kingdom (UK) is Business& Legal, with Education being its principal import profession.

Between-country migration and brain drain. The dyadiccountry-to-country brain-drain relations provide insight intothe high-skilled export and import capacity of each country aswell as the role of topology in the mobility network. In gen-eral, the network Mij,t is defined by aggregating the mobility

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FIG. 3: Comparative importers and exporters of high-skilled labor. (a) High-skilled mobility: before 2004, and in the periods before andafter the 2007 global financial crisis – by profession group. (b) Revealed comparative advantage (RCA) by country and profession. Blacksquares indicate countries with 0 counts for the specified time period. The color scale splits the range of values into 7 groups: six groups ofwidth 0.5 and one group for those extreme values for which RCAi,p > 3. Thus, blue values can be considered as significantly below andmaroon/borwn/purple/yellow/red values can be considered significantly above the baseline RCAi,p = 1 value.

data over an arbitrary time interval indexed by t and a givenprofession group. The absolute difference in the mobility be-tween two countries is given by ∆ij,t ≡ |Mij,t −Mji,t| fora given t. Figure 4 shows the mobility matrices for all theprofession groups after the 2004 enlargement.Bi,t measures the mobility polarization, with minimum

value Bi,t = −1 corresponding to entirely incoming mobilityand maximum value Bi,t = 1 corresponding to entirely out-going mobility. Figure 4 shows the mobility matrices,Oi,t,Ii,tand Bi,t for each country and profession. Bi,t is useful asa relative measure to compare countries with total mobilityrates that differ across several orders of magnitude. For con-sistency, we ordered the countries in each mobility matrix andbar chart in decreasing order of Bi,t calculated over the entireperiod 1997–2014.

In all, the countries with the largest mobility in, i.e. “brain-gain” corresponding to the columns of the Mij,t in Fig. 4(a)with the largest total counts – are DE, BE, UK, CH, and NO.Similarly, the countries with the largest mobility out – “brain

drain” (corresponding to the rows of the Mij,t in Fig. 4(a)with the largest total counts – RO, PL, GR, ES, SE, and DE.Thus, while UK is mainly a brain-gain hub, primarily forthe western European countries, DE is both a brain-gain anda brain-drain hub, primarily for the eastern European coun-tries. Bi,t measures the relative difference between the braindrain and the brain gain, indicating that the countries with thelargest net flow out are LT, EE, RO, and BG, whereas thecountries with the largest net flow in are UK, CH, LU, NO,and CY. Interestingly, CY exceeded in net brain-grain (mainlyfrom GR). One possible explanation, especially for the Busi-ness & Legal professions, is Cyprus’ history of liberal tax lawswhich made it an attractive relocation destination.

By profession the patterns vary, with the Medical profes-sions dominating in pure counts and the least sparse mobilitymatrix. The UK dominates most mobility matrices in termsof the largest incoming mobility as well as the broadest dis-tribution of source countries, except for in case of Technicalprofessions. Instead, for Technical professions, the countries

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FIG. 4: High-skilled mobility matrices separated by profession group. (a) Shown are the mobility matrices representing net headcountfrom row country i to column country j over the period 2005-2014. The aggregated matrix (“All”) is the total across all 5 profession classes.The color scale for each matrix visualization represents a partitioning of the log10 Mij matrix entries into sextiles to facilitate visual inspectionand for identifying the strongest dyadic flows. Below each matrix we also show for each country the total outgoing mobility Oi (red bars), totalincoming mobility Ii (green bars), and relative brain-drain Bi = (Oi−Ii)/(Oi+IiFigs). (b) Matrix showing the Pearson correlation betweeneach of the profession-specific mobility matrices shown in (a); correlation calculated between logarithmically scaled matrices, log10(1+Mij,t);correlation values are shown in the corresponding lower triangular cells.

with the largest brain-gain are DK, BE, and NO.

In order to provide a quantitative comparison by profes-sions, Fig. 4b shows a matrix with entries representing thePearson cross-correlation coefficient value calculated betweenany given pair of mobility matrices. Interestingly, we findthat Sci. & Eng. is the least-correlated profession, possiblya result of directed EU R&D policies aimed at establishingan integrated European innovation system [20, 22–24]. TheMedical and Education mobility matrices are the most highlycorrelated (Pearson correlation = 0.82).

Figure 5 provides a visualization of the country-professionbipartite networks, bringing together the information con-tained in Fig. 4, in particular showing the distribution of the

net flows by country and profession along the arc histograms.For example, in panel (b) a link connecting country i toprofession p (net outgoing) indicates that the country hadmore outgoing than incoming mobility in that profession –the link width represents the net difference. Conversely, a linkconnecting country i to profession p (net incoming) indicatesthat the country had more incoming than outgoing mobilityin that profession. UK has the largest brain-gain (of Medicalprofessionals) and DE and RO have the largest brain-drain(also of Medical professionals). PL shows a relatively largebrain-drain in Medical, Education, and Technical professionsand a small brain-gain in Science & Engineering professions.

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FIG. 5: High-skilled mobility by country and profession. (a) Bi-partite projection of the network between country mobility and professiontype following the 2004 EU enlargement (2005-2014). Each link shows the total amount of mobility by country i in profession p. Outerrings show the distribution of the total mobility, either by country or by profession; because this is a bipartite projection both outer ringsare redundant. (b) Brain-drain and brain-gain by country and profession. Bi-partite projection of the brain-drain network illustrating the netincoming or outgoing mobility by country for each profession for the period 2005-2014. Outer ring show the distribution across the total netflow, either by country or by profession; because this is a bipartite projection both outer rings are redundant. Countries are ordered accordingto 2004 EU membership status.

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FIG. 6: Converging integration of the European high-skilled mo-bility network. (a) Centrality time series’ (ci,t) for the incumbentEU members in 2004. (b) ci,t for the European countries that werenot EU members in 2004. (c) A select group of ci,t for countriestypically associated with brain drain (solid) and brain gain (dashed).For visual comparison, each panel includes a horizontal dashed linecorresponding to the uniform baseline c = 1/32 = 0.03125. Panels(a) and (b) also include the average ct (thick grey curve) calculatedacross the countries in each panel, respectively. Note that the y-axesis plotted on logarithmic scale. (d) Scatter plot of the PageRankcentrality of each country representing each country’s relative im-portance within the network, which we calculated using a standardalgorithm for weighted networks applied to the pre- and post-2004mobility networks. Points above (below) the diagonal dashed lineindicate that the country’s centrality increased (decreased) betweenthe two periods. We use a baseline (mean) centrality value equal to 1,as indicated by the dashed orange horizontal and vertical lines; dataplotted using logarithmic axes.

Evolution of the mobility network: 1997–2004. In order toinvestigate the relative importance of the 32 European coun-tries within the high-skilled mobility network, we applied theGoogle PageRank algorithm [28] using a variant modified forweighed networks. The algorithm takes as input the mobilitynetwork Mij,t in period t and produces a centrality measureci,t for each country, with normalization

∑i ci,t = 1 for a

given t.

This algorithm, among others, is well-suited to measure therelative importance, or “centrality”, of each country withinthe mobility network comprised of individuals migrating fromcountry to country. In short, this algorithm measures the like-lihood that a synthetic migrant (“random walker” ) traversingthe network would be found at country i, where the transitionprobabilities between countries (nodes) are proportional to theempirical Mij,t. Thus, the PageRank algorithm also incorpo-rates the direction of the network links into the calculation ofci,t, which is important here due to the emergence of the newwest to east mobility channels after 2004.

The baseline centrality value corresponding to a uniformnetwork where Mij = constant for all ij, is ci = 1/|M | =1/32 = 0.03125, where |M | is the number of countries (i.e.dimension of the mobility matrix). Note that the data plot-ted in Fig. 6d are normalized by 1/|M | so that their baselinecentrality value is equal to 1.

Figure 6 shows the evolution of each ci,t over time, includ-ing the average within the set of 2004 countries that were al-ready EU members, and the complementary set of non-EUcountries. Indeed, comparison of the average values – cEU,t

in Fig. 6(a) and cnonEU,t in Fig. 6(b) – signals the con-vergence of the EU high-skilled mobility network towards amore uniform network. Figure 6(c) shows the evolution ofci,t for three countries typically associated with brain gain –the United Kingdom, Germany, and Switzerland – and 4 newEU entrant countries associated with brain drain – Bulgaria,Romania, Greece, and Poland.

Interestingly, we find that UK and DE play dominant rolesin the high-skilled mobility network – with UK serving as thehub for the northern European countries and DE serving asthe hub for the eastern European entrants. Interestingly, thecentrality of Switzerland (CH) has also significantly increasedover the entire period, starting from nearly zero to reaching thebaseline value in 2003, demonstrating the positive externali-ties of the 2004 expansion.

By in large, the countries that were not in the EU in 2004have quickly become more prominent within the mobility net-work, with RO, GR, and PL all fluctuating around the base-line centrality level since 2007. A basic question is howlong until all countries have approximately the same central-ity? The decline in the standard deviation σt(c) over the 10year periods before and after 2004 (σbefore[c] = 0.0353 andσafter[c] = 0.0259) can be used to estimate a lower-bound forthe time to converge to σ∞ ≈ 0. Using a back-of-the-envelopeapproach, our estimation is convergence of centrality on theorder of σafter[c]/(σbefore[c]− σafter[c])× 10y ≈ 3 decades.

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DiscussionBrain-circulation by the numbers. In order to provide newinsights into the integration of high-skilled labor markets inEurope, we analyzed the “The EU Single Market Regulatedprofessionals” database, which tracks applications and out-comes for cross-border certifications across a wide spectrumof 390 high-skilled professions across 32 European countries.

The EU has expanded by 13 countries since 2004. Inthe meantime, roughly 338,000 Europeans have taken theirfirst migration step by receiving official cross-border certifi-cation of their professional credentials. Even following the2007/2008 global financial crisis there was no slowdown, withcross-border mobility averaging around 44,000 professionalsper year.

Figure 2 puts the big picture in perspective – that invest-ment in cross-cutting human and social capital is investmenttowards an integrated Europe. The links that extend in all di-rections capture the diversity of pathways between countries.Indeed, upon closer inspection, the mobility network pointsto the complex history of EU integration characterized by thedichotomy between brain-drain and integration.

On the one hand, there has been a drastic net flow fromthe new entrants (“eastern“) to the older incumbent EU mem-bers (“western”) following the 2004 expansion (see Fig. 1).Roughly 29% of the total mobility was from east to west overthis period, a percentage which has varied over time and byprofession. Meanwhile only 6.8% of the mobility was fromwest to east.

Despite this disparity in the east-west flow, it is importantto consider that both of these mobility channels were nearlynon-existent prior to 2004. That is, optimistically speaking,it is important to appreciate these new east-west channels asthe initial phase of the integration process towards uniformbrain-circulation levels.

We also categorized the mobility data into 5 broad pro-fession groups: Medical, Education, Technical, Science &Engineering, Business & Legal. Notably, the trend in thewest-to-east mobility channel is increasing for the Education,Science & Engineering, and Technical professions. Analysisof the data by profession also indicates which countries arerelatively competitive as importers and/or exporters of eachtype of high-skilled labor. For example, since 2008 many ofthe new entrants have shown a relatively high comparativeadvantage in the importing of Science & Engineering profes-sionals.

Convergence towards integration of high-skilled mobility.Two important questions are – by what means and to what ex-tent are Europe’s high-skilled labor markets unifying. To thisend, we calculated the ‘importance’ of each country withinthe mobility network using the Google PageRank algorithm,which estimates the likelihood that a hypothetical individ-ual, who randomly traverses the weighted network shown inFig. 2, might be at any given node (see the SI for further de-tails).

Not surprisingly, Germany (DE) and the United Kingdom(UK) are the most central countries. However, by analyzing

the topology of the network we find that these two countriesplays distinct roles: DE is a gateway hub for the more east-ern countries, whereas the UK is a gateway hub for the morewestern countries. Germany, however, shows more outgoingmobility than incoming, a possible sign of emerging home-migration channels.

With the emergence of west-to-east mobility channelsfollowing the 2004 enlargement, the eastern countries areslowly gaining centrality within the network. The extent towhich convergence towards a more unified labor market isbeing achieved is shown in Figure 6, which compares thecentrality measures before and after the 2004 enlargement.Running diagonal is an equivalence line which separatesthose countries that increased from those that decreasedover the sample period. Indeed, the oldest EU membersare mostly below the diagonal equivalence line (decreasingcentrality), whereas the new EU members are above thediagonal equivalence line (increasing centrality). In essence,there is good reason to be optimistic about the convergenceof EU high-skilled labor markets, largely because of thereturn-migration pathways that have emerged which leadaway from the larger high-skilled mobility hubs, back in thedirection of the southern and eastern countries historicallysuffering from the most brain drain.

Investing in brain-circulation. Knowledge economies willbe increasingly concentrated within high-skilled innovationhubs [11]. As such, it will be important to keep in mindthe long-term impact of creating and promoting opportunitiesfor professionals to leave and return to their home countryor region. Indeed, recent evidence indicates that brain draincan have positive effects, such as higher propensity for work-ers in the source country to invest in educational and posi-tive network externalities on trade and technological adoption[10, 13, 16, 29].

In order to foster long-term knowledge and social capitalinvestment within and across its borders, towards the ultimategoal of developing an efficient and competitive European in-novation system [24, 29], the EU should should continue todevelop policies that create beneficial conditions for brain cir-culation, including home-return [30, 31]. Ongoing effortsinclude the ‘europass’ system, an interoperable system forstreamlining and standardizing the intra-EU job-applicationprocess, as well as the ‘blue card’ program aimed at stimulat-ing opportunities on the international labor market.

The attractiveness of home-return could be improved by fo-cusing on work environment conditions and short-term eco-nomic incentives, such as tax waivers and prioritized jobplacement for returnees, so that the incentives to leave andreturn home are more symmetric. Indeed, recent survey ofmigrant research scientists indicates that issues relevant to sci-ence policy are the main factors considered when deciding toleave home, but that family and quality-of-life factors play thestrongest role in deciding to return home [19].

Finally, high-skilled mobility deserves discussion withinthe ‘Brexit’ debate. In addition to testing the reversibility ofEU membership, the 06/23/2016 UK referendum also bringsforth the possibility that one of the largest economic and po-

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litical units will split. Economists and policy makers havelargely warned about the impact on trade between and amongEU and non-EU countries, likely requiring a time-consumingand therefore costly renegotiation process.

While the implications of Brexit on international trade hasgained much attention, here we addressed a particularly im-portant although less-prominent facet – the import and exportof high-skilled labor in Europe. It is important that UK policymakers consider the privileges associated with being part of aunified labor market, in particular its access to large stocks ofhigh-skilled laborers who make considerable contributions tothe local economy.

Most importantly, mobile professionals are the basis forcross-border links that are crucial for cross-border knowledgetransfer and unity within Europe.

Acknowledgements We thank the developers of the open-source Circos circular network layout software [32] whichwe used to produce the network visualizations; we also thankPaolo Zacchia, Omar Doria, and Fabio Pammolli for helpfuldiscussions, and for the EU open data portal for providing ac-cess to the data. The authors also acknowledge support fromthe National Research Program of Italy (PNR) project “CRI-SIS Lab”.

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