THE MULTIPOLAR REGIONALIZATION OF CITIES IN …

Rozenblat,C.,Zaidi,F.,&Bellwald,A.(2017).Themultipolarregionalizationofcitiesinmultinationalfirms'networks.GlobalNetworks,17(2),171-194.

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THEMULTIPOLARREGIONALIZATIONOFCITIESINMULTINATIONALFIRMS’NETWORKS

Prof.CélineRozenblat,UniversityofLausanne,[email protected],UniversityofLausanne,[email protected],UniversityofLausanne,[email protected]

Thispaper identifies themost cohesivemulti-polar regionsof thenetworkofworld cities,whichdiffer

fromtheunipolarcenter-peripherymodellargelycreatedbythehighweightofcentralcityconnections.

Thepaperimplementsacommunitydetectionalgorithmthatoutlinesthehighdensitiesofcitynetworks

(inrelativeweights).Variouspatternsof industriesandservices,whicharedivided intotwoskill levels,

areidentified.Weuseaglobaldatabaseofthenetworkof1.2milliondirectandindirectownershiplinks

between the 800,000 subsidiaries of the top 3,000multinational groups in 2013, allowing build four

comparable networks of 503metropolitan areas. Comparing the obtained partitionswith continental,

regionalandeconomicbenchmarks,classesofcitiespartiallycorrespondtoFreeTradeZones(FTZ)but

exhibit interesting cross-continental patterns. A few cities, changing their classes according to the

activities,arediscussedinlightofthemultinationalfirms’strategies.

KEYWORDS

MULTINATIONALFIRMS,WORLDCITIESNETWORKS,COMPLEXSYSTEMS,CLUSTERING

INTRODUCTION

In amulti-scaled geographic system, intense economic specialization creates groupsof cities that are

becoming increasingly interrelated despite the distance between them. In particular, financial

specialization has generated the “global city” of New York, London and Tokyo (Sassen, 1991). It is

posited that other cities are connected to this central city system in a core/periphery pattern

(Friedmann,1986;Taylor,2001;Brownetal.,2010),creatingaregionalizationoflargezonessuchasthe

USA,theAsia-Pacificregion,Euro-GermanyandtheOldCommonwealth(Tayloretal,2002).Thus,the

network of global cities is a complex combination of global centrality and regionalization. However,

previousanalysesoftheregionalizationofworldcitiesworkedfromastrongaprioriassumptionofthe

existenceofaunipolarsystemofcitiesinglobalization(Tayloretal.,2002,2013;Derudderetal.,2003;

Alderson&Beckfield,2004;Aldersonetal.,2010).Thus,regionalpatternsoperatinginparalleltoglobal

centralitymaybeunder-evaluated.

Weassumethatthenetworkdensityofsomecommunitiesofcitiesreinforcesthepowerofthehighest

“world cities” that constitute multi-poles, bridging their internal communities through globalization.

Free Trade Zones (FTZ) may structure these cohesions, but other geographic associations may also


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matter to the organization of global economic linkages (Dicken, 2011; Pomfret, 2007; Rugman et al.

2012). Identifying the uneven geographical scales of these cities’ communities and verifyingwhether

theyvaryaccordingtotheirskilllevels(forindustryandservice)mustbeundertaken.

We propose to identify dense networks of cities at the world scale through a large sample of

multinationalfirms’networksthatincludealltypesofactivities.Wefocusonthenetworkpropertiesof

these communities,whichwill be distinguished in different levels of skills for services and industries.

The unipolar/multipolar organization is first discussed in relation to the regionalization of the global

integration of cities (section 1); The hypotheses and clustering methods are then proposed to be

implementedonaglobaldatabaseofnetworksofmultinationalfirmsincities(section2).Weevaluate

thesecities’ similaritieswithregionalbenchmarksandtheirmutualdifferences,underliningcities that

changetheirclassesaccordingtothedifferentactivities(section3)andwediscusstheresults(section

4).

1.REGIONALIZATIONOFCITIESBYMULTINATIONALFIRMS

Previousstudiesoftenbeginwithaclassificationofcitiesaccordingtotheirroles inmultinationalfirm

networks (Taylor et al., 2002, 2013; Derudder et al., 2003; Alderson & Beckfield, 2004). These roles

differ a great deal according to the sample of activities taken into account (1.1). The combination of

regionalizationandthehierarchyofcitiesleadtoareflectionontheplaceoftheunipolarconceptinthe

regionalvisionoftheworld(1.2).Fromamethodologicalperspective,theunderlyingprotocolsbehind

theclusteringmethodswillorientthechoiceofnetworkclassificationthatweimplementinthispaper

(1.3).

1.1 Multipleglobalizations

ThesystemofcontrolbetweencitiesdescribedbySassen(1991)stressesahighspatialconcentrationof

financialandspecializedservices insomecitiesfororganizingindustrialandservicemanagement.This

development, coupled with the emergence of new corporate financial networks, leads to a vertical

disintegration (Storper, 1997) and increases the complexity ofmultinational firms’ networks (Powell,

1990).Firmscoordinatetheirworldwideactivitiesina“globalvaluechain”accordingtothecomplexity

leveloftransactions(i.e.,theabilitytocodifythem)(Gereffietal.,2005).

Thus, multinational companies represent “networks within networks” (Dicken, 2011, p. 121) that

interactwithspatialpreferences,mixingnational,regionalandurbanspecializationsinthedevelopment

of their evolving “global production network” (Yeung, 2005; Coe et al., 2008; Dicken, 2011).

Multinationalfirmsdevelopsectorialactivitiesandarticulatefinancialandindustrialactivities,aswellas

differentlevelsofintensiveknowledge.Krätke(2014)identifiedadistinctiveworldwideorganizationof

multinational firms’ networks for one service sector and two industrial sectors, highlighting themain


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urbanspecializationsandshowingthat“worldcities”arethemostdiversified.Fromthisperspective,we

consider that different groups of cities emerge according to levels of skill and industry/services

distinctions,revealingdifferentspatialstrategiesof ‘multipleglobalizations’(Krätke,2014,p.125)that

firmsarticulate.

1.2Regionalizationorunipolarorganizationofworldcities?

Studies on the economic regionalization of the world began with the vision of domination between

countries.Myrdal(1957)andWallerstein(1974)statedthattheworldcanbeclassifiedintothreemain

zones as follows: the center, the semi-periphery and the periphery (Chase-Dunn, Rubinson, 1977;

Sanderson,2005).Hymer(1972)suggestedthatthepatternofregionalizationamongcitiesisconsistent

with this hierarchy of countries, and Alderson & Beckfield (2004) demonstrated this to be true. In

contrast,Friedmann (1986)andSassen (1991)assumedthataglobalnetworkofcitieswouldstrongly

differ fromthesystemformedbycountries,generatingadistinctiveurbansystembuilt intothe“new

internationaldivisionoflabor”.Thissystemiscomposedofa“complexspatialhierarchy”thatintegrates

both“hierarchicalandregionaltendencies”(Derudderetal.,2003;Liuetal.,2012;Tayloretal.,2013).

Hierarchy is herein conceived as a unipolar organization around the most central world cities. The

comparisonthatWalletal.(2011)madebetweentheassumptionsofAlderson&BeckfieldandTayloret

al., demonstrates thedifficulty in distinguishing theunipolarworld froma regionalization thatwould

underlinemulti-polarregionsinthesecities’complexnetworks.

1.3Clusteringmethodsandidentificationofmulti-polarregionalization

Previousapproachesappliedtoworldcitiesinmultinationalfirms’networksoftenincludetheunipolar

concept introduced at three levels of the analysis: in the data, in the methodology and in the

interpretation. For the data, the construction of the Globalization and World Cities group (GaWC)

networks,whichisbasedona[firmsXcities]matrix,buildsregionalizationonthespatialoverlapsofthe

expansions of various firms (Taylor, 2001; Neal, 2012). When clustering based on cliquishness was

applied, all strongly connected cities were present in every clique (Derruder & Taylor, 2005), which

underlines their unipolar centrality in the world cities system. From a methodological perspective,

Alderson & Beckfield (2004) used block modeling, taking into account the structural equivalence

between“levelsofcities”,andcomparedthesemembershipblocksofcitieswiththecentralityoftheir

countries (according to Bollen & Appold [1993]), which verified the core-periphery organization. The

unipolaroutputsofthesetwoapproacheslargelyresultfromtheweightofthestronglyconnectedcities

thatare, in fact,more likelytobe linkedtonumerouscitiesandtocreateauniquecentralpole.Neal

(2013) identified thisbias in theGaWC data,proposinga “randomsortingprocess” that removes the

masseffects.


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TheComplexSystemSciences(CSS)clusteringmethodsdevelopedclassificationsofnetworksaccording

tolocaldensitiesforming“communities”or“clusters”(Girvan&Newman,2002;Fortunato,2009;Sathik

etal.,2011).Communitydetectionmethods,whichareappliedonweightednetworks,standardizethe

calculationbytheedgeweights(Newman,2004).Thesemethodshavealreadybeenappliedtoairplane

flows connections, revealing regionalization patterns of cities thatwere consistentwith those of the

main continents (Guimeraet al., 2005; Rozenblatet al., 2013).Neal (2014), using theCSSmethodof

Louvain clustering (Blondel et al., 2008), compared the various clusterings of US cities’ air traffic

networks, finding continuous regions of cities in North America. Every application for airline traffic

outputproducescleargeographicalregionsratherthanacore-peripherypattern.Thiscanbeexplained

bythetwowellknownmainfactorsformingthesenetworks:weightofcitiesandgeographicdistances,

which together forma gravitationalmodel that iswell-known in geography (Ravenstein, 1885; Reilly,

1931) and was recently rediscovered by physicists for social phenomena (Barthelemy, 2011). In CSS

methodsstandardizingtheweightsofcities,distancemattersmoreandunderlinesregionalaspectsof

thesenetworkorganizations.

Because the world cities’ system of multinational firm networks also partially integrates some

gravitationalproperties (Walletal.,2011;Rozenblat,2015),weassumethatapplyingtheseclustering

methodstothisnetworkwouldunderlinetheregionalaspectsofworldcities.Wecanassumefurther

thattheresultingclusterswouldvaryaccordingtotypeofactivityandwouldbeclosertogeographical

delineationforunskilledactivitiesthanforskilledactivitiesthataremoreglobalizedthroughspecialized

internationalcities.

Moreover,theconcentrationofinternallinksortheconcentrationofexternallinksinsidetheclusterin

some nodes reveals internal hierarchies (Guimera et al., 2005) that outline the polarization of the

clusters following the classical definition of “polarized region” as opposed to “homogeneous region”

(Friedmann,1967),althoughtheterm“polarization”hasothermeaningsofoppositionbetweensocial

groups(Esteban&Ray,1994)orforthediversityofnodes’connections(VanNuffeletal.,2010).

Clusters also include uneven levels of openness that are often globally evaluated at the scale of the

graph, with the clustering index (Watts, Strogatz, 1998) and at the scale of the nodes with the

participationindex(Guimeraetal.,2005).Attheclusterlevel,Melançon&Rozenblat(2013)introduced

thecloseness index (shareofacluster’s internal linkages that remain internal),whichdiffers fromthe

closenesscentralitymeasuredatthelevelofthenodes(Beauchamp,1965).

Thus,thepolarizationandclosenessindicesrevealtwocomplementaryaspectsofclustersthatarenot

directly linked: the concentration of outreach linkages in one city (Polarization) and the internal

cohesion of the cities in each cluster (closeness). However, one can assume that the polarization of

clusterscanbecorrelatedwiththeirclosenessduetothedominationofonecity.


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2Methodologicalpremisesunderliningthemulti-polarregionalizationofworldcities

The network approach will help detect multi-polar aspects in the regionalization of world cities by

evaluatinghowcommunitiesmutuallyinteractwithoneanotherorhowtheyareinternallyorganized.

2.1Buildingcities’systemsusingmultinationalfirms’networks

To determine the position of cities within these multinational firm networks, we first constructed a

database consisting of theworld’s top 3,000 companies, based on their turnover (Orbis, Bureau Van

Dijk,2013,Fig.1.a),andtheir800,000directand indirectsubsidiaries locatedaroundtheworld.These

subsidiariesareconnectedby1.2million financial linksoperatingwithall successivesteps.This setof

networksissimilar(butlarger)topreviousdatasets.

Weaggregated these groups’ networks at the city level (Fig.1.b and Fig.1.c) basedon the locationof

eachofthe800,000subsidiaries(Fig.1.a).

Figure1:Buildingdata:fromindividualnetworksoffirmstocitynetworks

©Rozenblat,Zaidi,Bellwald,2015

To aggregate the firms’ location within comparable “cities”, metropolitan areas were identified and

delineatedas“LargeUrbanRegions”(LUR)1.Firms’ linkageswereaggregatedbyLURusingtheirorigin

and destination locations. This process yielded amatrix linking 1,205 cities around the world. These


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areas contain more than 85% of the overall links in the database2. The intercity relationships are

oriented, and they are weighted by aggregating firms’ links by pairs of cities (removing intra-urban

linkages)(Fig.1.c).

Wealsoconsidereddifferentgeographical territories,whichwill constitutebenchmarkswithwhichto

compareempiricalclustering.TheUNCTADlistofFTZs(2013)includesoverlappingzones.Weattributed

a unique relevantmembership to each country. Two other benchmarkswere built as follows: seven

largecontinents(UN,2013)andgeographicalproximities(orthodromicdistances).

2.2Networksofmultinationalfirmsbytheirlevelofknowledgeofactivities

Todistinguishtheglobalizationofindustry/servicesandofhigh/lowskill levels,weadoptedtheOECD-

EC classified activities (2009). This classification considers firms “as knowledge intensive if tertiary

educatedpersonsemployedrepresentmorethan33%ofthetotalemploymentinthatactivity”(OECD,

2009). TheOECDproduced twodistinct aggregations (high and low) for industries and for services in

fourcategories:

- Hightechandlowtechforindustry

- Knowledgeintensiveservices(KIS)andlessknowledgeintensiveservices(LKIS)forservices

Activitieswereattributedtoeachsinglefirmanditsascendantlinkages(agroupcanencompassseveral

activities).Wethuscreatedafour-layerednetwork(Fig.2).

Figure2:Multi-layeredcitynetworks

©Rozenblat,Zaidi,Bellwald,2015Tocomparethesefour layers, itwasnecessarytohavethesamenumberofcities;therefore,wekept

onlythosecitiespresentonallfourlevels(503citiesencompassingmorethan90%ofthetotallinkages).

The612,798remaininglinkswereaggregatedbycitycoupleinthemultilayerednetwork.


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2.3Clusteringmethod

TheCSS literature defines the detectionof communities or clusters as the identification of groups of

nodes densely connected to one another and sparsely connected to other clusters (Schaeffer, 2007).

Numerousalgorithmswere classifiedaccording topartitional/hierarchical, divisive/agglomerative, and

fuzzy/hard properties (Jain et al., 1999). Algorithms also differ if they can be applied to

directed/undirected networks, weighted/non-weighted networks or tree-like networks (Fortunato,

2009; Schaeffer, 2007). Another important distinction is the use of local and global optimization

methods (Schaeffer, 2007). Local methods attempt to optimize local functions, such asmodularity

(Newman, 2004),which is ameasure of the cohesiveness of groups (high intra-cluster edges vs. low

inter-clusteredges).Ontheotherhand,globaloptimizationmethodsrequireinformationontheentire

networkstructure(heavycomputation);thus,theyareunsuitableforlargedatasets(Fortunato,2009).

Another popular categorization for the clustering algorithms is dynamic processes, such as random

walks,spinmodels,andinformationpropagation(Pons&Latapy,2004).Thesemethodshaveproduced

severalfastandaccuratealgorithms(Fortunato,2009).

We selected seven appropriatemethods forweighted and oriented data belonging either to local or

global optimization methods3, and we compared them with modularity (Girvan & Newman, 2001;

Clausetetal.,2004;Newman,2012)4(Tab.1).

Table1:Comparisonofclusteringalgorithms

Algorithm Modularity

1 EdgeBetweenness(Girvan&Newman,2002) 0.022 WalkTrap(PonsandLatapy,2004) 0.123 InfoMap(Rosvalletal.,2009) 0.294 LabelPropagation(Raghavanetal.,2007) 0.035 FastGreedy(Newman,2004) 0.316 Louvain(Blondeletal.,2008) 0.317 SpinGlass(ReichardtandBornholdt,2006) 0.36


Thebestresults(highmodularity)wereobtainedusingtheSpinGlassclusteringalgorithmproposedby

Reichardt andBornholdt (2006). TheSpinGlass algorithm5 has several advantages, including that the

numberofclustersdonotneedtobeknownapriori.

2.4Comparingclusteringcommunities’similarities

The resulting clusters are compared with the benchmarks of regional areas. A number of cluster

similaritymeasureshavebeenproposed recently (Lancichinetti&Fortunato,2009).Weuse themost

widely acceptedmethod, theNormalizedMutual Information (NMI)method,whichwasproposedby

Danonetal.(2005).Giventwopartitionalstructuresofanetwork,thecalculationofNMIreturnsavalue

inarangebetween1(perfectsimilarity)and0(completedissimilarity).


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3Clusteringworldcitiesaccordingtomultinationalfirmnetworkswithdifferentknowledgelevels

TheSpinGlassclusteringappliedtothe503citiesresultsinonetotalclusteringandfourclusteringsfor

eachsub-network(fiveclusterings).Generalcomparisonsofthedifferentclusteringresults(3.1)willbe

explainedbytheirrespectivecharacteristics(3.2).Morespecificcomparisonswillalsopermittobetter

interpretthechangingcommunitymembershipofcitiesdependingonthevariousactivities(3.3).

3.1Generalcomparisonsofclusteringresults

Theresulting fiveclusterscanbecomparedaccordingto theirgeneralcharacteristics.Consideringthe

modularity index (Tab.2), the first main result is that lowermodularity indices qualify the clustering

outputsofthehigherlevelsofskill(HIGH-TECHandKIS).Thismodularityindexisnotcorrelatedtoother

propertiesofthenetwork,anditdoesnotvarywiththeaverageinternallinksbecauseitmeasuresboth

existingandnon-existingedges.

Table2:ApplicationofSpinGlassclusteringbytheskilllevelsofmultinationalfirmnetworks

Nodes(Cities)Number

TotalWeightedEdges

Density(totalweighted

edges/nodesnumber)

AlphaPowerLaw

ClusteringCoefficient(Triads)

ModularityofSpinGlassClustering

NumberofClusters

AverageInternalLinks(%)

HIGH-TECH 503 76,339 152 1.71 0.30 0.31 7 70%LOW-TECH 503 55,653 111 1.73 0.28 0.37 9 83%KIS:KNOWLEDGE-INTENSIVESERVICES 503 208,562 415 1.54 0.29 0.33 10 85%

LKIS:LESSKNOWLEDGE-INTENSIVESERVICES 503 146,938 292 1.66 0.30 0.43 11 93%

TOTALNETWORK 503 612,798 1,218 1.32 0.33 0.36 10 71% ©Rozenblat,Zaidi,Bellwald,2015

Lowmodularityindicesforhigh-skillnetworksmeanthatthesecommunitiesofcitiesareless“cohesive”

and exchangemore between clusters. The resultmakes sense: firms that participate in highly skilled

activities search for rare competencies in other communities, whereas firms that participate in less

skilledactivitiesarelocatedclosertomarketsorganizingtheirnetworksthroughstrongerroutinesand

creatingmore“cohesive”citycommunities.

Thenumberofclassesishigherforindustrialactivitiesclustering(7forHIGH-TECHand9forLOW-TECH)

than for services activities clustering (10 for KIS and 11 for LKIS), meaning a more partitioned

organizationofgroupsofcitiesthatarenotnecessarilymorecohesive.LOW-TECHwithfewerclusters

thanKIShasahighermodularityindex.Theexplanationofthissubtledifferencebetweenthenumberof

clustersandtheirmodularityoverlookscertainfactorsthatwillbeexploredlaterinthispaper.

The comparisonwithbenchmarks informs theproximityof theactivities’networksof cities regarding

regionalandspatialpatterns(Tab.3).


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Table3:NMIcomparisonofclusteringofcitieswithseveralbenchmarks

Clusteringofcitiesaccordingtofirms’networks

(1)TOTAL

Clustering

(2)UN7REGIONS

(3)FreeTradeZones

(4)UN22SUB-REGIONS

(5)Countries

(6)Distance-Based

ClusteringHIGH-TECH 0.67 0.62 0.63 0.59 0.54 0.54LOW-TECH 0.77 0.61 0.62 0.60 0.65 0.52KIS 0.86 0.54 0.58 0.61 0.77 0.52LKIS 0.82 0.52 0.63 0.63 0.77 0.52AVERAGE 0.78 0.55 0.60 0.60 0.70 0.52TOTALClustering 0.49 0.50 0.51 0.61 0.55 ©Rozenblat,Zaidi,Bellwald,2015

Unlikeindustrynetworks,theKISandLKISinterurbannetworksremainhighlyorganizedaroundnational

urbansystems.Theprincipalreasonforthisresultistheneedforservicestobeawareofnationalrules

and laws thatmaintain strong business organization at the national level (Sassen, 2007). Conversely,

HIGH-TECHinterurbannetworksresemblenationaldelineationsforonlyhalfoftheiraspects, implying

an extended international organization based on highly specialized city networks. These networks

remainlargely(two-thirds)withintheirrespectiveFTZs.

Approximately50%similarityisobservedbetweeneveryclusteringanddistance-basedclustering,which

islowerthanthesimilaritiesbetweenFTZs.ThisresultcontradictstheresultsthatBarigozzietal.(2011)

obtainedregardinginternationaltrade,wheredistancesmattermorethanbelongingtoanFTZ,butitis

notfoundatthesamescalebecausehere,distancesarealsomeasuredbetweencitieswithinthesame

country.Thus,distancemaynotbetheonlycriterionofinterurbaninteraction,andonecanassumethat

theurbanhierarchyofeachcountryalsomattersagreatdeal.

3.2Descriptionoftheclusteringresults

Clustering theentirenetwork results in10 clusters that canbe identifiedby thedominant regionsor

countriesoftheircitiesandbytheirmaininternallinks(Fig.3).


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Figure3:Clusteringofcities’networkswithallactivities


- NorthAmericaencompasses93NorthAmericancities,includingCanadiancities,Taipei,TelAvivand

Veracruz.ThisclassofcitiesisledbyNewYork(16.5%oftheinternallinks),followedbyPhiladelphia

(9.6%),Chicago(5.8%)andBoston(5.3%).

- The Asia-Pacific region is dominated by Chinese cities (Hong Kong: 17%, Beijing: 13.4%, Shanghai:

8.6%),regroupedSoutheastAsiancities(Singapore,KualaLumpur)andAustraliancities(Sydney:6%,

Melbourne:3%,PerthandBrisbane).Thisclassofcitiesincludestaxhavens,suchasGrandCayman

(8%),BermudaKindley(10%)andTortola(VirginIslands).

- Japanincludes31citiesasfollows:allJapanesecitiesplusBangkok,JakartaandMaastricht.Theclass

isdominatedbyTokyo,whichclaims45%ofthelinkages,andOsaka(25%).

- South Korea: includes all six main South Korean cities. Similar to Tokyo, Seoul claims 46% of the

internallinks,andPusanclaims20%.

- The Indiancommunityof10citieshighlights thenetworkcohesionof thissub-continentalcountry,

andalsoincludesMauritiusandColombo(SriLanka).Mumbaidominatesthisclasswith36%ofthe

internallinks,followedbyDelhiwith23%andChennaiwith8%.


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Europeancitiesareclusteredintofivecommunities:

- NorthernandEasternEuropecomprise130cities,whichincludeRussianandTurkishcities.Although

Amsterdampossessesthemostimportantrelationships(8.3%ofinternallinks),itdoesnotdominate.

Manyothercities,suchasVienna,Frankfurt,Brussels,Moscow,Luxembourg,Rotterdam,Hamburg,

MunichandWarsaw,interactequally,witheachconcentratinginternallinksbetween5%and3%.

- TheUKandCommonwealth regionsare comprisedof 49 cities anddominatedby London (35%of

total internal links).Thiscommunity isthemostspatiallywidespreadcommunity. InadditiontoUK

and Irish cities, theUK andCommonwealth regions encompass Swiss,Middle Eastern (AbuDhabi,

Kuwait,Riyadh,AmmanandKarachi) andAfrican cities (SouthAfrica’s fourmain cities), aswell as

Africancapitals,suchasCairo,Lagos,NairobiandGaborone.

- The Iberian and SouthAmerican groupof cities is dominatedbyMadrid,with 35%of the internal

links,andBarcelonawith14%,followedbyBilbao,Lisbon,SaoPaulo,Seville,Valencia,RiodeJaneiro,

MexicoCity,SantiagodeChileandBuenosAires.

- TheFrenchgroupofcitiesisdominatedbyParis(39%ofthetotalinternallinks),andincludesformer

French colonial cities in Africa (Tunis, Algiers, Douala, and Dakar) and French-speaking capitals

(Accra).

- Another national network includes the 35 Italian cities of our dataset plus Lugano (an Italian-

speakingcityinSwitzerland).

Thesystemofdominantrelationshipsbetweenclusters (Fig.3)highlights thecentralityof threeof the

clusters: the North American cluster, the Northern and Eastern European cluster, and the UK and

Commonwealth cluster. These three clusters dominatemost of the links between firms’ investments

goingtoorcomingfromotherclustersofcities(74%ofthetotalweightedlinkagesbetweenclusters).

ComparedwiththedifferentclusteringresultsproposedbyDerruderetal.(2003)andcompletedbyLiu

etal.(2013),aswellaswiththosecalculatedbyAlderson&Beckfield(2004),theSpinGlassclustering

methoddisconnectsthemainglobalcities, integratingthemintotheirappropriateregionalorcultural

groups.

In this form of regional organization, the more that global cities concentrate a large part of the

investmentscontrolledorattractedbythecluster’scitiesto/fromoutsidethecluster(polarization),the

moreclosedthecluster,verifyingourfirsthypothesis.Weplottedthesetwointernalproperties(Fig.4).


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Figure4:PolarizationandclosenessofclustersfortheTOTALnetwork


Some clusters are very polarized around one city based on either internal or external links (Paris for

France,SeoulforSouthKorea,TokyoforJapan,MilanforItaly,LondonfortheUKandCommonwealth)

and are closed systems. Other clusters aremulti-polar systemswith lower levels of closeness (North

America,NorthernandEasternEurope,IberiaandSouthAmerica,Asia-Pacific).

The less integrated cities within the clusters, determined by their share of internal linkages (Tab.4), are either

anomalies of geographical membership, such as Maastricht in the Japanese cluster and Mauritius in the Indian

cluster, or cities that could create bridges between clusters, such as South American cities that are partially

associated with North America or Europe, Swiss cities that are largely included in the UK and Commonwealth

clusterandintegratedwithallotherclusters,andtaxhavens,suchasBermudaKindley.

Table4:Citieswiththelowestintegrationinclusters(lessthan30%)

LargeUrbanRegion COUNTRY CLUSTER Linkagesofthecityinsidethecluster(in%ofthetotal

linkagesofthecity)MAASTRICHT NETHERLANDS JAPAN 11.6MANILA PHILIPPINES ASIA/PACIFIC 13.9JAKARTA INDONESIA JAPAN 14.6BANGKOK THAILAND JAPAN 18.1QUITO ECUADOR IBERIA&SOUTHAMERICA 19.1CARACAS VENEZUELA IBERIA&SOUTHAMERICA 19.3ACCRA GHANA NORTHAMERICA 21.3COLOMBO SRILANKA INDIA 21.4GUADALAJARA MEXICO IBERIA&SOUTHAMERICA 21.4ZURICH SWITZERLAND UK&COMMONWEALTH 22.6MEXICOCITY MEXICO IBERIA&SOUTHAMERICA 23.7PANAMACITY PANAMA IBERIA&SOUTHAMERICA 24.8MAURITIUS MAURITIUS INDIA 25.9SAOPAULO BRAZIL IBERIA&SOUTHAMERICA 26.5CAIRO EGYPT UK&COMMONWEALTH 26.7SAOJOSEDOSCAMPOS BRAZIL IBERIA&SOUTHAMERICA 26.9BERMUDAKINDLEY BERMUDA ASIA/PACIFIC 27.1GENEVA SWITZERLAND UK&COMMONWEALTH 28.4BUENOSAIRES ARGENTINA IBERIA&SOUTHAMERICA 29.8


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Clustering derived using the same methodology for the four activity networks allows for a better

understanding of the general network. We briefly describe each clustering but focus on their main

similaritiesanddifferences.Themaindifferenceinthecompositionoftheclustersliesinthedifference

between industrialnetworksandservicenetworks (Tab.5). Inparticular,HIGH-TECHclustersdifferthe

mostfromotherclusters.ThetwoclosestclusteringsaretheKISandLKISones.

Table5:NMIcomparisonoftheclusteringofcitiesbyactivityskilllevels

HIGH-TECH

LOW-TECH

KNOWLEDGE-INTENSIVESERVICES

LESSKNOWLEDGE-INTENSIVESERVICES

HIGH-TECH 1 LOW-TECH 0.72 1 KNOWLEDGE-INTENSIVESERVICES 0.65 0.67 1 LESSKNOWLEDGE-INTENSIVESERVICES 0.56 0.65 0.78 1 ©Rozenblat,Zaidi,Bellwald,2015

Someclustersmaintaina similar setof cities:NorthAmerica, Japan, theUKandCommonwealth,and

the Asia-Pacific region constitute stable clusters (Fig.5). For industrial clusters, Europe is a complete

communityminus theUK (and the Italian LOW-TECH cluster), and for services, Europe ismuchmore

fragmentedinseveralclusters.Conversely, for industrialsectors,Koreancitiesareseparated,whereas

forservices,theyareencompassedwithintheAsia-Pacificcluster.

Intermsoftheirsharesofweightedlinksinthenetworksasawhole,theweightsofthethreedominant

clusters,NorthAmerica,Europe,andtheUKandCommonwealth,rangefrom85%forhigh-skillactivities

relating to industries and services to 75% for low skill activities. This means that high-skill activity

networksareconcentratedinsidethesedominantcities’clusters,whichmakessensefromadiffusionof

innovationperspective,wherethemostskill-intensiveactivitiesremainclosertocentralcities.

Regardingthemutualpositionsbetweenclusters,theUKandCommonwealthcluster iscentralamong

theclustersfortheKIS(Fig.5.C).ForLKIS,theUKandCommonwealthshareacentralplacewithNorth

AmericaandEurope,developingmajorrelationshipswithotherclustersthatformsimilartosatellites.

ForLOW-TECH,centrality is sharedbetweenvariousclusters, forminga loopofclusters. Interestingly,

UK& Commonwealth cities preferentially invest in North American cities for the higher level of skill

found there (HIGH-TECH and KIS) while rather being oriented toward European cities for unskilled

activities(LOW-TECHandLKIS).

To comprehend the internal organization of the clusters, we plotted the polarization of the clusters’

outreach linkages inthehighestcityandtheaverage levelofclosenessofthecities intheclustersfor

eachactivity(Fig.6).


14


15

Figure5:Clusteringofcities’networksbyactivityskilllevels



16

Figure5(continuing):Clusteringofcities’networksbyactivityskilllevels



17

Figure6:Polarizationandclosenessofclustersbyactivitylevel


Thereisnolongercorrelationbetweenthetwopropertiesofclusters.Theuniqueregularityisvisiblefor

theNorthAmericanandfortheUK&Commonwealthclusters,thetwomostopenclustersforthemore

skilledactivities.Inthesecases,thetwoclustersarestronglycentralandencompassalargenumberof

cities.However,clustersareusuallyrecomposedandtransformedinfourdistinctways:

- First,theclustersaredividedintoseveralsub-clustersbetweenskilledandunskilledactivities

- Second,citiesshiftingfromoneclustertoanothercanradicallychangetheorganizationofthe

clusters.WhenFranceisaggregatedtoEurope,Parisbecomesthemostcentralcity.Iberianand

South American cities, which form a unique cluster for services, are divided between North

AmericaandEuropeforindustries.Thus,thesetwoclustersaretransformedbytheirnewcities’

compositions

- Third, the stable clustersaregenerallydominatedby the samecity,but thereareexceptions,

suchastheAsia-Pacificcluster,whichisdominatedbyBeijing.However,theAsia-Pacificcluster

isdominatedbyHongKongforLKISinternallinks,ShanghaiforHIGH-TECHoutreachedlinks,and

SeoulforKISoutreachedlinks

- Fourth,theroleofsecondarycitiesmattersdependingontheactivity.ForHIGH-TECH,Taipeiis

thesecondcityafterLondonintheUKandCommonwealthcluster,dominatingmorethan15%


18

of the total outreach links of the cluster. Osaka is second in the Japanese cluster and is

particularlystronginHIGH-TECH,dominatingmorethan20%oftheexternallinkages

Thus,thepropertiesoftheclustersarewidelyinfluencedbytheircities’compositionandbythebalance

between them. Shifts occur fromone cluster to another and from an internal position to a different

position according to activities that underline thedifferent aspects of globalization insertion for each

city.

Whenacityremainsinthesamecluster,whatevertheactivity,onecanconsiderthatithasastrongand

deepattachmenttoitscluster.Ontheotherhand,acitythatchangesitsmembershipfromonecluster

to another reflects different forms of integration into the process of globalization. Because clusters

change fromone activity to another, the changingmembership of citiesmust be consideredwithout

takingintoaccountthemajorre-compositionsoftheclusters.Forthisreason,weaggregatedclustersby

theirmaincompositionsinfivemajorstablecommunities:

- Europe:France,Italy,Spain,Europe,theUKandtheCommonwealth

- NorthAmerica:USAandCanada

- Asia:AsiancitiesandKorea

- Japan

- India

Amongthe503citiesexamined,428(85%)remainedinthesamemajorstablecommunityregardlessof

activity. Additionally, 75 cities moved from one cluster to another, sometimes following common

patterns.

TheEuropeancommunityhasapronouncedability to integratecities thatparticipate inhighly skilled

activities,thosehavingthecharacteristicsoftaxhavens(BermudaKindley,HongKong,GrandCayman,

Singapore,KualaLumpurandtheVirginIslands)andthosewithenergeticeconomies(Lagos,Almatyand

Astana).

However, North American cities have privileged high-skill links with South America and with highly

skilled cities suchas Zurich andTelAviv. Japanese intercitynetworks are alsopowerful in integrating

HIGH/LOW-TECHAsianandevenEuropeancities.ForKIS,IndiancitynetworksintegrateMiddleEastern

citiessuchasCairo,Alexandria,AbuDhabi,Riyadh,AmmanandKuwait.

4.Discussionofthemultipolarorganizationoftheworldcitiessystem

Overall,theanalysissupportsthenotionoftheworldcities’networkasa“multipolar”systembecause

of these cohesive clusters that form dense poles of interacting cities. The shift from a unipolar to a

multipolarvisionofworldcitiescorrespondstoawiderchangeinthecomprehensionofthefeedback


19

processesmaintainingor transformingthedistributionofpowerbetweencitiesand formingthebasis

forthepredominanceofsomeofthesecities.Theclassicalcore/peripheralsystemisreplacedbyatwo-

level system considering cores and peripheries both between and within clusters. This double level

between and inside clusters expresses a networking process dictated by steps in which firms’

investments often enter into a cluster of cities by top cities to reachother cities,where they diffuse

their investments. FTZs are important in this stepwise process, participating in the feedback

maintenanceandreinforcementoftheglobalstrengthofthecentralcitiesofeachcluster,andtheyalso

reinforcetheinternalcohesionofeachcluster.Inthissense,globallinkagesbetweenclustersandlocal

linkagesinsideclustersareintertwined.

Most of the dominant cities of the central clusters correspond to the cities that are classically

mentionedas“worldcities”:London,NewYork,Tokyo,Paris,andAmsterdam.Theregularityof these

cities’centralityintheserviceandindustrialsectorsconfirmsthecorrelationhighlightedbyWall&Van

derKnaap(2011).Capitalcitiesofperipheralregionsstillconstitute“pivotalintermediaries”forcitiesof

their subsystems, confirming the Meyer (1986) hypothesis. However, the level of their cluster

domination and their clusters’ hierarchical characteristics specify the core/hinterland results of the

previousstudiesontheregionalizationoftheworldcitynetworks(Tayloretal.,2002,2013;Derudderet

al.,2003;Alderson&Beckfield,2004).Thesespecificationsareevidentinthreemainresults.

First, the“classicalworldcities”donothavethesamelevelsofdominance(polarization) in theirown

clusters,whichinducesdifferentformsofglobalization:

- Ontheonehand,thegroupofcitiesthatdominatetheirclusterscomposemorethanhalfofthetotal

out-linkagesoftheirclusters.ThedominantcitiesareLondon,Tokyo,Paris,MilanandSeoul.These

citiesconcentrateahighintermediarycapacityfordecision,playingacentralroleintheglobalization

ofothercitiesintheirownsub-systems.ThebestexampleofthistypeofworldwideroleisLondon,

encompassing global control of numerous cities around world. Other cities, such as Tokyo, Paris,

MilanandSeoul,controltheirnationalurbansystems.

- On the other hand, New York for North American cities, Amsterdam for Northern and Eastern

Europeancities,andBeijingforAsian-Pacificcitiesbelongtomoredistributedsystemsinwhichmany

citiesexchange firms’ linkagesdirectlywithcities fromotherclusters.Firms’practicesexploit their

combinednetworkresourceslinkedoutsidetheclusters.

Second,themultipolarsystemofcitiesdoesnotfunctiononthesamescaleallovertheworld.Thefact

that some continental, inter-continental or national scales appear at the same score of modularity

expresses a wide range of levels of international openness/cohesion of cities by countries and

continents.ForLKIS,Japanese,Korean,Indian,Chinese,French,ItalianandevenSwisscitiesmaintaina

high levelofnationalmutual interdependencies.Thesenetworksbetweennational citiesproduce the


20

samelevelofdependenciesthatexistinmuchwidercommunities,suchasNorthAmerica,ortheUKand

theCommonwealth. In this respect,SpinGlassclusteringdoesnotverify theconclusion that“clusters

withlowaverageconnectivitytendtobemoreregionallyrestrictedinmembership”(Tayloretal.,2002,

p. 885). HIGH-TECH and KIS also highlight for theUK and Commonwealth group a higher geographic

magnitudethanfor lowerskilledactivities,whichcanbeexplainedbytheworldwidesearchforhighly

skilled, specialized competencies. For low-skilled activities, proximitymattersmore and this cluster is

alsomorelinkedtotheEuropeancities’cluster.

Third, the inter-cluster level not only reveals the mutual position of dominant cities but also the

organizationofthecompletesub-systems.ThestablecorecentralityofNorthAmerican,Europeanand

UK and Commonwealth cities according to their different activities is simultaneous with cities’

movements:nationalcitiescreatetheirownclustersforlessskillsactivitiesforwhichclustersaremore

numerousandlessdominatedbythethreemainclusters.Citiesthatmovefromoneclustertoanother

haveaparticularpositionintheglobalizationprocessbecausetheyareorientedtowardseveralgroups

of cities according to their activities. These cities are principally located in Asia, Australia and South

America, plus Zurich and Tel Aviv. Therefore, they constitute specialized or regional pivots in the

expansionof themultinational firms’ strategies, hosting regional or specialized centers of industryor

services.

Conclusion

The systematic method of clustering borrowed from CSS allows for ordering themultipolar regional

processesbetweencities.Clusteringrevealscohesivecommunitiesthatareunevenlypolarizedaround

one dominant city. In their own networks, firms articulate these skilled/less skilled activities and

industrialandservicefunctionsintheirglobalvaluechains.Inthissense,themulti-polarcitynetworks

represent the main sub-systems of city resources for high skill/low skills in industrial and service

activitiespracticedinworldwidefirmnetworks.Thepresenceofmulti-polarcitynetworksconfirmsthe

“multipleglobalizations”proposedbyKrätke(2014),specifyingthedifferentpositionsofcitiesinseveral

industrial or services systems. Further analysis by sectorwould better highlight city specializations in

specificglobalvaluechains.

Intermsofpolicy,thisnewvisionofferseachcityanoverviewofitsmaininterdependencies.Therefore,

this analysismay help cities build a strategy both inside the cluster to increase their linkage density,

whichmayfunctionasaneasyformofspecialization,andoutsidetheclusterbytargetingspecificcities

according to which groups of cities they would like to reach. The governments of cities that are

permanentlypolarizedbyothercitiesarewellawareoftheirdependencyonthesecitiesandattemptto

diminishthatdominancebyfosteringalternativelinkages.Conversely,citygovernmentsdominatedby

several groupscanuse thisproperty to strengthen thepositionof their citiesbyattractingnew firms


21

throughtargetedactivitiesandfromspecificcities.Giventheresilienceofthesecities’systemsinterms

ofthediversityoftheirinterdependencies,thisevolutionmustbefollowedtoevaluatetheprogression

of thediversity levelsof theentire system,ofeachcommunity,andofeachcity’sdependencywithin

communities.

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1‘LargeUrbanRegions’delineatedbyESPON(2012)forEurope,bytheMetropolitanStatisticalAreasfortheUSAandCanada,andbytheequivalentforthemaincitiesworldwidebasedonNationaldelineationswhenavailable(IGD-UNILLausanneandGeodivercityinParis).3Theseventestedalgorithmsare

- EdgeBetweenness(GirvanandNewman,2002)isaglobalalgorithmbasedonthecalculationofgeodesicdistances.Theedges lyingbetweenallpairsofnodesare removedrepeatedly tobreak theentirenetwork intodisconnectedcomponents,thusprovidingdifferentcommunities.

- WalkTrap(PonsandLatapy,2004)isaglobaloptimizationusingadynamicprocessofrandomwalkstocalculatethedistances between different nodes based on which nodes are grouped together to form clusters using Ward'sMethod.Modularityisusedtoselectthebestpartition.

- InfoMap(Rosvalletal.,2009)isanotherglobaloptimizationalgorithmbelongingtothecategoryofdynamicprocessas it also uses randomwalks,where the idea is to attempt to compress the information of this dynamic process,minimizingthedescriptionlengthoftherandomwalktoobtainclusters.

- Label Propagation (Raghavan et al., 2007) algorithm belongs to the category of local algorithms using a dynamicprocessofmajorityvoting.Randomlyuniquelabelsareassignedtoindividualnodes,whicharesubsequentlyupdatedusingmajorityvotingintheneighborhoodofthevertex,whichinturnresultsinthedetectionofcommunities.

- FastGreedy(Newman,2004)isalocalclusteringalgorithmthataggregatesnodesclosetoeachotherbasedontheoptimizationofModularity(exposedindetailbelow).

- Louvain (Blondel et al., 2008) algorithm is another local optimization algorithm based on modularity, where theaggregated nodes are replaced by new nodes in the graph, thus simplifying the original graph every time a newclusterisformed.Thismethodresultsinadifferentandfasterclusteringalgorithm.

- SpinGlass (ReichardtandBornholdt,2006)clusteringalgorithmisbasedonthe ideathat ifPottsspinvariablesareassignedtotheverticesofanetworkandiftheinteractionsarebetweenneighboringspins,structuralclusterscanbefound from the spin alignment of the system. Thus, a local optimization takes place to align neighboring nodes,resultingincommunities.

4Mathematically,Modularityisdefinedasfollows(Girvan&Newman,2002;Clausetetal.,2004;Newman,2012):

where

istheedgeofthegraphbetweennodesvandw(1ifvandwareconnected;0otherwise)

isthedegreeofv,and isthedegreeofw

isthetotalnumberofpossiblenon-orientededgesinthegraph

isthecommunityfunctionforvandw:1ifvandwareinthesamecommunity;0otherwise.

5Thespinglassmethods(Reichardt,Bornholdt,2006)usetheHamiltonianPottsmodelH[{s}]ofapartitions,whichmeasuresthedistancebetweenthenodesaccordingtotheirdirectorindirectlinkstothenetworksJvwandbasedontheirmembershipwithintheclassesbeingpartitionedδ(sv,sw):

Thespinglassmodeltakesintoaccounttheexistinglinksaswellasthemissinglinksinsideandbetweenclasses.Then,H[{s}]iscalculatedfor4cases:

Themodelmeasuresbothintra-communityandinter-communitylinks.Italsoevaluatesthe“temperature”,whichisminimizedwhenthenetworkisfartorandomlygraph(Blattetal.,1996).Itcalculatesdifferentpartitions,maximizingtheirmodularityand

Q =12m

× Avw −kvkw2m

#

$%&

'(vw∑ δ(cv,cw )

Avw =10

!"#

kv = Avww∑ kw = Avw

v∑

m =12

Avwvw∑

δ(cv,cw )

Η s{ }"# $%= − Jvwvw∑ δ(sv, sw )

Η s{ }"# $%= − avwJvwv≠w∑ δ(sv, sw )

internal _ links

+ bvw (1− Jvw )v≠w∑ δ(sv, sw )

internal _non_ links

+ cvwJvw (1−v≠w∑ δ(sv, sw ))

external _ links

+ dvw (1− Jvw )v≠w∑ (1−δ(sv, sw ))

ex ternal _non_ links


24

minimizingthetemperature.

Acknowledgments:

The research has supported by the FP7 FETMULTIPLEX on Complex System Science regrouping essentially

physicists. Inthisgroup,wewould liketospecificallyacknowledgePanosArgyrakis,MichaelMaragakis from

AristotleuniversityinThessaloniki,ShlomoHavlinfromBarIlanUniversityinTelAviv,andAntoniosGarasfrom

ETHZ inZurich, fortheir fruitfuladvicesanddiscussionsaboutmultiplecomplexnetworks.Wewould liketo

thanks also the Labri team in the BordeauxUniversitywho develop the TULIP softwarewe used for graph

visualizations.

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