THE DYNAMICS OF LINK FORMATION IN PATENT INNOVATOR NETWORKS

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1 Perspectves of Innovatons, Economcs & Busness, Volume 4, Issue 1, 2010 wwwpebcz THE DYNAMICS OF LINK FORMATION IN PATENT INNOVATOR NETWORKS JEL Classfcatons: O31 TAMAS SEBESTYEN, ANDREA PARAG Faculty of Busness and Economcs Unversty of Pecs, Hungary Key words: Innovaton, network evoluton, knowledge-transfer, cluster Abstract: The paper presents a smple extenson of the Barabas-Albert model of network evoluton Ths model s based upon the assumpton that new lnks are formed not only accordng to the centralty of other nodes n a network but geodetc dstance s also mportant n lnk formaton Smulaton results show that f lnk formaton s based on dstance then the resultng network s more clustered than n the case of centralty beng the domnant factor n lnk formaton Our emprcal results show that n European regonal patent nventor networks dstance s a consderably more mportant factor n lnk formaton than network centralty ISSN: (onlne) (prnt) PP21-25 Introducton Networks have attracted consderable attenton n the last decades Works from a broad spectrum of scentfc research have revealed that networks n qute dverse areas of lfe (eg the lvng cells, the World Wde Web, socal relatonshp networks, etc), although dfferent at the frst sght, share some basc common propertes, among whch the most strkng s ther nvarant scale-free characterstcs (Barabas and Albert, 1999, Barabas, 2003) At the same tme the lterature on nnovaton has focused on learnng and nnovaton networks, e networks of frms, researchers, specalzed nsttutons etc It s now clear that nnovaton can be regarded as an nteractve process whch requres relatonshps between dfferent agents of the process (nnovators, frms, unverstes, venture captal, etc) In ths context one can see for example Bathelt et al, 2004; Nonaka, 1994; Lundvall and Johnson, 1994 The nteracton among networks and regonal development s also an emergent feld of research through the noton of regonal clusters whch are meant to be the drvers of nnovatveness and therefore regonal economc success (for a general overvew see eg Karlsson, 2008) These two lnes of research have been synthetsed n the area of nnovaton networks whch tres to reveal the characterstcs and dynamc patterns of such networks The work n ths feld has proceeded along two dfferent methodologcal avenues Frst, emprcal studes made consderable efforts to gan nsght nto the characterstcs of real nnovaton networks These studes however, manly due to the lack of adequate data, grasp only a statc vew of the networks n queston, ther structural characterstcs and the relatonshp between these characterstcs and ther performance (Varga and Parag, 2009; Ozman, 2006) Whle nventor networks are wdely thought to enhance regonal nnovatve capablty, there exst few longtudnal studes of formaton and evoluton over tme (Flemng at al, 2007; Ter Wall, 2008) Some focus on examnng knowledge transfer from academy to ndustry showng academc nventors to be more central and better connected than nonacademc ones (Balcon at al, 2004) Others nvestgate the separate effects of nventor agglomeraton on metropoltan patentng and the structure of socal networks lnkng nventors wthn and across metropoltan areas They fnd that the structural features of the nventve networks are less mportant agglomeratve features of metropoltan areas than agglomeraton (Lobo and Strumsky; 2008) The paper of Ejermo and Karlsson (2006) explores the structure and the strength of nterregonal nventor networks as measured by the affnty between nventors to be co-authors n patents across regons It fnds that affntes extend more often to regons whch have hgh patentng, when they have hgh R&D levels, and to those wth more unversty R&D In ths paper we focus on the lnk formaton process n evolvng networks To ths end we present a smple model settng based on the model of Barabas and Albert (1999), then we use a newly bult database n order to capture basc characterstcs of lnk formaton n evolvng patent nnovaton networks Our database covers patent statstcs of European countres through the perod between 1978 and 2005 Ths longtudnal span offers us the possblty to analyse lnk formaton processes The paper proceeds as follows Frst, we present an extended verson of the Barabas-Albert model of network evoluton and analyse some of ts man mplcatons Then we brefly descrbe our database whch gves the bass of our followng emprcal analyss A smple, but extended model of network evoluton Our baselne model, to be extended afterwards, s the model of Barabas and Albert (1999) Ths model starts from an ntal random network and adds a new node to the network n each step and a new node forms a gven number of lnks to the already exstng nodes Lnk formaton s based on the so called preferental attachment whch assures that a new node forms a lnk wth a gven node wth hgher probablty f that gven node have more lnks, e f t occupes a more central poston n the network In the termnology of network 21 Internatonal Cross-Industry Journal

2 Perspectves of Innovatons, Economcs & Busness, Volume 4, Issue 1, 2010 wwwpebcz theory the number of lnks of a gven node s called the degree of that node, so we wll refer to ths knd of preferental attachment as drven by the degree dstrbuton of the network Let us denote the degree of node n the network as D In the model of Barabs and Albert (1999) the probablty of establshng a lnk wth (already exstng) node s smply P = D D Gven ths smple rule, we can buld networks where popular nodes (e those nodes whch have more lnks) become more popular as tme passes by However, there are two mportant consderatons to be mentoned wth regards to the model above, whch lead us to the extenson of the Barabas-Albert model Frst, preferental attachment s present n the Barabas- Albert model n the formaton of the frst lnk of a new node, e ts ntal attachment to the network as a whole However, t s ambguous to what extent new nodes are nformed about the degree dstrbuton of a network In some cases t mght be a reasonable assumpton, but n other cases do not Second, gven that a node has at least one lnk, t s stll questonable f t has perfect nformaton on the degree dstrbuton of the whole network If nformaton s not perfect, t s reasonable to assume that nformaton s more profound about that local subnetwork whch surrounds the gven node Ths leads us to the concluson that n addton to the centralty of nodes, ther dstance n the network (e geodetc dstance) s an mportant factor of lnk formaton as well Based upon these consderatons we extend the Barabas- Albert model n two aspects Frst, the ntal attachment of a gven node to the network s totally random, e the frst lnk can be establshed wth any of the exstng nodes wth equal probablty All other lnks are then formed upon consderng both the centralty (degree) and (geodetc) dstance of exstng nodes We defne the attractveness of node as D N L A = α + β N 1 N 1 where D s the degree of node, L s the geodetc dstance of node from the gven (newly added) node, N s the number of nodes (the sze of the network), whereas α and β are parameters defnng the weght of degree and dstance n lnk formaton Gven the defnton of attractveness above, the probablty of establshng a lnk wth node s for the frst lnk and P 1 P = N = A A for the second and further lnks of a node In order to evaluate the dfference between the standard preferental attachment model of Barabas and Albert (1999) and the extended verson gven above, we run some benchmark smulatons and evaluated two dfferent output measures referrng to dfferent characterstcs of the emergng network, namely clusterng and entropy Clusterng coeffcent Wth a verbal defnton we can thnk of the clusterng coeffcent as a measure of how much one s frends are frends of each other (Cowan, 2005) In other words, the clusterng coeffcent s able to capture local structures n a network: hgh clusterng means dense local structures n a network The clusterng coeffcent s calculated bascally for one specfc node of the network Let s denote the neghbourhood of node by Γ In ths case the cardnalty of ths set, denoted by Γ measures the number of neghbours node has In ths neghbourhood Γ ( Γ 1) / 2 lnks can be formed at most If the number of lnks n ths neghbourhood s the hghest possble, then the clusterng coeffcent s one If there s no lnks among s neghbours, the clusterng coeffcent s zero Let I ( j, = 1 f node j n the neghbourhood of l Γ s a neghbour of tself, and I ( j, = 0 f ths s not true Ths way the clusterng coeffcent of node can be wrtten as C = I ( j, ( Γ 1) j, l Γ Γ / 2 In order to gan an aggregate measure on the level of the network, we compute the average clusterng coeffcent, whch averages C over nodes: C C = N Entropy Usng statstcal entropy we can measure to what extent a gven network s charactersed by scale-free propertes, e to what extent ts degree dstrbuton s exponental meanng that few nodes have lot of lnks whle lot of nodes have few lnks In ths paper we use the specfc relatve entropy measure descrbed by Wu et al (2007) Frst defne I as the relatve degree frequency of node : D I = D Gven ths, the absolute entropy of the gven network s E = I ln I 22 Internatonal Cross-Industry Journal

3 Perspectves of Innovatons, Economcs & Busness, Volume 4, Issue 1, 2010 wwwpebcz However, there s a maxmum and a mnmum for ths expresson Its value s maxmal when all nodes have the same number of lnks In ths case I = 1/ N for all, thus Emax = ln N The value of entropy s mnmal when the network s totally centralsed, e one node has N 1 lnks and the other nodes have only one lnk In ths case E mn = ln(4( N 1)) / 2 The value of normalsed entropy s gven by: NE max = E E max E E The value of NE s 0 when statstcal entropy s maxmal, e when the network s not centralsed (all nodes have the same number of lnks) and ts value s 1 f the entropy s mnmal, e n the case of a totally centralsed network mn Smulaton results As mentoned above, we run some benchmark smulatons wth the models above More specfcally, we run two smulatons One n whch only the degree of other nodes are consdered when establshng a new lnk (e α = 1 and β = 0 n the equaton for attractveness), and one n whch only dstance was consdered ( α = 0 and β = 1 ) The results show two mportant nsghts Frst, t becomes clear that the preferental attachment based on centralty alone s not a necessary condton for the emergence of scale-free networks A growng network n tself can be a suffcent condton leadng to scale-free networks as older nodes per defnton posess more lnks even f lnk formaton s totally random Second, and more nterestng s the result for the two output measures Our smulatons show that hgher role for degree n lnk formaton leads to less clustered networks whle the role for dstance results n more clustered networks That s, the underlyng lnk formaton process has mportant effects on the structure of the emergng network In what follows, we present an emprcal analyss of lnk formaton processes wth regards to the role of degree and dstance n patent nventor networks The database From the data of the European Patent Offce (EPO) we bult up networks of patent nventors across European regons The patent data of the EPO contan nformaton about the address of the nventors and obvously the sector to whch the gven patent belongs We took ths data from 1978 to 2005 and from ths nformaton we extracted co-nventorshps n the case of each patent and bult up the network of patent nventors In the next step ths network was aggregated nto European NUTS2 regons That s, we do not consder network of ndvduals but network of regons, however behnd ths network les the network of ndvduals Further, the network among regons s a weghted one, meanng that an edge between two dfferent regons has a weght referrng to the number of patents on whch nventors of the two regons had worked together 1 Thus we have a network of regons n whch the ntensty of nterregonal relatonshps s reflected by the number of co-nvented patents, nevertheless, the networks are constructed for every year n the perod between 1978 and 2005 The database covers the hgh-tech sector as used by the Eurostat methodology In ths classfcaton the hgh-tech sector covers three subsectors as follows: (1) avaton; (2) computer and automated busness equpment; (3) communcaton technology; (4) lasers; (5) mcro-organsms and genetc engneerng; (6) sem-conductors 2 The database s beng constructed for all European countres, however only part of the countres statstcs s already avalable thus we restrcted our analyss to the three major countres actve n the patent feld Accordng to the patent statstcs of the Eurostat, these countres are Germany, France and the Unted Kngdom, wth reference to the total number of patent applcatons to the EPO Lnk formaton n European co-nventorshp networks In order to carry out ths analyss we bult up a secondary database from the network data Every tme a new lnk was formed n the networks, two records were taken, accordng to the two nodes whch had a new lnk We put the degree of the partner and ther geodetc dstance nto each record Then, n order to yeld comparable results we calculated the rato of the degree measures to the hghest n the actual network and took the nverse of the geodetc dstance Ths way f we have a value of 1 for degree, ths means that the actual node chose the most central node n the network as partner, e the one wth the most lnks A close to zero value, n contrast, shows that a perpheral node was chosen as partner Smlarly n the case of dstance, a value of one represents the closest nodes and a close-to-zero value means a far-away node as partners 3 In our frst analyss we smply cumulated the lnks year after year, so we dsregarded those lnks whch were abandoned (n other words the network of 2005 contans all lnks formed snce 1978) In addton, we consdered the choce of only those nodes whch were not new n the networks, e they had possessed at least one lnk n the prevous year Table 1 contans our man results regardng the calculatons descrbed above The table gves the weghts of 1 Note that the weght of an edge between two regons refers not to the number of personal contacts but the number of co-nvented patents between the two regons 2 The assocated IPC codes are: (1) [B64B, B64C, B64D, B64F, B64G]; (2) [B41J, G06C, G06D, G06E, G06F, G06G, G06J, G06K, G06M, G06N, G06T, G11C]; (3) [H04B, H04H, H04J, H04K, H04L, H04M, H04N, H04Q, H04R, H04S]; (4) [H01S]; (5) [C12M, C12N, C12P, C12Q]; (6) [H01L] 3 It s mportant to note that n ordnary networks the value of 1 n the case of geodetc dstance s meanngless, because these are the neghbours of a node, thus there s no reason to make a new lnk between them In our case, however, lnks are weghted accordng to the number of cooperatons n patent-nventorshp Thus a new lnk among neghbours s acceptable and nterpreted as a more dense cooperaton between two regons 23 Internatonal Cross-Industry Journal

4 Perspectves of Innovatons, Economcs & Busness, Volume 4, Issue 1, 2010 wwwpebcz degree and dstance n new lnk formaton, accordng to the schemes gven above We can not observe substantal dfferences among the dfferent subsectors, however there s a sgnfcant dfference between the weghts of degree and dstance, showng that dstance s a more mportant decson varable than degree Ths fndng supports our remark about the mportance of dstance The overall pcture shows that geodetc dstance s the most mportant factor n lnk formaton whle degree s less mportant, although not nsgnfcant TABLE 1 THE WEIGHT OF DEGREE AND DISTANCE IN LINK FORMATION ON 1 YEAR BASE, DISREGARDING DISSOLVING LINKS Degree Dstance Avaton Computer Communcaton Laser Semconductors Mcro-Genetcs Hgh-tech In order to gve a benchmark to the fndngs above we calculated the same measures but now takng nto account dssolvng lnks as well (see Table 2) The basc dfference here s that the degree of a node can decrease over tme, whle the dstance between two nodes can ncrease due to dssolvng lnks However, the pcture s qualtatvely the same as before wth a slghtly hgher varance n the data Dfferences among subsectors are not sgnfcant and dstance seems to be the mportant choce varable As a fnal queston, t would be nterestng to see f the mportance of these decson varables changed over the years In order to tackle ths ssue, we calculated these measures for every year The basc pcture s smlar to that of presented n Tables 1 and 2, so we only nsert here the overall values for the whole hgh-tech sector TABLE 2 THE WEIGHT OF DEGREE AND DISTANCE IN LINK FORMATION ON 4 YEARS BASE, WITH DISSOLVING LINKS Degree Dstance Avaton Computer Communcaton Laser Semconductors Mcro-Genetcs Hgh-tech As t s clear from Fgure 1, dstance s nvarably the more mportant decson factor durng the years wthout remarkable trend To conclude, we observe that n our sample of nterregonal patent nventor networks geodetc dstance rather than degree seems to be the most mportant decson factor when choosng a partner, and ths pattern of lnk formaton does not change over our examnaton perod Conclusons and further avenues for research In ths paper we presented a straghtforward extenson of the Barabas-Albert model of network evoluton emphaszng the role of geodetc dstance n lnk formaton Our smulaton results show that there are ndeed mportant dfferences n the resultng network structure dependng on the lnk formaton process If dstance s more mportant n lnk formaton, the emergng networks are more clustered, whle f degree s more mportant, the resultng networks are relatvely more centralzed, e they are charactersed by more sgnfcant scale-free propertes FIGURE 1 THE EVOLUTION OF WEIGHTS FOR DEGREE AND DISTANCE IN LINK FORMATION 24 Internatonal Cross-Industry Journal

5 Perspectves of Innovatons, Economcs & Busness, Volume 4, Issue 1, 2010 wwwpebcz Our emprcal results, on the other hand, show that n the case of European patent nventor networks dstance seems to be the mportant decson varable n lnk formaton as opposed to centralty However, there are two mportant remarks Frst, these results do not state that geodetc dstance s the domnant factor n lnk formaton n all networks: n other networks dfferent factors may be mportant Second, as our database gves regonal networks of nventors, the queston arses, to what extent geography are present n our model Although geodetc and geographc dstance are not the same, they are obvously nterrelated One of the possble tasks for future research s to specfy to what extent lnk formaton depends on geographc and not geodetc dstance A straghtforward way would be to measure how much geodetc and geographc dstances are correlated However, the queston remans that whch s the cause and whch s the effect Varga, A, Parag, A, 2009 Academc knowledge transfers and the structure of nternatonal research networks, n: Attla Varga (ed), Unversty knowledge transfers and regonal development: Geography, entrepreneurshp and polcy, Edward Elgar Publshers, pp Wu, J, Tan Y-J, Deng, H-Z and Zhu, D-Z, 2007 Normalzed entropy of rank dstrbuton: A novel measure of heterogenety of complex networks, Chnese Physcs, 16, pp References Balcon, M, Bresch, S, Lsson, F, 2004 Networks of nventors and the role of academa: An exploraton of Italan patent data, Research Polcy 33, pp Barabás, A, 2003 Lnked: How everythng s connected to everythng else what t means for busness, Scence and Everyday Lfe, Pengung Group, USA Barabás, A, Albert, R, 1999 Emergence of scalng n random networks, Scence 286, pp Barabás, A, Albert, R, Jeong, H, 2000 Scale-free characterstcs of random networks: The topology of the world wde web, Physca A 281, pp Bathelt, H, Malmberg, A, Maskell, P, 2002 Clusters and knowledge: Local buzz, global ppelnes and the process of knowledge creaton, DRUID Workng Papers 02-12, DRUID, Copenhagen Busness School, Department of Industral Economcs and Strategy/Aalborg Unversty, Department of Busness Studes Ejermo, O, Karlsson, C, 2006 Interregonal nventor networks as studed by patent conventorshps, Research Polcy, Elsever, vol 35(3), pp Karlsson, C, 2008 Handbook of research on cluster theory, Edward Elgar, Chelthenham, UK Lobo, J, Strumsky, D, 2007 Metropoltan patentng, nventor agglomeraton and socal networks: A tale of two effects, Journal of Urban Economcs 63, pp Lundvall, B, Johnson, B, 1994 The learnng economy, ndustry & nnovaton, , Vol 1, Issue 1, pp Nonaka, I, 1994 A Dynamc theory of organzatonal knowledge creaton, Organzaton Scence, Vol 5, No 1, pp Ozman, M, 2006 Networks and nnovaton : A survey of emprcal lterature, Workng Papers of BETA , Bureau d'econome Théorque et Applquée, ULP, Strasbourg Ter Wal, A, 2008 Cluster emergence and network evoluton: a longtudnal analyss of the nventor network n Sopha- Antpols, Papers n Evolutonary Economc Geography, Internatonal Cross-Industry Journal