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ABSTRACT
Centrality of regions in R&D networks: a new measurement approach using the concept of bridging paths. Regional Studies. This paper introduces a novel measure of regional centrality in the context of research and development (R&D) networks. It first demonstrates some substantial problems of social network analysis (SNA)-based centrality measures to cope with regional R&D networks in a meaningful way. It then proposes a new measurement approach of regional network centrality based on the concept of interregional bridging paths (indirect connections at the regional level). The paper shows that the formal definition of the regional bridging centrality measure can be expressed in terms of three simple components: the participation intensity of a region in interregional R&D collaborations; its relative outward orientation in terms of all established links; and its diversification of R&D collaborations among partner regions. The measure and its behaviour with respect to other conventional centrality measures are illustrated by its application to the European co-patent network at the NUTS-2 level.
摘要
区域在研发网络中的核心性：运用“连结路径”概念的崭新测量方法。Regional Studies. 本文引介一个测量区域在研发（R&D）网络脉络中的核心性之创新方法。本文首先証实根据社会网络分析（SNA）的核心性测量的若干重大问题，以有意义的方式应对区域?R&D网络。本文接着提出根据“跨区域连结路径（区域层级的间接连结）)”概念的区域网络核心性之崭新测量方法。本文显示，区域连结核心性测量的正式定义，能够以三大简单的元素表现之：区域在跨区域R&D合作中参与的强度；其就所有已建立的连结而言的相对对外倾向；以及其与伙伴区域之间?R&D合作的多样性。本文透过将该测量方法运用于欧盟在NUTS－2层级的共同专利网络，描绘该测量及其之于其他传统核?心性测量的作用。
RÉSUMÉ
La centralité des régions dans les réseaux de R et D: une nouvelle méthode de mesure employant la notion de liens de connexité. Regional Studies. Cet article présente une mesure originale de la centralité régionale dans le cadre des réseaux de recherche et de développement (R et D). Il démontre, dans un premier temps, certains problèmes importants concernant des mesures de la centralité basées sur l'analyse des réseaux sociaux (Social Network Analysis; SNA) pour faire face aux réseaux de R et D de façon significative. Il propose ensuite une nouvelle méthode de mesure de la centralité des réseaux régionaux fondée sur la notion de liens de connexité interrégionaux (des liens indirects au niveau régional). L'article montre que la définition officielle de la mesure des liens de connexité régionale peut être exprimée en termes de trois composants très simples: le taux de participation d'une région aux collaborations en R et D; son orientation relative vers l'extérieur en termes de toutes les connexions bien établies; et sa diversification des collaborations en R et D parmi les régions partenaires. La mesure et son comportement par rapport à d'autres mesures de la centralité sont illustrés par l'application de l'exemple du réseau européen en matière de brevets conjoints au niveau NUTS 2.
ZUSAMMENFASSUNG
Zentralität von Regionen in F&E Netzwerken: Ein neuer Messansatz unter Verwendung des 'bridging paths' Konzeptes. Regional Studies. In dieser Arbeit wird ein neues Maß zur Erfassung der Zentralität von Regionen in F&E Netzwerken vorgestellt. Ausgehend von konzeptionellen Problemen bei der Verwendung konventioneller Maße der Sozialen Netzwerkanalyse (SNA) bei der Anwendung auf diskrete räumliche Aggregate, wie zB Regionen, wird ein neuer Messansatz vorgeschlagen. Basierend auf dem Konzept der 'bridging paths' (indirekte Verknüpfungen zwischen Regionen) wird gezeigt, dass die sogenannte 'Bridging'-Zentralität einer Region formal eine Funktion von drei Komponenten darstellt: die Beteiligungsintensität einer Region im Netzwerk, deren relative Außenorientierung und die Diversifikation ihrer Verbindungen. Die Funktionsweise des neuen Maßes wird durch dessen Anwendung auf das europäische Ko-Patentnetzwerk auf der Ebene von NUTS-2 Regionen illustriert.
RESUMEN
Centralidad de las regiones en redes de I+D: un nuevo enfoque de medición mediante el concepto de rutas vinculadas. Regional Studies. En este artículo introducimos una nueva medida de centralidad regional en el contexto de las redes de investigación y desarrollo (I+D). Primero mostramos algunos problemas sustanciales de las medidas de centralidad basadas en el análisis de las redes sociales a la hora de tratar con las redes regionales de I+D mediante un método lógico. Luego proponemos un nuevo enfoque de medición de la centralidad de las redes regionales basado en el concepto de rutas vinculadas interregionales (conexiones indirectas de ámbito regional). Mostramos que la definición formal de la medida de la centralidad de vínculos regionales puede expresarse en términos de tres componentes simples: la intensidad de la participación de una región en las colaboraciones interregionales de I+D, su relativa orientación externa en términos de todos los vínculos establecidos y su diversificación de las colaboraciones de I+D entre las regiones asociadas. La medida y su comportamiento con respecto a otras medidas de centralidad convencionales se ilustran por su aplicación en la red europea de patentes compartidas en el nivel NUTS-2.
ACKNOWLEDGEMENTS
The authors thank the three anonymous referees for providing helpful comments.
DISCLOSURE STATEMENT
No potential conflict of interest was reported by the authors.
SUPPLEMENTAL DATA
Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/00343404.2016.1269885
Notes
1. The effectiveness of interregional network linkages is further driven by other dimensions working at the micro-level and assignable to the characteristics of organizations within a region, such as the distinct institutional background and capabilities (Singh, Citation2005; Ponds, van Oort, & Frenken, Citation2007) as well as the degree of cognitive proximity of partners (Nooteboom, Van Haverbeke, Duysters, Gilsing, & van den Oord, Citation2007). The individual knowledge base, absorptive capacity and internal resources of actors to manage a wider range of (explorative and exploitative) network ties might further play a decisive role in how R&D linkages are established and in which way regional organizations can benefit from them (Giuliani, Citation2007).
2. This model is an adaptation of the one in Bergé (Citation2016).
3. Assuming that the matching mechanism is based on preferential attachment instead of being purely random would not lead to any significant changes to the closed form of the expected number of bridging paths. Indeed, the ENB under preferential attachment would merely be an inflation of the ENB under the random matching (the theoretical details are provided in Bergé, Citation2016, appx B).
4. The proof is given in Appendix A1 in the supplemental data online.
5. The assumption of proportionality between the number of actors and the number of R&D interactions is not limiting. Indeed, to assess empirically whether this were the case, we used data on patents, detailed in the fifth section. Here we identify the R&D interactions as co-patents and the actors of the network as the inventors. Further, we used a simple algorithm to identify the inventors (two inventors from the same region are considered identical if they have the same first and last names). The results show a 98% correlation between the number of inventors in a given region and the number of patents produced by this region.
6. Degree is calculated here as the number of unique R&D interactions in which the actors of a region are involved. The eigenvector and betweenness centrality are computed using the package igraph available in the statistical software R. Both measures are based on the weighted regional co-patent network where the nodes are regions, and the linkages between any two regions are the number of patents co-invented by actors from these two regions. Due to the nature of the network, we used the weighted version of both the betweenness and the eigenvector centrality.
7. The use of different time frames to build the dataset, such as 2004–06 or 2008–10, implies no important differences on the results.
8. We use the location of inventors to map the interregional collaboration network. This choice is made in order to ensure that a patent’s location matches the place where it has been produced. Indeed, an alternative way to locate the patents would have been to use the applicants’ addresses. However, an applicant’s address often refers to the firm’s headquarters, whose location is likely to be different to that of the place of production. Therefore, using applicants’ addresses to locate the patents would have yielded another network that could have been interesting to analyse. Nevertheless, we stick here to interregional collaborations between ‘places of production’, in line with the literature (e.g., Fleming, King, & Juda, Citation2007b).
9. Formally, the transformation applied to each centrality measure is: .
10. The spatial distribution of all four centrality measures over the EU is shown by Figure C3 in the supplemental data online.
11. The performance of German regions is not merely driven by the fact that German NUTS-2 regions are usually smaller geographical aggregates than NUTS-2 regions in other EU countries, which could drive up their number of interregional collaborations at the national level. Indeed, when we redo the analysis taking German regions at the NUTS-1 level while keeping other regions at the NUTS-2 level, German regions still trust the top of the rankings.
12. The national versus international nature of collaborations and its effects on regional network centrality might deserve further attention and constitute an interesting route for the further development of the regional bridging centrality measure. We thank an anonymous reviewer for raising this issue.