The Community Structure of European R&D Collaboration

Abstract

We characterize the geography of communities in the European R&D network using data on R&D projects funded by the fifth European Framework Programme. Communities are subnetworks whose members are more tightly linked to one another than to other members of the network. We characterize the communities by means of spatial interaction models, and estimate the impact of separation factors on the variation of cross-region collaboration activities in a given community at the level of 255 NUTS-2 regions. The results demonstrate that European R&D networks are made up of distinct, relevant substructures characterized by spatially heterogeneous community groups.

Appendices

Appendix 1

NUTS is an acronym of the French for the “nomenclature of territorial units for statistics”, which is a hierarchical system of regions used by the statistical office of the European Community for the production of regional statistics. At the top of the hierarchy are NUTS-0 regions (countries) below which are NUTS-1 regions and then NUTS-2 regions. This study disaggregates Europe’s territory into 255 NUTS-2 regions located in the EU-25 member states (except Cyprus and Malta) plus Norway and Switzerland. We exclude the Spanish North African territories of Ceuta y Melilla, the Portuguese non-continental territories Azores and Madeira, and the French Departments d’Outre-Mer Guadeloupe, Martinique, French Guayana and Reunion.

Appendix 2

We list here the most active regions for the eight communities considered in depth in this paper. For each community, we give the 20 regions with the highest number of participations in projects from the community. The number of participations is shown parenthetically. Regions are given in descending order of the number of participations.

Aerospace:	Île de France (1232), Comunidad de Madrid (691), Oberbayern (581), Danmark (526), Noord-Holland (440), Köln (365), Attiki (320), Inner London (306), Lombardia (285), Greater Manchester (276), Bedfordshire & Hertfordshire (271), Etelä-Suomi (269), Campania (266), Midi-Pyrénées (248), Dytiki Ellada (247), Outer London (243), Lazio (241), Liguria (239), Hampshire & Isle of Wight (225), País Vasco (224)
Aquatic Resources:	Agder og Rogaland (97), North Eastern Scotland (93), Danmark (91), Comunidad de Madrid (73), Flevoland (67), Noord-Holland (67), Hamburg (57), Algarve (55), Kriti (49), Attiki (47), Northern Ireland (39), Southern and Eastern (38), East Anglia (31), Andalucía (26), País Vasco (25), Galicia (24), Prov. West-Vlaanderen (22), Etelä-Suomi (21), Eastern Scotland (18), Vestlandet (17)
Electronics:	Île de France (3537), Oberbayern (1390), Attiki (1182), Rhône-Alpes (1012), Comunidad de Madrid (863), Köln (831), Lombardia (768), Lazio (728), Zuid-Holland (578), Danmark (563), Berkshire, Buckinghamshire & Oxfordshire (559), Berlin (540), Région lémanique (531), Noord-Brabant (523), Inner London (519), Cataluña (509), Prov. Vlaams-Brabant (483), Southern and Eastern (471), Stuttgart (433), Outer London (430)
Environment:	Île de France (1020), Danmark (782), Aττική/ Attiki (627), Etelä-Suomi (580), Lazio (565), Zuid-Holland (526), Noord-Holland (479), Comunidad de Madrid (426), East Anglia (414), Lombardia (395), Southern and Eastern (378), Cataluña (373), Stockholm (357), Gelderland (355), Wien (350), Andalucía (326), Utrecht (306), Karlsruhe (305), Agder og Rogaland (295), Hampshire & Isle of Wight (294)
Ground Transport:	Île de France (846), Stuttgart (698), Piemonte (587), Köln (385), Zuid-Holland (346), Lombardia (323), Oberbayern (293), Västsverige (290), Etelä-Suomi (226), Berkshire, Buckinghamshire & Oxfordshire (218), Kentriki Makedonia (200), Lazio (177), Hannover (175), País Vasco (168), Comunidad de Madrid (144), Steiermark (141), Noord-Holland (127), Prov. Vlaams-Brabant (123), Rhône-Alpes (119), Darmstadt (118)
Information Processing:	Eastern Scotland (40), Lombardia (21), Etelä-Suomi (20), Lazio (18), Zuid-Holland (16), Hampshire & Isle of Wight (14), Île de France (12), Attiki (11), Outer London (11), Stockholm (10), Sør-Østlandet (10), Danmark (7), Darmstadt (7), Southern and Eastern (7), Noord-Holland (5), Comunidad de Madrid (4), Essex (4), Limburg (NL) (4), Luxembourg (Grand-Duché) (4), Espace Mittelland (3)
Life Sciences:	Île de France (1860), Danmark (1055), Gelderland (843), Outer London (703), Lombardia (658), East Anglia (637), Comunidad de Madrid (636), Inner London (605), Cataluña (569), Zuid-Holland (547), Utrecht (538), Lazio (529), Stockholm (521), Karlsruhe (519), Prov. Vlaams-Brabant (495), Rhône-Alpes (494), Southern and Eastern (481), Oberbayern (458), Région de Bruxelles-Capitale/Brussels Hoofdstedelijk Gewest (442), Eastern Scotland (396)
Sea Transport:	Danmark (190), Liguria (144), Hamburg (137), Île de France (135), Outer London (115), South Western Scotland (105), Agder og Rogaland (99), Zuid-Holland (88), Attiki (76), Pays de la Loire (61), Bremen (58), Surrey, East & West Sussex (48), Västsverige (43), Comunidad de Madrid (40), Etelä-Suomi (36), Friuli-Venezia Giulia (35), Gelderland (35), Hampshire & Isle of Wight (33), Trøndelag (32), Région de Bruxelles-Capitale/Brussels Hoofdstedelijk Gewest (30)

Appendix 3

Raghavan et al. (2007) proposed a label propagation algorithm (LPA) for identifying communities in networks. Community membership is tracked by labels assigned to the graph vertices; a community is a set of all vertices with a particular label. Each vertex is assigned a single label, and thus belongs to a single community.

Call a label satisfactory for a vertex when no other label occurs more frequently among its neighbors. The core of the LPA is a process of replacing unsatisfactory labels with satisfactory ones, continuing until all vertices have satisfactory labels. This idea is illustrated in Fig. 9.3 using a toy network with visually apparent community structure. In Fig. 9.3a, there are three different labels, shown by the vertex shading. The black and white labels are all satisfactory for their vertices. Of the three gray labels, two are unsatisfactory for their vertices, shown by double borders on the vertices: one neighbors a single gray vertex and two black vertices, the other neighbors a single gray vertex and three white vertices. The third gray label is satisfactory: the vertex neighbors two gray vertices and two black vertices. In Fig. 9.3b, all vertices have satisfactory labels.

Fig. 9.3

Community identification with label propagation

The algorithm begins from a state where all vertices have different labels (and thus are generally all unsatisfactory). Taken in random order, the vertices are considered to see whether their labels are satisfactory and updated to be satisfactory when not; if multiple labels would be satisfactory, one is chosen at random. For the example network shown in Fig. 9.3a, the two vertices with gray labels must then be updated, one to have a black label, the other to have a white label; note that changing these two gray labels will cause the third gray label to become unsatisfactory. Multiple relabeling passes are made through the vertices, with the algorithm halting when all vertices have a satisfactory label, such as in Fig. 9.3b.

The LPA offers a number of desirable qualities. As described above, it is conceptually simple, being readily understood and quickly implemented. The algorithm is efficient in practice. Each relabeling iteration through the vertices has a computational complexity linear in the number of edges in the graph. The total number of iterations is not a priori clear, but relatively few iterations are needed to assign the final label to most of the vertices (typically over 95 % of vertices in 5 iterations, see Raghavan et al. 2007; Leung et al. 2009).

The LPA defines communities procedurally, rather than as optimization of an objective function, and thus provides no intrinsic measure for the quality of communities found. To assess community quality, we can introduce an auxiliary measure, such as the popular modularity measure (Newman and Girvan 2004); in this work, more suitable is a version of modularity specialized to bipartite networks (Barber 2007). Using modularity, communities found using LPA are seen to be of high quality (Raghavan et al. 2007): label propagation is both fast and effective. Indeed, Leung et al. (2009) have proposed extensions to the label propagation algorithm that make it comparable to the best algorithms for community detection in quality and efficient enough to analyze very large networks.

Barber and Clark (2009) have elucidated the connection between label propagation and modularity, showing that modularity can be maximized by propagating labels subject to additional constraints and proposing several variations of the LPA. In this paper, we make use of a hybrid, two-stage label propagation scheme, consisting of the LPAr variant followed by the LPAb variant (see Barber and Clark 2009 for details). LPAr is defined similarly to the original LPA presented above, but with additional randomness to allow the algorithm to avoid premature termination. In practice, this produces better communities as measured by modularity than does LPA. LPAb imposes constraints on the label propagation so that the algorithm identifies a local maximum in the bipartite modularity. The overall hybrid algorithm thus belongs to the recent class of algorithms based on modularity maximization (for a survey, see Fortunato 2010).