Repeated collaboration of inventors across European regions

Figures & data

Figure 1. Schematic visualization of deriving the inter-regional co-inventor network. Source: Own illustration.

Figure 2. Schematic visualization of the network variables. Source: Own illustration.

Table 1. Descriptive statistics and correlation of the standardized main explanatory variables.

	Mean	Min	Max	Cosine	Proximity	Jaccard
Cosineij	0	−1.564	3.376	1
Proximityij	0	−2.749	8.364	0.258	1
Jaccardij	0	−0.776	12.021	0.401	0.652	1

Source: Own calculation based on OECD REGPAT 2015.

Table 2. Characteristics of the co-inventor network and the repeated collaboration network.

	Collaboration	Repeated Collaboration
Number of Individual Collaborations	772,378	41,883
Number of Region Ties	46,857	6,200
Density of the Region Network	0.05	0.006
Number of Communities in the Region Network*	7	23
Modularity of the Region Network	0.372	0.584
Relative Modularity of the Region Network	0.329	0.379

Source: Own calculation based on OECD REGPAT 2015.

Note: *Communities of size 1 are excluded.

Figure 3. Spatial patterns of inventor collaboration and repeated collaboration networks of European regions. Source: Own calculation based on OECD REGPAT 2015. Note: (A) The maximum spanning tree of the collaboration network across NUTS 3 regions in Europe reveals the importance of national centers. (B) Most of the repeated collaborations remain within country borders, and strongest ties are concentrated within close proximity of innovative hubs. (C) The 7 communities of the collaboration network span across countries, with the exception of Germany that is divided into two communities and Italy, but are mostly concentrated in large regions. (D) Repeated collaboration is organized into 23 smaller-scale clusters.

Figure 4. The probability of collaboration and repeated collaboration as a function of region-to-region characteristics. Source: Own calculation based on OECD REGPAT 2015. Note: (A) Distance ($D_{b=20\mathrm{k}\mathrm{m}}$) decay is smooth for geographically proximate collaboration and repeated collaboration, following a linear decay on log-log scale with the exponents −1.05 and −1.27 for distances larger than 100  km. (B) The overlap between technological profiles of regions, measured by cosine similarity ($C_{b=0.025}$), increases the probability of collaboration with a growing intensity as similarity rises. (C) The probability of collaboration grows linearly on a logarithmic scale as the share of common third connected regions, measured by Jaccard similarity ($J_{b=0.01}$), increases. The exponent is 3.86 for collaboration and 5.67 for repeated collaboration.

Figure 5. Results of the multivariate estimations. Source: Own calculation based on OECD REGPAT 2015. Note: (A) Considering single effects only, we observe that the probability of collaboration is mostly increased by common third partners, while repeated ties gain probability if regions are geographically proximate. (B) Interaction effects reveal that repeated ties gain extra probability if regions are geographically proximate, technologically similar and connected to the same set of regions at the same time.