In the current study, we examine a multiplex collaboration network to find out if there is a preference in forming extended, triangularly shaped, collaborations or just regular links. The first layer corresponds to the collaborations that have accomplished for the creation of patents, while the second one to the collaborations between scientists that took part in Framework Programme projects. The nodes of the multiplex are the NUTS2 geographic regions of the inventors-scientists, while a link between two such regions exists when scientists from different regions collaborate. In our analysis we use the notion of triangles, which is a fully connected network between any three nodes. Initially, we split the data into 28 networks, each one having a span of 6 years. At the end of each network we calculate the number of triangles on the patent and the FP layer, as well as their common network. In order to identify whether the observed behavior is the anticipated one, we shuffle the data, repeat the analysis, and compare the two results using z-score. We also repeat the procedure, this time by calculating clustering coefficient, which is the number of triangles over the number of possible triangles. Both metrics show that the FP collaborations tend to be extended, while on the patent and the common layer, they tend to be more isolated. Finally, we rank the NUTS2 regions according to their clustering coefficient over time and produce a map with these values for all regions, figure 1. The current analysis could prove useful for policy makers in order to understand the spatial dimension of research and innovation collaboration networks.
