The evolution of triangular research and innovation collaborations in the European area

In the current study, we examine the multiplex network of patents and European Research Framework Programmes (FPs) aiming to uncover temporal variations in the formation patterns of triangles (a fully connected network between any three nodes). The multiplex network that we study consists of two layers whose nodes are the NUTS2 regions, and collaborations between scientists or inventors of different regions result to a link. We split the network temporally into 28 shorter sub-networks with a span of 6 years each, and calculate the number of triangles formed at the end of the 6-year period. Next, we shuffle the data creating 50 randomized networks for each of the 28 six-year sub-networks, in order to identify whether there is a hidden mechanism that favors a non-random behavior. Real and shuffled data are compared using a z-score, a measure of the differences of standard deviations between them. In addition, we repeat the same analysis using the clustering coefficient whose large value can signify a strong collaboration pattern for a given node. The results from the temporal analysis of real vs randomized multiplex networks, show that triangular FP collaborations tend to be favored over random ones, while in patents the case is strongly the opposite. Furthermore, results using triangles tend to be more comprehensive as opposed to those of the clustering coefficient. Finally, we identify which NUTS2 regions frequently exhibit a high clustering coefficient in either of the layers, and we present a map with these values for all regions. The results of this research can help policy making organizations understand the spatial dimension of subsidized research and patented innovation collaboration networks and perhaps to strengthen regional collaboration.