  In the current study, we examine the multiplex network of patents and
European Framework Programmes (FPs) aiming to uncover temporal variations in
the formation patterns of triangles (a fully connected network between any
three nodes). More specifically, the multiplex network consists of two layers
whose nodes are the NUTS2 regions. On the first layer we depict the regions of
the inventors that collaborated for the creation of a patent, and on the second
those of the scientists in European Framework Programme (FP) funded projects. A
link between two nodes exists when scientists or inventors from different
regions collaborate. 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
again 28 six-year randomized 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, which is the number of triangles over the number of triples
(possible triangles). The results 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.
