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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.