Figure 1
Outreach index.
The outreach index 
of a cross-border community measures the fraction of cross border and external ties (dashed lines in the plot), weighted by distance and relational intensity. The home base of the community is defined according to three criteria: simple |dQ|, |dQ| * S, where S is the node strengh and internal link density Wint. When boundaries constrain the span of network communities – as for European R&D collaborations – the outreach index lean towards zero. Conversely, if borders do not affect the shape of network communities – like in the 
. The topology of the network is conditioned by the presence of borders, which significantly reduces the probability of cross-border connectivity.
