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We investigate the impact of borders on the topology of spatially embedded networks. Indeed territorial subdivisions and geographical borders significantly hamper the geographical span of networks thus playing a key role in the formation of network communities. This is especially important in scientific and technological policy-making, highlighting the interplay between pressure for the internationalization to lead towards a global innovation system and the administrative borders imposed by the national and regional institutions. In this study we introduce an outreach index to quantify the impact of borders on the community structure and apply it to the case of the European and US patent co-inventors networks. We find that (a) the US connectivity decays as a power of distance, whereas we observe a faster exponential decay for Europe; (b) European network communities essentially correspond to nations and contiguous regions while US communities span multiple states across the whole country without any characteristic geographic scale. We confirm our findings by means of a set of simulations aimed at exploring the relationship between different patterns of cross-border community structures and the outreach index.
Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years a multitude of diverse, ad hoc solutions to this problem have been introduced. Here we propose that simple and well-understood
Researchers use community-detection algorithms to reveal large-scale organization in biological and social networks, but community detection is useful only if the communities are significant and not a result of noisy data. To assess the statistical s
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