Cerina Federica, Chessa Alessandro, Pammolli Fabio, Riccaboni Massimo
1] Università degli Studi di Cagliari, Cagliari, Italy [2] Linkalab, Complex Systems Computational Laboratory, Cagliari 09129, Italy.
1] IMT Institute for Advanced Studies Lucca, Lucca 55100, Italy [2] Linkalab, Complex Systems Computational Laboratory, Cagliari 09129, Italy.
Sci Rep. 2014 Apr 1;4:4546. doi: 10.1038/srep04546.
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.
我们研究边界对空间嵌入网络拓扑结构的影响。实际上，领土划分和地理边界显著阻碍了网络的地理跨度，因此在网络社区的形成中起着关键作用。这在科技政策制定中尤为重要，凸显了推动国际化走向全球创新体系的压力与国家和地区机构施加的行政边界之间的相互作用。在本研究中，我们引入一个拓展指数来量化边界对社区结构的影响，并将其应用于欧美专利共同发明人网络的案例。我们发现：（a）美国的连通性随距离的幂次衰减，而我们观察到欧洲的衰减速度更快，呈指数衰减；（b）欧洲网络社区基本上对应于国家和相邻地区，而美国的社区跨越全国多个州，没有任何特征性的地理尺度。我们通过一组模拟来验证我们的发现，这些模拟旨在探索跨境社区结构的不同模式与拓展指数之间的关系。
