Potsdam Institute for Climate Impact Research (PIK)-Member of the Leibnitz Association, Telegrafenberg A31, 14473 Potsdam, Germany.
Department of Physics, Humboldt University, Newtonstraße 15, 12489 Berlin, Germany.
Phys Rev E. 2019 Jan;99(1-1):012301. doi: 10.1103/PhysRevE.99.012301.
Spatially embedded networks have attracted increasing attention in the past decade. In this context, network characteristics have been introduced which explicitly take spatial information into account. Among others, edge directionality properties have recently gained particular interest. In this work, we investigate the applicability of mean edge direction, anisotropy, and local mean angle as geometric characteristics in complex spherical networks. By studying these measures, both analytically and numerically, we demonstrate the existence of a systematic bias in spatial networks where individual nodes represent different shares on a spherical surface, and we describe a strategy for correcting for this effect. Moreover, we illustrate the application of the mentioned edge directionality properties to different examples of real-world spatial networks in spherical geometry (with or without the geometric correction depending on each specific case), including functional climate networks, transportation, and trade networks. In climate networks, our approach highlights relevant patterns, such as large-scale circulation cells, the El Niño-Southern Oscillation, and the Atlantic Niño. In an air transportation network, we are able to characterize distinct air transportation zones, while we confirm the important role of the European Union for the global economy by identifying convergent edge directionality patterns in the world trade network.
在过去的十年中，嵌入空间的网络引起了越来越多的关注。在这种情况下，已经引入了网络特征，这些特征明确考虑了空间信息。其中，边缘方向性特性最近引起了特别的兴趣。在这项工作中，我们研究了平均边缘方向、各向异性和局部平均角度作为复杂球面网络中的几何特征的适用性。通过分析和数值研究这些措施，我们证明了在空间网络中存在个体节点代表球面不同份额的系统偏差，并且我们描述了一种校正这种效应的策略。此外，我们还说明了所提到的边缘方向性特性在不同的真实空间网络示例中的应用，包括球面几何中的功能气候网络、交通和贸易网络（根据每个具体情况是否进行几何校正）。在气候网络中，我们的方法突出了相关模式，例如大规模环流细胞、厄尔尼诺-南方涛动和大西洋尼诺。在航空运输网络中，我们能够描述不同的航空运输区域，同时通过识别世界贸易网络中收敛的边缘方向性模式，我们确认了欧盟对全球经济的重要作用。
