Edge directionality properties in complex spherical networks

Abstract

Spatially embedded networks have attracted increasing attention in the last decade. In this context, new types of 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 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 like 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.

References in corpus (18)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Community structure in social and biological networks
• The architecture of complex weighted networks
• Spatial Networks
• Topology of the World Trade Web
• The backbone of the climate network
• The spatial structure of networks
• Random planar graphs and the London street network
• A Random Growth Model for Power Grids and Other Spatially Embedded Infrastructure Networks
• Urban road networks -- Spatial networks with universal geometric features? A case study on Germany's largest cities
• Disentangling different types of El Niño episodes by evolving climate network analysis
• From brain to earth and climate systems: Small-world interaction networks or not?
• Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes
• Mapping and discrimination of networks in the complexity-entropy plane
• Node-weighted interacting network measures improve the representation of real-world complex systems
• Hierarchical structures in Northern Hemispheric extratropical winter ocean-atmosphere interactions
• Edge anisotropy and the geometric perspective on flow networks