Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks

Abstract

Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data. Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the fields of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere's three-dimensional geopotential height field uncovers known as well as interesting novel features of the atmosphere's vertical stratification and general circulation. Specifically, the new measure "cross-betweenness" identifies regions which are particularly important for mediating vertical wind field interactions. The promising results obtained by following the coupled climate subnetwork approach present a first step towards an improved understanding of the Earth system and its complex interacting components from a network perspective.

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• Percolation in Multiplex Networks with Overlap
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• Towards real-world complexity: an introduction to multiplex networks
• Structure of Triadic Relations in Multiplex Networks
• Successful strategies for competing networks
• Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package
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• Geometric detection of coupling directions by means of inter-system recurrence networks
• Multiple Tipping Points and Optimal Repairing in Interacting Networks
• Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting networks ensembles
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• Percolation framework to describe El Niño conditions
• Resilience of Networks Formed of Interdependent Modular Networks
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• Robustness of a Network Formed of Spatially Embedded Networks
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• Climate Network Structure Follows North Atlantic Oscillation Phases
• Time Series Analysis via Network Science: Concepts and Algorithms
• Node-weighted interacting network measures improve the representation of real-world complex systems
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• Correlations between weights and overlap in ensembles of weighted multiplex networks
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• Global Climate network evolves with North Atlantic Oscillation phases: Coupling to Southern Pacific Ocean
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