Node-weighted interacting network measures improve the representation of real-world complex systems

¹ Potsdam Institute for Climate Impact Research - P.O. Box 60 12 03, 14412 Potsdam, Germany, EU
² Department of Physics, Humboldt University - Newtonstr. 15, 12489 Berlin, Germany, EU
³ Stockholm Resilience Centre, Stockholm University - Kräftriket 2B, 114 19 Stockholm, Sweden, EU
⁴ Institute for Complex Systems and Mathematical Biology, University of Aberdeen - Aberdeen AB24 3FX, UK, EU

^(a) marcw@physik.hu-berlin.de
^(b) donges@pik-potsdam.de

Received: 4 January 2013
Accepted: 5 April 2013

Abstract

Many real-world complex systems are adequately represented by networks of interacting or interdependent networks. Additionally, it is often reasonable to take into account node weights such as surface area in climate networks, volume in brain networks, or economic capacity in trade networks to reflect the varying size or importance of subsystems. Combining both ideas, we derive a novel class of statistical measures for analysing the structure of networks of interacting networks with heterogeneous node weights. Using a prototypical spatial network model, we show that the newly introduced node-weighted interacting network measures provide an improved representation of the underlying system's properties as compared to their unweighted analogues. We apply our method to study the complex network structure of cross-boundary trade between European Union (EU) and non-EU countries finding that it provides relevant information on trade balance and economic robustness.