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Network theory provides a rich toolbox consisting of methods, measures, andmodels for studying the structure and dynamics of complex systems found innature, society, or technology. Recently, it has been pointed out that manyreal-world complex systems are more adequately mapped by networks ofinteracting or interdependent networks, e.g., a power grid showinginterdependency with a communication network. Additionally, in many real-worldsituations it is reasonable to include node weights into complex networkstatistics to reflect the varying size or importance of subsystems that arerepresented by nodes in the network of interest. E.g., nodes can representvastly different surface area in climate networks, volume in brain networks oreconomic capacity in trade networks. In this letter, combining both ideas, wederive a novel class of statistical measures for analysing the structure ofnetworks of interacting networks with heterogeneous node weights. Using aprototypical spatial network model, we show that the newly introducednode-weighted interacting network measures indeed provide an improvedrepresentation of the underlying system's properties as compared to theirunweighted analogues. We apply our method to study the complex networkstructure of cross-boundary trade between European Union (EU) and non-EUcountries finding that it provides important information on trade balance andeconomic robustness.

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