Node-weighted measures for complex networks with directed and weighted edges for studying continental moisture recycling

D. C. Zemp, M. Weidermann, J. Kurths, A. Ramming, J. F. Donges

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18 Citations (Scopus)


In many real-world networks nodes represent agents or objects of different sizes or importance. However, the size of the nodes is rarely taken into account in network analysis, possibly inducing bias in network measures and confusion in their interpretation. Recently, a new axiomatic scheme of node-weighted network measures has been suggested for networks with undirected and unweighted edges. However, many real-world systems are best represented by complex networks which have directed and/or weighted edges. Here, we extend this approach and suggest new versions of the degree and the clustering coefficient associated to network motifs for networks with directed and/or weighted edges and weighted nodes. We apply these measures to a spatially embedded network model and a real-world moisture recycling network. We show that these measures improve the representation of the underlying systems' structure and are of general use for studying any type of complex network.
Original languageEnglish
Article number58005
Number of pages5
JournalEurophysics Letters
Issue number5
Publication statusPublished - 3 Sept 2014

Bibliographical note

This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP. JFD acknowledges funding from the Stordalen Foundation and BMBF (project GLUES). The research of JK is partly supported by the grant No. 02.B.49.21.0003 with Lobachevsky State University of Nizhny Novgorod. AR acknowledges funding from EU-FP7 AMAZALERT (raising the alert about critical feedbacks between climate and long-term land-use change in the Amazon) project, grant agreement No. 282664 and MW acknowledges funding from the IRTG 9751 and the German Federal Ministry for Science and Education via the BMBF Young Investigators Group CoSy-CC2 (grant No. 01LN1306A). We thank R. J. van der Ent for providing us with the model output, C.-F. Schleussner for discussions and K. Thonicke for comments on the manuscript.


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