Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes

Marc Wiedermann, Jonathan F. Donges, Jürgen Kurths, Reik V. Donner

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30 Citations (Scopus)
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Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their macroscopic properties. Here, we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve global and local statistics associated with the nodes' embedding in a metric space. Comparing the original network's and the resulting surrogates' global characteristics allows to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links. We apply our framework to various real-world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes' spatial embedding. Depending on the actual performance of the proposed null models, the networks are categorized into different classes. Since many real-world complex networks are in fact spatial networks, the proposed approach is relevant for disentangling underlying complex system structure from spatial embedding of nodes in many fields, ranging from social systems over infrastructure and neurophysiology to climatology.
Original languageEnglish
Article number042308
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number4
Publication statusPublished - 12 Apr 2016

Bibliographical note

MW and RVD have been supported by the German Federal Ministry for Education and Research (BMBF) via the Young Investigators Group CoSy-CC2 (grant
no. 01LN1306A). JFD thanks the Stordalen Foundation and BMBF (project GLUES) for financial support. JK acknowledges the IRTG 1740 funded by DFG and FAPESP. MT Gastner is acknowledged for providing his data on the airline, interstate, and Internet network. P Menck thankfully provided his data on the Scandinavian power grid. We thank S Willner on behalf of the entire zeean team for providing the data on the world trade network. All computations have been performed using the Python package pyunicorn [41] that is available at


  • physics.soc-ph
  • cs.SI


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