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

TL;DR

This paper introduces a hierarchy of null models for spatially embedded networks to distinguish structural features arising from spatial embedding versus other factors, improving understanding of complex systems across various fields.

Contribution

It proposes novel null models that preserve spatial statistics, enabling better analysis of how spatial embedding influences network structure compared to standard models.

Findings

Models better capture macroscopic properties than standard random models

Networks categorized based on null model performance

Framework applicable across diverse real-world spatial networks

Abstract

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.