Inferring hierarchical structure of spatial and generic complex networks through a modeling framework

TL;DR

This paper introduces a modeling framework to infer hierarchical and community structures in spatial and complex networks, enabling multi-resolution analysis and applied to US interstate migration data.

Contribution

It presents a novel inference mechanism for uncovering hierarchical and community structures at various resolutions in complex and spatial networks.

Findings

Successfully inferred hierarchical structures in US interstate migration network.

Demonstrated the method's ability to identify space-independent community structures.

Provided a versatile approach applicable to different types of complex networks.

Abstract

Our recent paper [Grauwin et al. Sci. Rep. 7 (2017)] demonstrates that community and hierarchical structure of the networks of human interactions largely determines the least and should be taken into account while modeling them. In the present proof-of-concept pre-print the opposite question is considered: could the hierarchical structure itself be inferred to be best aligned with the network model? The inference mechanism is provided for both - spatial networks as well as complex networks in general - through a model based on hierarchical and (if defined) geographical distances. The mechanism allows to discover hierarchical and community structure at any desired resolution in complex networks and in particular - the space-independent structure of the spatial networks. The approach is illustrated on the example of the interstate people migration network in USA.