Extracting the hierarchical organization of complex systems

TL;DR

This paper presents an unsupervised method for accurately extracting the hierarchical organization of complex biological, social, and technological networks, validated on both synthetic and real-world data to provide multi-scale insights.

Contribution

The paper introduces a novel unsupervised approach for hierarchical extraction in complex networks, validated with synthetic models and applied to diverse real-world systems.

Findings

The method accurately captures multi-scale hierarchy in networks.

Validated on synthetic ensembles of nested random graphs.

Successfully applied to real-world networks like air-transportation and metabolic systems.

Abstract

Extracting understanding from the growing ``sea'' of biological and socio-economic data is one of the most pressing scientific challenges facing us. Here, we introduce and validate an unsupervised method that is able to accurately extract the hierarchical organization of complex biological, social, and technological networks. We define an ensemble of hierarchically nested random graphs, which we use to validate the method. We then apply our method to real-world networks, including the air-transportation network, an electronic circuit, an email exchange network, and metabolic networks. We find that our method enables us to obtain an accurate multi-scale descriptions of a complex system.