Geometric detection of hierarchical backbones in real networks

TL;DR

This paper introduces a geometric method to detect hierarchical backbones in real networks, capturing the interplay of node popularity and similarity, and demonstrates its effectiveness across various domains.

Contribution

It presents a novel geometric framework and a similarity filter for extracting hierarchical backbones, addressing challenges posed by cycles and clustering in complex networks.

Findings

Backbones preserve local topological features.

Similarity backbones promote cooperation in social dilemmas.

Method applicable to diverse real-world networks.

Abstract

Hierarchies permeate the structure of real networks, whose nodes can be ranked according to different features. However, networks are far from tree-like structures and the detection of hierarchical ordering remains a challenge, hindered by the small-world property and the presence of a large number of cycles, in particular clustering. Here, we use geometric representations of undirected networks to achieve an enriched interpretation of hierarchy that integrates features defining popularity of nodes and similarity between them, such that the more similar a node is to a less popular neighbor the higher the hierarchical load of the relationship. The geometric approach allows us to measure the local contribution of nodes and links to the hierarchy within a unified framework. Additionally, we propose a link filtering method, the similarity filter, able to extract hierarchical backbones containing the links that represent statistically significant deviations with respect to the maximum entropy null model for geometric heterogeneous networks. We applied our geometric approach to the detection of similarity backbones of real networks in different domains and found that the backbones preserve local topological features at all scales. Interestingly, we also found that similarity backbones favor cooperation in evolutionary dynamics modelling social dilemmas.