Latent geometry explains nested patterns in complex group interactions
Latent geometry organizes higher-order interactions
Social and Information Networks
Summary
Complex systems often have interactions involving groups of different sizes that nest inside each other. The authors created a simple geometric model that links these interactions through a hidden space, causing nested patterns to appear naturally. They analyzed and simulated the model, showing how nestedness stays strong or fades depending on system size and geometry. Their model also matches nested structures seen in real-world data from different domains. This suggests that a hidden geometric organization might be behind how complex group interactions are arranged.
What this means in practice
- •For network engineers: Model communication or social networks with accurate nested group interactions to improve network design and analysis.
- •For data analysts: Use a geometric organizing principle to better detect and interpret nested group patterns in complex datasets across fields.
Authors
Berné L. Nortier, Jasper van der Kolk, Robert Jankowski, Simon Dobson, M. Ángeles Serrano, Federico Battiston, Marián Boguñá
Abstract
Higher-order structures offer a natural representation of complex systems that involve interactions between groups of different sizes. A widespread feature of their higher-order structure is nestedness, whereby interactions involving smaller groups are contained within larger ones. Yet, why interactions of different orders organise into nested structures remains largely unexplained. Here, we introduce an analytically tractable geometric model of higher-order networks in which a single latent geometric space couples interactions across orders, leading to the spontaneous emergence of nestedness. We show analytically and numerically that nestedness undergoes a transition between a nested geometric regime, where it remains finite in the thermodynamic limit, and a regime where it vanishes with system size. In this regime, we uncover a weakly geometric range characterized by an anomalously slow finite-size decay, allowing substantial nestedness to persist in finite systems even when its asymptotic value vanishes. Finally, with a single geometric coupling parameter, the model reproduces the nestedness profiles observed in real-world hypergraphs across different domains. Our results reveal latent geometry as a simple organising principle underlying the nested organisation of higher-order interactions.