# A Q-analysis package for higher-order interactions analysis in Python and its application in network physiology

## TL;DR

This paper introduces a Python package for analyzing complex, multi-node interactions in networks using Q-analysis, with applications in social and brain networks.

## Contribution

A new Python package implementing Q-analysis for higher-order network interactions, with tools for machine learning and statistical inference.

## Key findings

- Simulation study showed distinct higher-order topological signatures in different network types.
- DBLP dataset analysis revealed evolving collaboration structures over 30 years.
- MDD brain networks showed disrupted higher-order organization in fMRI data.

## Abstract

Real-world networks possess complex, higher-order structures that are not captured by traditional pairwise analysis methods. Q-analysis provides a powerful mathematical framework based on simplicial complexes to uncover and quantify these multi-node interactions. However, its adoption has been limited by a lack of accessible software tools.

We introduce a comprehensive Python package that implements the core methodology of Q-analysis. The package enables the construction of simplicial complexes from graphs or simplex lists and computes a suite of descriptive metrics, including structure vectors (FSV, SSV, TSV) and topological entropy. It features high-performance routines, integration with scikit-learn for machine learning workflows, and tools for statistical inference, such as permutation tests.

We demonstrate the package’s capabilities through a simulation study, revealing distinct higher-order topological signatures in scale-free versus configurational networks despite identical degree distributions. Application to the DBLP co-authorship dataset uncovered the evolution of collaborative structures over three decades, showing increased collaboration scale and shifts in higher-order connectivity patterns. Finally, in a network physiology application, the package identified significant disruptions in the higher-order organization of fMRI-derived brain networks in Major Depressive Disorder (MDD), characterized by a loss of high-dimensional functional components and increased fragmentation.

The developed package makes Q-analysis accessible to a broad research audience, facilitating the exploration of higher-order interactions in complex systems. The presented applications validate its utility across diverse domains, from social networks to neuroscience. By providing an open-source tool, this work bridges a gap in network science, enabling quantitative analysis of the intricate, multi-node structures that define real-world networks.