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

Nikita Smirnov¹Semen Kurkin²Alexander E Hramov^2*

• ¹Baltijskij federal'nyj universitet imeni Immanuila Kanta, Kaliningrad, Russia
• ²Research Institute for Applied Artificial intelligence and Digital Dolutions, Plekhanov Russian University of Economics, Moscow, Russia

Real-world networks have complex, higher-order structures that are invisible to traditional pairwise methods. Q-analysis provides a powerful exploratory framework to uncover and quantify these structures. This paper introduces a Python package in the form of a tutorial that makes this methodology accessible for analyzing both simplicial complexes and the underlying community structures of conventional graphs. The package contains a suite of descriptive metrics, including structure vectors and other graded parameter sets, that provide a structural lens for examining network topology. The package includes tools for statistical analysis, such as permutation tests, and supports machine learning workflows through scikit-learn compatible transformers. First, we showcase the package's capabilities through a simulation study comparing Q-analysis metrics across different network types. Next, we apply the package to the DBLP (Digital Bibliography & Library Project) co-authorship dataset and analyze the evolution of its collaborative structures over time. Finally, we present an example of using the package to study a physiological problem, such as identifying disruptions in the fMRI-derived brain network caused by major depressive disorder. By providing an open-source tool for Q-analysis, this package aims to make higher-order network analysis more accessible to researchers, facilitating the quantitative analysis of higher-order structures in complex systems, including network models in physiology.