PyRigi -- a general-purpose Python package for the rigidity and flexibility of bar-and-joint frameworks

TL;DR

PyRigi is an open-source Python package that provides robust algorithms for analyzing the rigidity and flexibility of graphs and frameworks, facilitating research in rigidity theory with practical computational tools.

Contribution

It introduces a comprehensive, easy-to-use Python package implementing algorithms for rigidity analysis, bridging theoretical concepts with practical computational applications.

Findings

Enables determination of finite realizations of graphs in the plane.

Identifies whether a framework has a unique embedding.

Supports analysis after edge removal to assess rigidity properties.

Abstract

We present PyRigi, a novel Python package designed to study the rigidity properties of graphs and frameworks. Among many other capabilities, PyRigi can determine whether a graph admits only finitely many ways, up to isometries, of being drawn in the plane once the edge lengths are fixed, whether it has a unique embedding, or whether it satisfied such properties even after the removal of any of its edges. By implementing algorithms from the scientific literature, PyRigi enables the exploration of rigidity properties of structures that would be out of reach for computations by hand. With reliable and robust algorithms, as well as clear, well-documented methods that are closely connected to the underlying mathematical definitions and results, PyRigi aims to be a practical and powerful general-purpose tool for the working mathematician interested in rigidity theory. PyRigi is open source and easy to use, and awaits researchers to benefit from its computational potential.