GeneralisedFormanRicci 0.0.4

A class to compute the Generalised Forman-Ricci curvature for a Simplicial Complex from a given point cloud data.

GeneralisedFormanRicci

This code computes the Forman Ricci Curvature for simplicial complex generated from a given point cloud data. The implementation is based on the combinatorial definition of Forman Ricci curvature defined by Robin Forman. This implementation generalises beyond the simplified version implemented in saibalmars/GraphRicciCurvature github.

Many thanks to stephenhky and saibalmars for their packages MoguTDA and GraphRicciCurvature respectively. Partial code was modified from MoguTDA for the computation of the boundary matrices.

Installation

pip install GeneralisedFormanRicci

Upgrading via pip install --upgrade GeneralisedFormanRicci

Package Requirement

• NetworkX >= 2.0 (Based Graph library)
• GUDHI (Simplicial Complex Library)
• NumPy

Simple Example

from GeneralisedFormanRicci.frc import GeneralisedFormanRicci

data = [[0.8, 2.6], [0.2, 1.0], [0.9, 0.5], [2.7, 1.8], [1.7, 0.5], [2.5, 2.5], [2.4, 1.0], [0.6, 0.9], [0.4, 2.2]]
for f in [0, 0.5, 1, 2, 3]:
    sc = GeneralisedFormanRicci(data, method = "rips", epsilon = f)
    sc.compute_forman()

References

• MoguTDA: https://github.com/stephenhky/MoguTDA
• GraphRicciCurvature: https://github.com/saibalmars/GraphRicciCurvature
• Forman, R. (2003). Bochner's method for cell complexes and combinatorial Ricci curvature. Discrete and Computational Geometry, 29(3), 323-374.
• Forman, R. (1999). Combinatorial Differential Topology and Geometry. New Perspectives in Algebraic Combinatorics, 38, 177.

Cite

If you use this code in your research, please considering cite our paper: