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# 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 via conda-forge
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Installing `generalisedformanricci` from the `conda-forge` channel can be achieved by adding `conda-forge` to your channels with:
```
conda config --add channels conda-forge
```
Once the `conda-forge` channel has been enabled, `generalisedformanricci` can be installed with:
```
conda install generalisedformanricci
```
It is possible to list all of the versions of `generalisedformanricci` available on your platform with:
```
conda search generalisedformanricci --channel conda-forge
```
Alternatively, `generalisedformanricci` can be installed just by `conda install -c conda-forge generalisedformanricci`.
## Installation via pip
![PyPI](https://img.shields.io/pypi/v/GeneralisedFormanRicci)
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`pip install GeneralisedFormanRicci`
Upgrading via `pip install --upgrade GeneralisedFormanRicci`
## Package Requirement
* [NetworkX](https://github.com/networkx/networkx) >= 2.0 (Based Graph library)
* [GUDHI](https://github.com/GUDHI) (Simplicial Complex Library)
* [NumPy](https://github.com/numpy/numpy)
* [SciPy](https://github.com/scipy/scipy)
## 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()
sc.compute_bochner()
```
## 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: