https://github.com/sandergi/conformal-rigidity

Exploring the relationship between conformal rigidity, spectral properties, and genus of graphs.
https://github.com/sandergi/conformal-rigidity

combinatorics graphs spectral-theory

Last synced: about 1 year ago
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Exploring the relationship between conformal rigidity, spectral properties, and genus of graphs.

• Host: GitHub
• URL: https://github.com/sandergi/conformal-rigidity
• Owner: SanderGi
• License: mit
• Created: 2025-03-25T06:53:52.000Z (about 1 year ago)
• Default Branch: main
• Last Pushed: 2025-03-25T07:01:18.000Z (about 1 year ago)
• Last Synced: 2025-03-25T08:19:51.699Z (about 1 year ago)
• Topics: combinatorics, graphs, spectral-theory
• Language: Jupyter Notebook
• Homepage:
• Size: 4.77 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# Conformal Rigidity and Topological Obstructions: A Spectral Perspective on Graph Genus

Exploring the relationship between conformal rigidity, spectral properties, and genus of graphs.

## Setup

Choose one of Pyenv or Conda to manage your Python environment.

### With Pyenv

1. Install Python 3.10.12

    - [Install pyenv](https://github.com/pyenv/pyenv?tab=readme-ov-file#installation)

    - Run `pyenv install 3.10.12`

    - Pyenv should automatically use this version in this directory. If not, run `pyenv local 3.10.12`

2. Create a virtual environment

    - Run `python -m venv ./venv` to create it

    - Run `. venv/bin/activate` when you want to activate it

        - Run `deactivate` when you want to deactivate it

    - Pro-tip: select the virtual environment in your IDE, e.g. in VSCode, click the Python version in the bottom left corner and select the virtual environment

3. Install dependencies with `pip install -r requirements.txt` 

### With Conda

1. Install miniconda or anaconda

    - [Install miniconda](https://docs.conda.io/en/latest/miniconda.html)

    - Or [install anaconda](https://docs.anaconda.com/anaconda/install/)

2. Create a virtual environment

    - Run `conda create --prefix ./venv python=3.10.12` to create it

    - Run `conda activate ./venv` when you want to activate it

        - Run `conda deactivate` when you want to deactivate it

    - Pro-tip: select the virtual environment in your IDE, e.g. in VSCode, click the Python version in the bottom left corner and select the virtual environment

3. Install dependencies with `pip install -r requirements.txt` 

## Usage

Open any of the `.ipynb` notebooks in VS Code or Jupyter Notebook to run the code.

- `conformal_rigidity.ipynb` contains the code for checking whether a graph is conformally rigid.

- `spectral_bound.ipynb` contains delta_g plots

## References

- [Conformally Rigid Graphs](https://arxiv.org/abs/2402.11758) by Steinerberger and Thomas

- [Conformal upper bounds for the eigenvalues of the Laplacian and Steklov problem](https://www.sciencedirect.com/science/article/pii/S0022123611002928) by Asma Hassannezhad