- Colab — open the starter notebook in Google Colab
- Binder — launch a temporary JupyterLab session from this repo
- Streamlit — local/web UI over the Python package (see below)
Study of graph evolution using cellular automaton-like methods, packaged as a modern uv Python project.
Documentation: https://graphnet-automata.readthedocs.io/
This study was inspired by the recent announcement from Wolfram concerning his project to find the fundamental theory of physics. Although graphnet-automata's approach is not as elegant, it involves the conversion of "seed graphs" to matrices for manipulation using cellular automaton-like methods.
Starting from an undirected graph with a few nodes (a "seed graph"), graphnet-automata manipulates its node connections, represented as a matrix, by first padding the matrix with one layer (adding two new nodes). Depending on the number of neighboring node connections, the matrix is updated, much like in a cellular automaton. This is repeated in a recursive fashion (i.e. "evolved"), and the resulting matrix is converted into a graph. To further characterize the graph, a community detection method is employed to visualize the number of communities that have formed.
For example, a seed graph of three nodes
evolves into a graph that is distinctly separated into two communities.
Initial experiments have shown that the evolved graph shows a "bonding" or "anti-bonding" graph, depending on whether the number of nodes in the seed graph are odd or even, like so:
evolves into:
Other novel structures found so far include a whip-like structure:
See the notebook directory for details. Pre-NetworkX-3 snapshots are frozen under notebooks/archive/.
.
├── app.py # Streamlit interactive demo
├── data/ # Generated HDF5 datasets
├── docs/ # Sphinx / Read the Docs sources
├── images/ # Example figures
├── notebooks/ # Active notebooks (NetworkX 3+)
│ └── archive/ # Frozen NetworkX 2-era snapshots
├── src/graphnet_automata/ # Installable package (uv src layout)
│ ├── generator.py # Shared automaton core
│ ├── degree.py # Degree-count kernel search
│ ├── generate.py # Dataset generation
│ ├── optimize.py # Optuna seed optimization
│ └── search.py # Entropy-based kernel search
├── requirements.txt # Streamlit Cloud / Binder install list
├── tests/
├── pyproject.toml
└── .python-version
- Python 3.10+
- Managed via uv
Core libraries: NetworkX, NumPy, SciPy, Numba, python-louvain, Matplotlib, h5py, Optuna.
Install uv, then from the repository root:
uv syncOptional extras:
uv sync --extra dev --extra viz # notebooks / pyvis
uv sync --extra app # Streamlit demo
uv sync --extra docs # Sphinx documentationRun the interactive UI locally:
uv sync --extra app
uv run streamlit run app.pyTo publish on Streamlit Community Cloud: sign in with GitHub, pick this repository, set the main file to app.py, and deploy (uses requirements.txt).
After uv sync, run the CLI entry points:
uv run graphnet-automata # list commands
uv run graphnet-automata-degree # search by degree-count average
uv run graphnet-automata-generate # write data/GA_seed_13_0.05_50.h5
uv run graphnet-automata-search # search by degree-distribution entropy
uv run graphnet-automata-optimize # Optuna optimization (slow)Or import the shared generator from Python / notebooks:
from graphnet_automata import GeneratorState, kernel_from_index
kernel = kernel_from_index(448)
gen = GeneratorState(nodes=13, prob=0.05, kernel=kernel, steps=100)
adjacency = gen.run()Exploratory work remains in the Jupyter notebooks under notebooks/. Recursive calculations may take a minute or more depending on your environment.
Hosted docs: https://graphnet-automata.readthedocs.io/
Sphinx sources live in docs/. Build locally:
uv sync --extra docs
uv run sphinx-build -b html docs docs/_build/htmluv sync --extra dev
uv run pytest- Masakazu Yamagiwa
- Email: myamagiwa@gmail.com
graphnet-automata is under the MIT license.