Graph Theory Dashboard

An interactive Dash-based tool for exploring and analyzing graphs through spectral graph theory, Laplacian decomposition, and interactive visualizations.

Features

• Interactive Graph Generation:

  • Erdős–Rényi, Barabási–Albert, Watts–Strogatz, Scale-Free, Star, Lattice, and Delaunay Triangulation.

• Spectral Analysis:

  • Compute and visualize the Laplacian matrix and its eigen decomposition.
  • Explore spectral filters defined by: $$L = (D^E A D^E)^K$$

• Graph Manipulation:

  • Add, remove, and edit nodes and edges interactively.

• Matrix Aggregation:

  • Analyze effects of multiple (E, K) parameter pairs.

• Detailed In-App Documentation:

  • Comprehensive explanations of spectral graph theory concepts.

Installation

Clone the repository and install required dependencies:

git clone <repo-url>
cd <repo-directory>
pip install -r requirements.txt

Running the Dashboard

Launch the dashboard locally:

python eigen_app.py

Open your browser and navigate to:

http://127.0.0.1:8050

Project Structure

.
├── eigen_app.py            # Main Dash application
├── eigen_documentation.py  # Documentation content
├── requirements.txt        # Python dependencies
├── readme.md               # Readme

Planned Features

• Clustering visualizations and community detection
• Graph import/export functionality
• Enhanced node and edge manipulation tools

Resources

• Dash documentation
• NetworkX documentation
• Plotly Python reference

Contributions

Contributions, bug reports, and feature requests are welcome. Please open an issue or submit a pull request.

License

MIT License.