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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

Contributions

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

License

MIT License.