Graph Visualization Widget [WIP]

Dependencies

This project uses the following dependencies:

• eframe: For creating the GUI.
• nalgebra: For linear algebra operations.
• rand: For generating random numbers.

Methods Used

Graph partitioning was achieved using the Fielder vector.

1. Calculate the normalized Laplacian matrix.

$L = D^{-1/2} A D^{-1/2}$

where $D$ is the degree matrix and $A$ is the adjacency matrix.

2. Calculate the eigenvectors of the Laplacian matrix.

The Fiedler vector is the eigenvector corresponding to the second smallest eigenvalue of the Laplacian.

3. Partition the graph.

Use the signs of the components of the Fiedler vector to partition the graph:

$\text{Partition 1} = \{ i \mid \mathbf{v}_2(i) \geq 0 \}$

$\text{Partition 2} = \{ i \mid \mathbf{v}_2(i) < 0 \}$

Screenshots