Spectral Graph



Spectral layout is a class of algorithm for drawing graphs. The layout uses the eigenvectors of a matrix, such as the Laplace matrix of the graph, as Cartesian coordinates of the graph's vertices.

How to use:

  1. Set the number of nodes
  2. Edit edge weights in the table (higher values = stronger connections)
  3. Click "Read Table" to update the graph
  4. Click "Simplify" to remove weak edges

How it works: The algorithm solves an eigenvalue problem on the graph's Laplacian matrix. The eigenvectors corresponding to the smallest eigenvalues give coordinates that:

  • Minimize edge crossing
  • Place connected nodes close together
  • Reveal community structure
  • Create aesthetically pleasing layouts

This technique is used in network visualization, dimensionality reduction (spectral clustering), and understanding the structure of social networks, molecules, and the internet.