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Interactive 3D/Spectral Graph Theory
Left: graph colored by Fiedler value  |  Right: Laplacian matrix + v₂ bar chart
λ₁ = 0  |  λ₂ (Fiedler) = 5.1642  |  Alg. connectivity: 5.1642
Graph Size
n nodes7
Edge Toggles
Interpretation
Nodes colored blue=negative, red=positive Fiedler value.
The cut separates positive vs negative sign nodes - the optimal 2-way partition.
λ₂ near 0 = graph barely connected. Large λ₂ = well-connected.
Color Legend
Positive
Negative

Spectral Graph Theory - Interactive Visualization

The graph Laplacian L = D - A captures connectivity structure. Its second smallest eigenvalue (Fiedler value λ₂) measures algebraic connectivity - how well the graph is connected. The corresponding Fiedler vector reveals natural bi-partitions: nodes with positive values form one cluster, negative values another. Spectral clustering uses multiple eigenvectors for k-way partition.

  • See graph Laplacian L = D - A as a colored matrix
  • See Fiedler vector (2nd eigenvector) as a bar chart
  • Nodes colored by Fiedler vector reveal natural clusters
  • Click Cut to see spectral bisection partition
  • Foundation for spectral clustering, graph signal processing, and GNNs

Part of the EngineersOfAI Interactive 3D - free interactive visualizations covering every major concept in machine learning and AI engineering. Hover any element for a plain-English explanation. No code required.