Spectral Clustering & Graph Laplacian
Eigenvectors of the Laplacian L=D−A reveal hidden cluster structure
Fiedler vector (2nd smallest eigenvector) bipartitions the graph. k-way: use k Fiedler vectors as features, k-means in eigenspace.
Left: graph colored by spectral cluster. Right: eigenvalue spectrum (Fiedler gap visible for well-separated clusters).