Random graph partitioned by the Fiedler vector (eigenvector of second-smallest Laplacian eigenvalue). Nodes colored by sign of Fiedler component reveal the min-cut bipartition.
The Fiedler value λ₂ (algebraic connectivity) measures how well-connected a graph is. The Fiedler vector provides the optimal spectral bipartition — this is the foundation of spectral clustering algorithms like Shi-Malik normalized cuts.