The graph Laplacian L = D − A has eigenvalues 0 = λ₁ ≤ λ₂ ≤ … The Fiedler value λ₂ (algebraic connectivity) and its eigenvector v₂ reveal the graph's bottleneck. Sign(v₂ᵢ) gives the optimal 2-partition — this is normalized spectral clustering.
Graph colored by Fiedler vector
Fiedler vector components
λ₂ (Fiedler) = — | Partition: — vs — nodes
Random geometric graph: nodes connected if distance < r. Blue = partition A (v₂ > 0), orange = partition B (v₂ < 0).