Laplacian
L = D - A where D = diagonal degree matrix, A = adjacency. Symmetric positive semi-definite.
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Fiedler vector
Second-smallest eigenvector = Fiedler vector. Sign partitions graph into 2 balanced parts (approximately).
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Normalization
Normalized Laplacian L_sym = D^(-1/2) L D^(-1/2). More robust for varying degrees.
Complexity
Eigendecomposition: O(V³) exact. Sparse Lanczos: O(k · E · iterations). For huge graphs: approximate methods.