sentences:  Spectral clustering is well known to relate to partitioning of a mass-spring system, where each mass is associated with a data point and each spring stiffness corresponds to a weight of an edge describing a similarity of the two related data points.Specifically, the classical reference  explains that the eigenvalue problem describing transversal vibration modes of a mass-spring system is exactly the same as the eigenvalue problem for the graph Laplacian matrix defined as 
  where formula_7 is the diagonal matrix
  The masses that are tightly connected by the springs in the mass-spring system evidently move together from the equilibrium position in low-frequency vibration modes, so that the components of the eigenvectors corresponding to the smallest eigenvalues of the graph Laplacian can be used for meaningful clustering of the masses.A popular related spectral clustering technique is the normalized cuts algorithm or "Shi–Malik algorithm" introduced by Jianbo Shi and Jitendra Malik, commonly used for image segmentation.