Consider the Normalized Laplacian associated to a similarty graph $$ L = D^{-1/2}SD^{-1/2} $$
I have two sources stating that, in the "ideal case of zero noise", the eigenvectors corresponding to eigenvalue 1 (or near 1) represent clusters (while the eigenvectors corresponding to 0 represent connected components, as it is known).
Clustering of Vehicle Trajectories, Stefan Atev, Grant Miller, and Nikolaos Papanikolopoulos, IEEE Transactions on Intelligent Transportation Systems · October 2010
Self-Tuning Spectral Clustering, Lihi Zelnik-Manor, January 2004 Advances in Neural Information Processing Systems 17 Conference: Advances in Neural Information Processing Systems (NIPS)
I really can't understand why. How can I see this?