Does there exist a flavor of spectral clustering (graph construction, type of laplacian, et cetera) that results in a clustering (on arbitrary data sets) that is similar to the k-means clustering "in spirit", i.e. finds a partition of the data into isotropic high density regions? (Of course, I don't expect exact equivalence.)
Whenever I've seen spectral clustering, it has seemed to go more after manifolds (i.e. non-isotropic clusters), but that may be because commonly spectral clustering is presented using k-NN type graphs. Of course, a k-NN (or epsilon-neighborhood) graph contains no large-scale information on the relative positions of points, hence it is in no way "encouraged" towards isotropy.