A fun review of spectral clustering with MATLAB demos I made for the NU machine learning meetiup in 2014. A nice pdf writeup on spectral clustering summarizes the motivation and math behind spectral clustering, and the associated MATLAB demos reproduce many of the figures shown there (see text for further details).

Some cool figures shown in the writeup - that you can also reproduce using the associated code include:

Visualize a graph, with adjacency matrix of your choice from nearest neighbor / gaussian weighting, based on a set of input points - then you can easily compare the results of K-means and spectral clustering on these datasets