Below is my experiment visualization result for applying kmeans to an unevenly distributed Gaussian blobs, which is obtained by python kmeans-experiment.py.

The desired result is not the minimal value of the object function (or kmeans assumption on unit variance).

Below is my experiment visualization result for applying spectral clustering to three circle dataset, which is obtained by python spectral-experiment.py.

The optimal gamma is in a wide range from about 1085 to 10420.

I think too big gamma reduces the accuracy because points within the same community have too small similarity. Small gamma also does not work well because of the dense property of the Laplacian matrix. That is, points from different clusters also have large similarity.