Setting out to visualize eigenvectors of a graph's Laplacian matrix. A work in progress...
Here are the 10 eigenvectors of the standard Laplacian matrix of the double-star network, in no particular order.
I'm using black/gray for positive numbers, and red/pink for negative, blending into white near zero.
It looks like the last one is the dominant eigenvalue (all entries equal), and the second-to-last one is the "Fiedler vector" that you would use for clustering.