Going off of the answer here: sorting adjacency matrix by the Fiedler vector

So here, Jesse the answerer plotted the first 3 eigenvectors associated with non-zero eigenvalues of the Laplacian against each other in order to see more distinguishable clusters.

My 2 questions about this are:

1) Why did he choose specifically the first 3 eigenvectors to plot, as opposed to for example, just the first 2? Like what determines how many eigenvectors you should compare?

2) Is there a way to quantify connectivity between clusters? For example, when looking at the graph Jesse originally made, is there a way to tell from plotting the eigenvector values that the top cluster is more closely connected to the second top most cluster than the bottom most cluster?


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