It is my understanding that the multiplicity of the smallest eigenvalue (the zero eigenvalue) of the graph laplacian $L=D-A$ equals the number of connected components of a graph, while the second smallest eigenvalue bounds values like the isoperimetric number of the graph (tellings us things about the how "strongly connected" the graph is). Do the eigenvalues beyond the first and the second smallest eigenvalues of $L$ (and their corresponding eigenvectors) indicate anything meaningful about the graph?
2026-03-26 11:05:43.1774523143
Do graph laplacian eigenvectors/values beyond the second smallest eigenvalue mean anything?
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