The principal eigenvector of the adjacency matrix of a graph gives us some notion of vertex centrality.
What do the second, third, etc. eigenvectors tell us?
Motivation: A standard information retrieval technique (LSI) uses a truncated SVD as a low-rank approximation of a matrix. If we truncate to rank 1, then we essentially have a PageRank algorithm. I was wondering if there are ways of interpreting the corrections introduced by higher eigenvectors.
Something similar to what the moments of a distribution tell us (e.g. first moment gives us the mean, second tells us the variance, third gives us skewness, etc).