There's an easily understandable intuitive understanding of the 1st eigenvector (for the eigenvalue == 1) of the pagerank matrix (loosely speaking: assuming you browse a-la the pagerank matrix, the ith component of the (unit) eigenvector for the 1.0 eigenvalue is ~the same as lim n->infinity of #(of visits to i-th page on the internet)/n; some details are getting blurred (of course) but it's a helpful intuitive explanation).

Does anyone have any insight into intuitive interpretations of the eigenvectors fpr the eigenvalues < 1? I'm drawing blanks.

(Edited: to be clear, I understand what the linked algorithm is doing and I think it is very clever, and I am not surprised that it works reasonably well for finding similar topics on wikipedia. I'm just at a blank for what it means to say that 'the i-th component of the (unit) eigenvector for the k-th largest eigenvalue is X'.)