3
$\begingroup$

Given a $d$-regular undirected graph and an eigenvector of its adjacency matrix, how can I get an edge cut from it?

My idea was to do something similar as in the proof of the Cheeger inequality, but so far I was not successful.

Thanks

1 Answers 1

3

You could threshold the eigenvector at some arbitrary value and define edge cut by all edges that cross from 0 valued vertex to 1 valued vertex. A more common technique with spectral clustering is to take first few eigenvectors of the Laplacian of the graph and apply k-means clustering to the vertices with coordinates taken from those eigenvectors.

  • 0
    than$k$s do you have an $i$dea if its possible to infer something about the cutsize from the eigenvalue of this eigenvector?2011-04-13