Getting edge cut from eigenvector of adjacency matrix

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

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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.

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thanks do you have an idea if its possible to infer something about the cutsize from the eigenvalue of this eigenvector? –  user9547 Apr 13 '11 at 16:04