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
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
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.