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function [p,v,d] = cs_fiedler (A)
%CS_FIEDLER the Fiedler vector of a connected graph.
% [p,v,d] = cs_fiedler(A) computes the Fiedler vector v (the eigenvector
% corresponding to the 2nd smallest eigenvalue d of the Laplacian of the graph
% of A+A'). p is the permutation obtained when v is sorted. A should be a
% connected graph.
%
% Example:
% [p,v,d] = cs_fiedler (A) ;
%
% See also CS_SCC, EIGS, SYMRCM, UNMESH.
% Copyright 2006-2007, Timothy A. Davis.
% http://www.cise.ufl.edu/research/sparse
n = size (A,1) ;
if (n < 2)
p = 1 ; v = 1 ; d = 0 ; return ;
end
opt.disp = 0 ; % turn off printing in eigs
opt.tol = sqrt (eps) ;
S = A | A' | speye (n) ; % compute the Laplacian of A
S = diag (sum (S)) - S ;
[v,d] = eigs (S, 2, 'SA', opt) ; % find the Fiedler vector v
v = v (:,2) ;
d = d (2,2) ;
[ignore p] = sort (v) ; % sort it to get p
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