Fan Chung has written extensively on spectral graph theory.

Her sgt papers are here:

[http://www.math.ucsd.edu/~fan/cgi-bin/papers.pl?kwd=eigen](http://www.math.ucsd.edu/~fan/cgi-bin/papers.pl?kwd=eigen)

she also has a couple of books on the subject.

She advocates the use of the normalized Laplacian matrix,

where both the rows & columns are scaled by the square root of the degree of the corresponding node,

making the matrix symmetric and with ones on the diagonal.

Her sgt papers are here:

[http://www.math.ucsd.edu/~fan/cgi-bin/papers.pl?kwd=eigen](http://www.math.ucsd.edu/~fan/cgi-bin/papers.pl?kwd=eigen)

she also has a couple of books on the subject.

She advocates the use of the normalized Laplacian matrix,

where both the rows & columns are scaled by the square root of the degree of the corresponding node,

making the matrix symmetric and with ones on the diagonal.