New Post: Eigenvalues / Eigenvector

Hallo all,

I looked into Math.NET for usage in my Research. More specific I am looking for a library that can compute the Eigenvectors and Values of medium (500+) matrices. I need this for graph matching and graph drawing. My background is Architecture with a little bit of knowledge in programming and math but unfortunatly not enough to understand all the problems of the implementation of algorithms calculating eigenvalues/eigenvectors. The aim is to use graphMatching within the field of Architecture for the generation of layouts.

I have had a quick look into the .evd() function and it works better than other libraries I have looked at. But a few questions have poped up about the outputs:

1. Laplacian Matrix
   All publications read so far on Laplacian matrices asure me that the resulting eigenvalues should be equal or larger than 0 for a symetric matrix. (e.g. http://en.wikipedia.org/wiki/Laplacian_matrix)
   However with a spares matrix of 553*553 enteries the smallest Eigenvalues is given with -1.
   

What did I miss?

1. Different outputs for the same Matrix
   If have checked the outputs for the following laplacianMatrix with different libraries (MATH.net and Wolfram Alpha):
   [ {4,-1,-1,-1,-1},{-1,4,-1,-1,-1},{-1,-1,4,-1,-1},{-1,-1,-1,4,-1},{-1,-1,-1,-1,4}]
   This is the Laplacian Matrix of the K5 Graph.
   

This will output the Eigenvalues of 0, 5, 5, 5, 5.
The Eigenvector for the Eigenvalue 0 will be the same in both cases but the other Eigenvalues do not match at all.

Thx for any help,

Best Richard