Recent content by kosmos

Sorry for posting it in this thread ... I should have done it in the other one. I got the problem. The portion of my implementation which checked if the nodes where adjacent had a mistake. So it was producing wrong first eigenvalue. Now it works fine. I am getting the required number of zeroes...

I get the following eigenvalues for the matrix attached as text file. It can be viewed in spreadsheet as it is in csv format. The first eigen value is supposed to be zero. There are 20 nodes in graph. There are 3 pairs of nodes which are connected only to each other. So there are 15 partitions...

The problem was with the reference I was using. It defined that entry is 1 whenever i==j and missed out the consition deg(i)!=0 ... thanks for your help! But though I do get the 0 as eigenvalues but the first eigenvalue is still coming out to be negative. That is supposed to be a zero as I...

Page no. 9 of this pdf file http://www.math.ucsd.edu/~sbutler/PDF/spectral1.pdf ... and i think this reference has missed that out! ...thanks for helping out mate!

The value is 0 if the degree is 0 as per definition. So we will get an identity matrix. http://www.math.ucsd.edu/~sbutler/spectral/

Oh yes... that will crosscheck my implementation to generate normLaplacian of the graph. Thanks! ... Let me try that and come back!

No they do not. But why should that be the case, because the diagonals of a normalized laplacian are all 1s. And rest of the cells are filled by -1/sqrt(degree_u*degree_v). So they need not add to -1. I am using this source for reference. www.math.ucla.edu/~butler/PDF/spectral1.pdf

According to theory the eigenvalues of a completely disconnected graph (no two nodes are connected) must be all 0. But the normalized Laplacian of such a graph will be an identity matrix whose eigenvalues will be all 1s. Please correct me!

Hi ... I used 0 as the index. Also exported my 400x400 matrix to a csv file and got the same result using Octave too. So I guess there is nothing wrong with implementation. Something wrong with my matrix. But its symmetric ... I checked in the excel sheet.

This is related to spectral graph theory. I am getting the following eigenvalues for a 400x400 matrix which is a normalized laplacian matrix of a graph. The graph is not connected. So why am i getting a> a negative eigenvalue. b> why is not second eigenvalue 0? ... I used colt(java) and octave...