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From: shahnaz fatima on 1 Aug 2010 09:41
can anybody explain me what does spectrum of graph mean.
i read an example.
G is the graph with V as vertices and E as edges ie, G= (V, E).
in example, V ={ 1 2 3} and E ={( 1,2) , (2,3)}.

laplacian of graph is defined as LG, each element is l(i,j)=-1 if (i,j)belongs to E, degree if i=j, 0 otherwise.

in this example it will become [0 -1 0; -1 0 -1; 0 -1 0]
i understand that ( 1,1,1 ) is an eigenvector of eigen value 0 of LG. then
i dint understand this part i.e finding the other eigenvectors

We'll just compute the value we get at the second node when we multiply this vector by LG. First, we get 2 times the value that was there, 1. We then subtract off the value at each of its neighbors, also 1. Thus, we get 0.

plz explain.
-1 0 1 and 1 -2 1 are other eigenvectors given how is that found
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