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Can graph spectrums be derived from incident matrices? 
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#1
Feb1512, 02:33 PM

P: 46

Will the set of eigenvalues of an incident matrix derive an equivalent notion of a graph spectrum as it does with an adjacency matrix?
Specifically: Let s_{a} be the set of eigenvalues of an adjacency matrix for graph G. And, Let s_{i} be the set of eigenvalues of an incident matrix for graph G. What are the differences between s_{a} and s_{i}? Could these both be considered spectrums of the graph? If not, why? Thanks much! 


#2
Feb1612, 08:19 PM

P: 2

What is your definition for incident matrix? If it's the usual definition, then it's likely not a square (nxn) matrix so it doesn't make sense to talk about eigenvalues. You can however look at its singular values which I think are related to eigenvalues of the line graph of G.



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