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Can graph spectrums be derived from incident matrices?

by 1Truthseeker
Tags: derived, graph, incident, matrices, spectrums
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Feb15-12, 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?


Let sa be the set of eigenvalues of an adjacency matrix for graph G.


Let si be the set of eigenvalues of an incident matrix for graph G.

What are the differences between sa and si? Could these both be considered spectrums of the graph? If not, why?

Thanks much!
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Feb16-12, 08:19 PM
spikedmath's Avatar
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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