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KConrad
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Discrete Laplace operator and it'sits eigenvalues

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Ricardo Andrade
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Stas
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Discrete Laplace operator and it's eigenvalues

I wonder is there any geometric interpretation of the eigenvalues ​​of the discrete Laplace operator on graphs? Maybe there is a relationship between the eigenvalues ​​and combinatorial properties of the graph?

I would like to know what information eigenvalues contain.

Thanks for the answer.