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Keywords:
eigenvalue; irreducible nonnegative matrix; averaged minimal cut
eigenvalue; irreducible nonnegative matrix; averaged minimal cut
Summary:
We present a lower and an upper bound for the second smallest eigenvalue of Laplacian matrices in terms of the averaged minimal cut of weighted graphs. This is used to obtain an upper bound for the real parts of the non-maximal eigenvalues of irreducible nonnegative matrices. The result can be applied to Markov chains.
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