Geodesic
Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 537-544

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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.
Classification : 05C50, 15A42, 15A48, 60J10
Keywords: eigenvalue; irreducible nonnegative matrix; averaged minimal cut 
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     author = {Zhang, Xiao-Dong and Luo, Rong},
     title = {Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices},
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     pages = {537--544},
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     zbl = {1014.15013},
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Zhang, Xiao-Dong; Luo, Rong. Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 537-544. http://geodesic.mathdoc.fr/item/CMJ_2002__52_3_a7/