Geodesic
Interlacing for weighted graphs using the normalized Laplacian
The electronic journal of linear algebra, Tome 16 (2007), pp. 90-98.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The problem of relating the eigenvalues of the normalized Laplacian for a weighted graph G and G - H, for H a subgraph of G is considered. It is shown that these eigenvalues interlace and that the tightness of the interlacing is dependent on the number of nonisolated vertices of H. Weak coverings of a weighted graph are also defined and interlacing results for the normalized Laplacian for such a covering are given. In addition there is a discussion about interlacing for the Laplacian of directed graphs.
Classification : 05C50, 15A42
Keywords: Laplacian matrix, interlacing, directed Laplacian, weak coverings 
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     author = {Butler, Steve},
     title = {Interlacing for weighted graphs using the normalized {Laplacian}},
     journal = {The electronic journal of linear algebra},
     pages = {90--98},
     publisher = {mathdoc},
     volume = {16},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2007__16__a30/}
}
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Butler, Steve. Interlacing for weighted graphs using the normalized Laplacian. The electronic journal of linear algebra, Tome 16 (2007), pp. 90-98. http://geodesic.mathdoc.fr/item/ELA_2007__16__a30/