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.
CITATION STYLE
Butler, S. (2007). Interlacing for weighted graphs using the normalized Laplacian. Electronic Journal of Linear Algebra, 16, 90–98. https://doi.org/10.13001/1081-3810.1185
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