Interlacing for weighted graphs using the normalized Laplacian

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Steve Butler


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.

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