Interlacing for weighted graphs using the normalized Laplacian
By S. Butler. 2007
59 citations recorded by the source corpus.
The problem of relating the eigenvalues of the normalized Laplacian for a weighted graph G and GH ,f orH 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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fe65d9ef865a2a22cdbe9881089928e53507d7b8
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Eigenvalues and structures of graphs (2008, background): “A similar result for directed graphs for the results in Section 4.3.2 is more problematic as there is often no well defined normalized Laplacian for a directed graph, see for example Chung [12] and Butler [8].”