On the spectrum of the normalized graph Laplacian

Details On the spectrum of the normalized graph Laplacian On the spectrum of the normalized graph Laplacian

2007-05-25

arxiv.org/abs/0705.3772v1

Mathematics

Combinatorics

9 pages, no figures

Scientific paper

The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this spectrum under local and global operations like motif doubling, graph joining or splitting. The eigenvalue 1 plays a particular role, and we therefore emphasize those constructions that change its multiplicity in a controlled manner, like the iterated duplication of nodes.

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