期刊
ADVANCES IN MATHEMATICS
卷 244, 期 -, 页码 303-336出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2013.05.007
关键词
Normalized graph Laplacian; Combinatorial Laplacian; Hypergraph Laplacian; Graph Laplacian; Simplicial complex
类别
资金
- European Research Council under the European Union [267087]
- Volkswagen Foundation
- International Max-Planck Research School Mathematics in the Sciences
We first develop a general framework for Laplace operators defined in terms of the combinatorial structure of a simplicial complex. This includes, among others, the graph Laplacian, the combinatorial Laplacian on simplicial complexes, the weighted Laplacian, and the normalized graph Laplacian. This framework then allows us to define the normalized Laplace operator Delta(up)(i) on simplicial complexes which we then systematically investigate. We study the effects of a wedge sum, a join and a duplication of a motif on the spectrum of the normalized Laplace operator and identify some of the combinatorial features of a simplicial complex that are encoded in its spectrum. (C) 2013 Elsevier Inc. All rights reserved.
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