Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/16833
Title: The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph
Authors: Hu, S
Qi, L 
Keywords: Eigenvector
Hypergraph
Laplacian
Partition
Tensor
Issue Date: 2014
Publisher: Elsevier
Source: Discrete applied mathematics, 2014, v. 169, p. 140-151 How to cite?
Journal: Discrete Applied Mathematics 
Abstract: In this paper, we show that the eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector associated with the zero eigenvalue of the Laplacian or signless Laplacian tensor have the same modulus. Moreover, under a canonical regularization, the phases of the components of these eigenvectors only can take some uniformly distributed values in {exp(2jπk)|ja∈[k]}. These eigenvectors are divided into H-eigenvectors and N-eigenvectors. Eigenvectors with maximal support are called maximal. The maximal canonical H-eigenvectors characterize the even (odd)-bipartite connected components of the hypergraph and vice versa, and maximal canonical N-eigenvectors characterize some multi-partite connected components of the hypergraph and vice versa.
URI: http://hdl.handle.net/10397/16833
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.12.024
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