H+-eigenvalues of Laplacian and signless Laplacian tensors

Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

115 Citations (Scopus)


We propose a simple and natural definition for the Laplacian and the signless Laplacian tensors of a uniform hypergraph. We study their H+-eigenvalues, i.e., H-eigenvalues with nonnegative H-eigenvectors, and H++-eigenvalues, i.e., H-eigenvalues with positive H-eigenvectors. We show that each of the Laplacian tensor, the signless Laplacian tensor, and the adjacency tensor has at most one H++-eigenvalue, but has several other H+-eigenvalues. We identify their largest and smallest H+-eigenvalues, and establish some maximum and minimum properties of these H+-eigenvalues. We then define analytic connectivity of a uniform hypergraph and discuss its application in edge connectivity.
Original languageEnglish
Pages (from-to)1045-1064
Number of pages20
JournalCommunications in Mathematical Sciences
Issue number6
Publication statusPublished - 27 Mar 2014


  • H -eigenvalue +
  • Laplacian tensor
  • Signless Laplacian tensor
  • Uniform hypergraph

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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