Primitive tensors and directed hypergraphs

Lu Bin Cui, Wen Li*, Kwok Po NG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

Primitivity is an important concept in the spectral theory of nonnegative matrices and tensors. It is well-known that an irreducible matrix is primitive if and only if the greatest common divisor of all the cycles in the associated directed graph is equal to 1. The main aim of this paper is to establish a similar result, i.e., we show that a nonnegative tensor is primitive if and only if the greatest common divisor of all the cycles in the associated directed hypergraph is equal to 1.

Original languageEnglish
Pages (from-to)96-108
Number of pages13
JournalLinear Algebra and Its Applications
Volume471
DOIs
Publication statusPublished - 15 Apr 2015

Scopus Subject Areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

User-Defined Keywords

  • Directed hypergraph
  • Irreducible tensor
  • Nonnegative tensor
  • Primitive tensor

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