Primitive tensors and directed hypergraphs

Lu Bin Cui; Wen Li; Michael K. Ng

doi:10.1016/j.laa.2014.12.033

Primitive tensors and directed hypergraphs

Lu Bin Cui, Wen Li^*, Michael K. Ng

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

19 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 language	English
Pages (from-to)	96-108
Number of pages	13
Journal	Linear Algebra and Its Applications
Volume	471
DOIs	https://doi.org/10.1016/j.laa.2014.12.033
Publication status	Published - 15 Apr 2015

User-Defined Keywords

Directed hypergraph
Irreducible tensor
Nonnegative tensor
Primitive tensor

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10.1016/j.laa.2014.12.033

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AU - Li, Wen

AU - Ng, Michael K.

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AB - 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.

KW - Directed hypergraph

KW - Irreducible tensor

KW - Nonnegative tensor

KW - Primitive tensor

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VL - 471

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EP - 108

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Primitive tensors and directed hypergraphs

Abstract

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