@article{7ef439d4cd124b47a7d3abc120cc0351,
title = "Primitive tensors and directed hypergraphs",
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.",
keywords = "Directed hypergraph, Irreducible tensor, Nonnegative tensor, Primitive tensor",
author = "Cui, {Lu Bin} and Wen Li and Ng, {Michael K.}",
note = "This author (Lu-Bin Cui) is supported in part by Foundation of Henan Educational Committee of China and Research Fund for the Doctoral Program of Henan Normal University (5101019170128). This author (Wen Li) is supported by NSF of Guangdong province (S20130100112530, S2012010009985), NNSF of China (0971075, 11271144) and Research Fund for the Doctoral Program of Higher Education of China (20104407110001) and Project of Department of Education of Guangdong Province (2013KJCX0053). Research supported in part by RGC GRF Grant No. 201812. Publisher Copyright: {\textcopyright} 2015 Elsevier Inc. All rights reserved.",
year = "2015",
month = apr,
day = "15",
doi = "10.1016/j.laa.2014.12.033",
language = "English",
volume = "471",
pages = "96--108",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",
publisher = "Elsevier Inc.",
}