Primitive tensors and directed hypergraphs

Linear Algebra and Its Applications - Tập 471 - Trang 96-108 - 2015
Lu-Bin Cui1, Wen Li2, Michael K. Ng3
1School of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, PR China
2School of Mathematical Sciences, South China Normal University, Guangzhou, PR China
3Department of Mathematics, Hong Kong Baptist University, Hong Kong

Tài liệu tham khảo

Ausiello, 1983, Graph algorithms for functional dependency manipulation, J. ACM, 30, 752, 10.1145/2157.322404 Ausiello, 1986, Minimal representation of directed hypergraphs, SIAM J. Comput., 15, 418, 10.1137/0215029 Ausiello, 2001, Directed hypergraphs: problems, algorithmic results, and a novel decremental approach, vol. 2202, 312 Bapat, 1997, Nonnegative Matrices and Applications, vol. 64 Bermann, 1979 Buló, 2009, New bounds on the clique number of graphs based on spectral hypergraph theory, 45 Chang, 2008, Perron–Frobenius theorem for nonnegative tensors, Commun. Math. Sci., 6, 507, 10.4310/CMS.2008.v6.n2.a12 Chang, 2013, On the uniqueness and non-uniqueness of the positive Z-eigenvector for transition probability tensors, J. Math. Anal. Appl., 408, 525, 10.1016/j.jmaa.2013.04.019 Chang, 2011, Primitivity the convergence of the NZQ method, and the largest eigenvalue for nonnegative tensors, SIAM J. Matrix Anal. Appl., 32, 806, 10.1137/100807120 Chen Cooper, 2012, Spectra of uniform hypergraphs, Linear Algebra Appl., 436, 3268, 10.1016/j.laa.2011.11.018 P. Drineas, L. Lim, A multilinear spectral theory of hypergraphs and expander hypergraphs, Stanford University, Stanford, CA, preprint, 2005. Friedland, 2013, Perron–Frobenius theorem for nonnegative multilinear forms and extensions, Linear Algebra Appl., 438, 738, 10.1016/j.laa.2011.02.042 Gallo, 1993, Directed hypergraphs and applications, Discrete Appl. Math., 40, 177, 10.1016/0166-218X(93)90045-P Horn, 1985 Hu, 2012, Algebraic connectivity of an even uniform hypergraph, J. Comb. Optim., 24, 564, 10.1007/s10878-011-9407-1 Hu, 2014, The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph, Discrete Appl. Math., 169, 140, 10.1016/j.dam.2013.12.024 Levin, 2008 Li, 2013, The Z-eigenvalues of a symmetric tensor and its application to spectral hypergraph theory, Numer. Linear Algebra Appl., 20, 1001, 10.1002/nla.1877 Li, 2014, On the limiting probability distribution of a transition probability tensor, Linear Multilinear Algebra, 62, 362, 10.1080/03081087.2013.777436 Li, 2013, The perturbation bound for the Perron vector of a transition probability tensor, Numer. Linear Algebra Appl., 20, 985, 10.1002/nla.1886 Li, 2012, Har: hub, authority and relevance scores in multi-relational data for query search, 141 Ng, 2009, Finding the largest eigenvalue of a nonnegative tensor, SIAM J. Matrix Anal. Appl., 31, 1090, 10.1137/09074838X Ng, 2011, MultiRank: co-ranking scheme for objects and relations in multidimensional data, 1217 Pearson Pearson, 2014, On spectral hypergraph theory of the adjacency tensor, Graphs Combin., 30, 1233, 10.1007/s00373-013-1340-x Qi, 2014, H+-eigenvalues of Laplacian tensor and signless Laplacians, Commun. Math. Sci., 12, 1045, 10.4310/CMS.2014.v12.n6.a3 Xie, 2013, H-eigenvalues of the signless Laplacian tensor for an even uniform hypergraph, Front. Math. China, 8, 107, 10.1007/s11464-012-0266-6 Xie, 2013, On the Z-eigenvalues of the signless Laplacian tensor for an even uniform hypergraph, Numer. Linear Algebra Appl., 20, 1030, 10.1002/nla.1910 Yang, 2011, Further results for Perron–Frobenius theorem for nonnegative tensors II, SIAM J. Matrix Anal. Appl., 32, 1236, 10.1137/100813671