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Research Article

A spectral method to incidence balance of oriented hypergraphs and induced signed hypergraphs

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Pages 4804-4818 | Received 18 Oct 2020, Accepted 28 Feb 2021, Published online: 10 Mar 2021

References

  • Reff N, Rusnak LJ. An oriented hypergraphic approach to algebraic graph theory. Linear Algebra Appl. 2012;437:2262–2270.
  • Rusnak LJ. Oriented hypergraphs: introduction and balance. Electron J Combinat. 2013;20(3):48.
  • Yu G-H, Yuan X-Y, Qu H. Signed k-uniform hypergraphs and tensors. Linear Algebra Appl. 2019;580:1–13.
  • Shi CJ. A signed hypergraph model of the constrained via minimization problem. Microelectron J. 1992;23(7):533–542.
  • Shi CJ, Brzozowski JA. A characterization of signed hypergraphs and its application to VLSI via minimization and logic synthesis. Discrete Appl Math. 1999;90(1-3):223–243.
  • Zaslavsky T. Orientation of signed graphs. Europ J Comb. 1991;12:361–375.
  • Chen V, Rao A, Rusnak LJ, et al. A characterization of oriented hypergraphic balance via signed weak walks. Linear Algebra Appl. 2015;485:442–453.
  • Reff N. Spectral properties of oriented hypergraphs. Electron J Linear Algebra. 2014;27:373–391.
  • Reff N. Intersection graphs of oriented hypergraphs and their matrices. Australas J Combin. 2016;65:108–123.
  • Reff N, Skogman H. A connection between Hadamard matrices, oriented hypergraphs and signed graphs. Linear Algebra Appl. 2017;529:115–125.
  • Cooper J, Dutle A. Spectra of uniform hypergraphs. Linear Algebra Appl. 2012;436:3268–3292.
  • Fan Y-Z, Bao Y-H, Huang T. Eigenvariety of nonnegative symmetric weakly irreducible tensors associated with spectral radius and its application to hypergraphs. Linear Algebra Appl. 2019;564:72–94.
  • Fan Y-Z, Huang T, Bao Y-H, et al. The spectral symmetry of weakly irreducible nonnegative tensors and connected hypergraphs. Trans Amer Math Soc. 2019;372(3):2213–2233.
  • Lu L, Man S. Connected hypergraphs with small spectral radius. Linear Algebra Appl. 2016;509:206–227.
  • Nikiforov V. Hypergraphs and hypermatrices with symmetric spectrum. Linear Algebra Appl. 2017;519:1–18.
  • Pearson K, Zhang T. On spectral hypergraph theory of the adjacency tensor. Graph Combin. 2014;30(5):1233–1248.
  • Qi L. H+-eigenvalues of Laplacian and signless Laplacian tensor. Commu Math Sci. 2014;12:1045–1064.
  • Schrijver A. Combinatorial optimization: polyhedra and efficiency. vol. a-c, Algorithms Combin., vol. 24, Springer-Verlag; 2004.
  • Harary F. On the notion of balance of s signed graph. Michigan Math J. 1953;2(2):143–146.
  • Cartwright D, Harary F. Structural balance: a generalization of Heider's theory. Psychol Rev. 1956;63:277–293.
  • Harary F, Kabell JA. A simple algorithm to detect balance in signed graphs. Math Soc Sci. 1980;1(1):131–136.
  • Hou Y, Li J, Pang Y. On the Laplacian eigenvalues of signed graphs. Linear Multilinear Algebra. 2003;51(1):21–30.
  • Zaslavsky T. Signed graphs. Discrete Appl Math. 1982;4:47–74.
  • Feng K, Li WCW. Spectral of hypergraphs and applications. J Number Theory. 1996;60:1–22.
  • Cardoso K, Trevisan V. The signless Laplacian matrix of hypergraphs. arXiv: 1909.00246v1.
  • Rodríguez JA. On the Laplacian eigenvalues and metric parameters of hypergraphs. Linear Multilinear Algebra. 2002;50(1):1–14.
  • Lim L-H. Singular values and eigenvalues of tensors: a variational approach. Proceedings of the 1st IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing. 2005. p. 129–132.
  • Qi L. Eigenvalues of a real supersymmetric tensor. J Symbolic Comput. 2005;40(6):1302–1324.
  • Chang KC, Pearson K, Zhang T. Perron-Frobenius theorem for nonnegative tensors. Commu Math Sci. 2008;6:507–520.
  • Friedland S, Gaubert S, Han L. Perron-Frobenius theorem for nonnegative multilinear forms and extensions. Linear Algebra Appl. 2013;438:738–749.
  • Shao J-Y. A general product of tensors with applications. Linear Algebra Appl. 2013;439:2350–2366.
  • Yang Y, Yang Q. Further results for Perron-Frobenius theorem for nonnegative tensors. SIAM J Matrix Anal Appl. 2010;31(5):2517–2530.
  • Yang Y, Yang Q. Further results for Perron-Frobenius theorem for nonnegative tensors II. SIAM J Matrix Anal Appl. 2011;32(4):1236–1250.
  • Yang Y, Yang Q. On some properties of nonnegative weakly irreducible tensors. arXiv: 1111.0713v2.
  • Fan Y-Z, Wang Y, Bao Y-H, et al. Eigenvectors of Laplacian or signless Laplacian of hypergraphs associated with zero eigenvalue. Linear Algebra Appl. 2019;579:244–261.
  • Shao J-Y, Shan H-Y, Wu B-F. Some spectral properties and characterizations of connected odd-bipartite uniform hypergraphs. Linear Multilinear Algebra. 2015;63:2359–2372.
  • Khan M, Fan Y-Z. On the spectral radius of a class of non-odd-bipartite even uniform hypergraphs. Linear Algebra Appl. 2015;480:93–106.

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