Liu, Tianhang; Wei, Yimin The abstract Laplacian tensor of a hypergraph with applications in clustering. (English) Zbl 1497.15028 J. Sci. Comput. 93, No. 1, Paper No. 7, 22 p. (2022). Summary: The normalized abstract Laplacian tensor of a weighted hypergraph is investigated. The connectivity of the hypergraph is associated with the geometric multiplicity of the smallest eigenvalue of the abstract Laplacian tensor. There is an inequality between the normalized cut of the hypergraph and the second smallest eigenvalue of the abstract Laplacian tensor. An optimization method of the hypergraph clustering is established and analyzed. Numerical examples illustrate that our method is effective. Cited in 1 Document MSC: 15A69 Multilinear algebra, tensor calculus 15A18 Eigenvalues, singular values, and eigenvectors 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C65 Hypergraphs Keywords:hypergraph clustering; abstract tensor; Laplacian tensor; tensor eigenvalue PDFBibTeX XMLCite \textit{T. Liu} and \textit{Y. Wei}, J. Sci. Comput. 93, No. 1, Paper No. 7, 22 p. (2022; Zbl 1497.15028) Full Text: DOI References: [1] Absil, P-A; Mahony, R.; Sepulchre, R., Optimization Algorithms on Matrix Manifolds (2009), Princeton, NJ: Princeton University Press, Princeton, NJ · Zbl 1147.65043 [2] Amghibech, S., Eigenvalues of the discrete p-Laplacian for graphs, Ars Combin., 67, 283-302 (2003) · Zbl 1080.31005 [3] Ausiello, G.; Laura, L., Directed hypergraphs: introduction and fundamental algorithms - a survey, Theoret. Comput. 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