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http://hdl.handle.net/10397/85156
DC Field | Value | Language |
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dc.contributor | Department of Applied Mathematics | - |
dc.creator | Hu, Shenglong | - |
dc.identifier.uri | https://theses.lib.polyu.edu.hk/handle/200/7238 | - |
dc.language.iso | English | - |
dc.title | Spectral hypergraph theory | - |
dc.type | Thesis | - |
dcterms.abstract | The main subject of this thesis is the study of a few basic problems in spectral hypergraph theory based on Laplacian-type tensors. These problems are hypergraph analogues of some important problems in spectral graph theory. As some foundations, we study some new problems of tensor determinant and non-negative tensor partition. Then two classes of Laplacian-type tensors for uniform hypergraphs are proposed. One is called Laplacian, and the other one Laplace-Beltrami tensor. We study the H-spectra of uniform hypergraphs through their Laplacian, and the Z-spectra of even uniform hypergraphs through their Laplace-Beltrami tensors. All the H⁺-eigenvalues of the Laplacian can be computed out through the developed partition method. Spectral component, an intrinsic notion of a uniform hypergraph, is introduced to characterize the hypergraph spectrum. Many fundamental properties of the spectrum are connected to the underlying hypergraph structures. Basic spectral hypergraph theory based on Laplacian-type tensors are built. With the theory, we study algebraic connectivity, edge connectivity, vertex connectivity, edge expansion, and spectral invariance of the hypergraph. | - |
dcterms.accessRights | open access | - |
dcterms.educationLevel | Ph.D. | - |
dcterms.extent | xii, 107 p. : ill. ; 30 cm. | - |
dcterms.issued | 2013 | - |
dcterms.LCSH | Calculus of tensors. | - |
dcterms.LCSH | Hong Kong Polytechnic University -- Dissertations | - |
Appears in Collections: | Thesis |
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