Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor | Department of Applied Mathematics | en_US |
| dc.creator | Hu, Shenglong | - |
| dc.identifier.uri | https://theses.lib.polyu.edu.hk/handle/200/7238 | - |
| dc.language | English | en_US |
| dc.publisher | Hong Kong Polytechnic University | - |
| dc.rights | All rights reserved | en_US |
| dc.title | Spectral hypergraph theory | en_US |
| 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. | en_US |
| dcterms.extent | xii, 107 p. : ill. ; 30 cm. | en_US |
| dcterms.isPartOf | PolyU Electronic Theses | en_US |
| dcterms.issued | 2013 | en_US |
| dcterms.educationalLevel | All Doctorate | en_US |
| dcterms.educationalLevel | Ph.D. | en_US |
| dcterms.LCSH | Calculus of tensors. | en_US |
| dcterms.LCSH | Hong Kong Polytechnic University -- Dissertations | en_US |
| dcterms.accessRights | open access | en_US |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| b26527650.pdf | For All Users | 1.14 MB | Adobe PDF | View/Open |
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