| Author: | Hu, Shenglong |
| Title: | Spectral hypergraph theory |
| Degree: | Ph.D. |
| Year: | 2013 |
| Subject: | Calculus of tensors. Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Applied Mathematics |
| Pages: | xii, 107 p. : ill. ; 30 cm. |
| Language: | English |
| 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. |
| Rights: | All rights reserved |
| Access: | open access |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| b26527650.pdf | For All Users | 1.14 MB | Adobe PDF | View/Open |
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