Language: | Slovenian |
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Year of publishing: | 2010 |
Source: | Maribor |
Typology: | 2.11 - Undergraduate Thesis |
Organization: | UM FNM - Faculty of Natural Sciences and Mathematics |
Publisher: | [V. Balan] |
UDC: | 51(043.2) |
COBISS: |
18046984
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Views: | 735 |
Downloads: | 37 |
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Metadata: |
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Secondary language: | English |
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Secondary title: | KRONECKER GRAPHS |
Secondary abstract: | This graduation thesis focuses on the study of Kronecker graphs. First the motivation for introduction and investigation of Kronecker graphs is presented. Next are the definitions of the Kronecker or tensor product of matrices and the Kronecker product of graphs, introduced together with their basic properties. In the following chapters the focus is oriented to the study of the properties of Kronecker and stochastic Kronecker graphs. One of the important properties is the behaviour of the degree distribution. This result is folowed by the proof of the densification power law between the number of edges and the number of nodes and the proof of the conservation of the size of the effective diameter regarding the initiator graph. Next, necessary and sufficient conditions are proven for the connectivity and the existance of a giant component in the stochastic Kronecker graphs. From this follows that: under the parameters that the graph is connected, it also has a constant diameter. For conclusion examples for practical use of the theory presented throughout the thesis are given. |
Secondary keywords: | Kronecker graphs;stochastic Kronecker graphs;network graphs;direct product of graphs;Kronecker product of matrices; |
URN: | URN:SI:UM: |
Type (COBISS): | Undergraduate thesis |
Thesis comment: | Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo |
Pages: | 62 f. |
Keywords (UDC): | mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika; |
ID: | 8716096 |