diplomsko delo
Vesna Balan (Author), Dominik Benkovič (Mentor)

Abstract

Diplomsko delo se osredotoča na preučevanje Kroneckerjevih grafov. Najprej je predstavljena motivacija za vpeljavo in študij Kroneckerjevih grafov. V nadaljevanju je definiran Kroneckerjev ali tenzorski produkt matrik ter Kroneckerjev produkt grafov in njune osnovne lastnosti. V naslednjih poglavjih se pozornost nameni lastnostim Kroneckerjevih in stohastičnih Kroneckerjevih grafov. Predstavljen je porazdelitveni zakon stopnje posameznih vozlišč teh grafov. Dokazana sta zgostitveni potenčni zakon med številom vozlišč in številom povezav in ohranjanje efektivnega premera glede na začetni graf. Pri stohastičnih Kroneckerjevih grafih so podani potrebni in zadostni pogoji za povezanost in obstoj velike povezane komponente tega grafa. Dokazano je, če je graf povezan, je premer v tem grafu konstanten. Na koncu so prikazani primeri praktične uporabe teorije, predstavljene v diplomskem delu.

Keywords

Kroneckerjevi grafi;stohastični Kroneckerjevi grafi;grafi omrežij;diplomska dela;

Data

Language: Slovenian
Year of publishing:
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 Link will open in a new window
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Other data

Secondary language: English
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
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