20.500.12556/DKUM-16826 KRONECKERJEVI GRAFI KRONECKER GRAPHS 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 ter ohranjanje efektivnega premera glede na začetni graf. Pri stohastičnih Kroneckerjevih grafih so podani potrebni in zadostni pogoji za povezanost ter obstoj velike povezane komponente tega grafa. Dokazano je tudi, če je graf povezan, je premer v tem grafu konstanten. Na koncu so prikazani primeri praktične uporabe teorije, predstavljene skozi vso diplomsko nalogo. 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. Kroneckerjevi grafi stohastični Kroneckerjevi grafi grafi omrežij direktni produkt grafov Kroneckerjev produkt matrik Kronecker graphs stochastic Kronecker graphs network graphs direct product of graphs Kronecker product of matrices true true false [V. Balan] Slovenski jezik Angleški jezik Diplomsko delo 2010-11-24 13:27:25 2011-09-06 20:33:01 2022-04-13 08:56:36 2023-12-21 03:19:22 2010 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 18046984 URN:SI:UM:DK:RTT6VWZD UNI_Balan_Vesna_i2010.pdf UNI_Balan_Vesna_i2010.pdf 1 97A1F02D0622A0CED5558FF531BBF4ED fabcf28d21f1f0dc89021b53197a62e8637b944c9abc655d43d00d8a5105ceff bd5f49f3-7c04-11eb-bb7a-00155d0001ca 20.500.12556/dkum/1121b348-58fd-449e-a7ab-8b8cf3279033 https://dk.um.si/Dokument.php?lang=slv&id=24554 Fakulteta za naravoslovje in matematiko 0 0 0