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[{"key": "dc.contributor.advisor", "value": "Laitinen, Anni", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.advisor", "value": "Leskel\u00e4, Lasse", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Pentik\u00e4inen, Kerttu", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2025-02-20T11:04:35Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2025-02-20T11:04:35Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2025", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/100360", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa tutustutaan satunnaiseen painotettuun leikkausverkkoon ja sen klusteroitumiseen. Maria Deijfen ja Willemien Kets esittelev\u00e4t verkkomallin artikkelissaan Random Intersection Graphs with Tunable Degree Distribution and Clustering. T\u00e4llaisia matemaattisia malleja voidaan k\u00e4ytt\u00e4\u00e4 laajojen oikean el\u00e4m\u00e4n yhteis\u00f6jen ja verkkojen mallintamiseen.\n\nSatunnaisen painotetun leikkausverkon j\u00e4senet eli solmut linkittyv\u00e4t toisiinsa ryhmien kautta. Jos kaksi solmua kuuluu samaan ryhm\u00e4\u00e4n, niin niiden v\u00e4lill\u00e4 on linkki. Verkkomallissa kullekin solmulle annetaan oma satunnainen painokerroin, joka vaikuttaa siihen, mill\u00e4 todenn\u00e4k\u00f6isyydell\u00e4 solmu kuuluu yksitt\u00e4iseen ryhm\u00e4\u00e4n.\n\nSatunnaisen painotetun leikkausverkon koon kasvaessa keskeisten ominaisuuksien kannalta mielenkiintoisin tilanne muodostuu, kun verkon solmujen ja ryhmien m\u00e4\u00e4r\u00e4t ovat suoraan verrannolliset. T\u00e4ll\u00f6in solmun asteen eli sen kavereiden lukum\u00e4\u00e4r\u00e4n rajajakaumaa ja verkkomallin klusteroituneisuutta eli linkkitiheytt\u00e4 voidaan s\u00e4\u00e4t\u00e4\u00e4 verkon parametrien avulla.\n\nKlusteroituneisuutta on ty\u00f6ss\u00e4 mitattu ns. klusteroitumiskertoimen ja sen raja-arvon avulla. Klusteroitumiskerroin on todenn\u00e4k\u00f6isyys sille, ett\u00e4 kahden solmun v\u00e4lill\u00e4 on linkki, kun tiedet\u00e4\u00e4n ett\u00e4 kumpikin n\u00e4ist\u00e4 solmuista linkittyy jo kolmanteen solmuun.\n\nSymmetrian vuoksi k\u00e4yd\u00e4\u00e4n l\u00e4pi solmun asteen rajajakauma ja verkon klusteroituminen my\u00f6s niiss\u00e4 tilanteissa, kun solmujen m\u00e4\u00e4r\u00e4 kasvaa hitaammin tai nopeammin kuin verkon ryhmien lukum\u00e4\u00e4r\u00e4.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2025-02-20T11:04:35Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2025-02-20T11:04:35Z (GMT). No. of bitstreams: 0\n Previous issue date: 2025", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "88", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": null, "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "leikkausverkot", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "klusteroituminen", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Satunnaisen painotetun leikkausverkon klusteroituminen", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202502202148", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": null, "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": null, "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Stokastiikka ja todenn\u00e4k\u00f6isyysteoria", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Stochastics and Probability", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.copyright", "value": "This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited.", "language": "fi", "element": "rights", "qualifier": "copyright", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.yso", "value": "verkkoteoria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "todenn\u00e4k\u00f6isyyslaskenta", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matemaattiset mallit", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "solmut", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}]
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