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[{"key": "dc.contributor.advisor", "value": "Leskel\u00e4, Lasse", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.advisor", "value": "Laitinen, Anni", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Meyer, Henrik", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2015-09-02T16:30:59Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2015-09-02T16:30:59Z", "language": "", "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2015", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1494191", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/46745", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Duncan J. Watts ja Steven H. Strogatz m\u00e4\u00e4rittiv\u00e4t vuonna 1998 verkon klusterointikertoimen, joka on yleisesti k\u00e4ytetty tilastollinen mitta verkon klusteroituneisuuden analysointiin. Esimerkiksi sosiaalisen verkoston henkil\u00f6iden tuttavapiireill\u00e4 on taipumus klusteroitua siten, ett\u00e4 monet henkil\u00f6n tuttavista ovat my\u00f6s kesken\u00e4\u00e4n tuttavia.\r\nVerkon klusterointikerroin laskee keskiarvoisen murtoluvun henkil\u00f6n tuttavapareista, jotka ovat my\u00f6s kesken\u00e4\u00e4n tuttavia. Alain Barrat ja Martin Weigt sek\u00e4 Mark E. J. Newman, Duncan J. Watts ja Steven H. Strogatz m\u00e4\u00e4ritt\u00e4v\u00e4t verkon transitiivisuuskertoimen vaihtoehtoisena klusterointikertoimena. Sosiaalisessa verkostossa se laskee mill\u00e4 todenn\u00e4k\u00f6isyydell\u00e4 kaksi henkil\u00f6\u00e4, jotka ovat saman henkil\u00f6n tuttavia ovat my\u00f6s kesken\u00e4\u00e4n tuttavia.\r\nSatunnaisverkkomalleja on pitk\u00e4\u00e4n k\u00e4ytetty isojen monimutkaisten verkostojen analysointiin. Klusterointikertoimen k\u00e4ytt\u00f6\u00f6notosta alkaen on ollut mahdollista osoittaa tilastollisesti, ett\u00e4 monet sosiaaliset verkostot sek\u00e4 ihmisten tekem\u00e4t verkostot ovat pieni maailma -verkkoja. Esimerkiksi Facebook ja Internet ovat pieni maailma -verkkoja, eli harvoja ja hyvin klusteroituneita verkkoja, joissa verkon solmuparien keskim\u00e4\u00e4r\u00e4inen et\u00e4isyys on lyhyt. On osoittautunut, ett\u00e4 pieni maailma -verkkorakennetta ei ole mahdollista mallintaa perinteisill\u00e4 satunnaisverkoilla tai s\u00e4\u00e4nn\u00f6llisill\u00e4 hiloilla. D. J. Watts ja S. H. Strogatz esittiv\u00e4t vuonna 1998 uuden satunnaisverkkomallin, jolla on mahdollista generoida pieni maailma -verkkoja. Mallillaan he tutkivat muun muassa epidemian levi\u00e4mist\u00e4 sek\u00e4 signaalin etenemisnopeutta pieni maailma -verkoissa.\r\nT\u00e4m\u00e4n tutkielman tarkoitus on laskea matemaattiset lausekkeet Wattsin ja Strogatzin verkkomallin satunnaisverkon klusterointikertoimelle ja transitiivisuuskertoimelle. Tutkielmassa m\u00e4\u00e4ritell\u00e4\u00e4n matemaattisesti verkon tilastolliset klusterointi- ja transitiivisuuskertoimien eri muodot sek\u00e4 esitet\u00e4\u00e4n lauseita niiden yhteyksist\u00e4 ja\r\neroista. Lis\u00e4ksi m\u00e4\u00e4ritell\u00e4\u00e4n satunnaisverkon klusterointi- ja transitiivisuuskerroin matemaattisesti tarkkaan sek\u00e4 esitet\u00e4\u00e4n kaavoja n\u00e4iden laskemiseen. Wattsin ja Strogatzin verkkomallin satunnaisverkolle lasketaan solmuparien kytkent\u00e4todenn\u00e4k\u00f6isyydet, joiden avulla lasketaan matemaattiset lausekkeet verkkomallin satunnaisverkon klusterointi- ja transitiivisuuskertoimelle.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Henrik Meyer (hemeyer) on 2015-09-02 16:30:56.970038. Form: Pro gradu -lomake (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake). JyX data: [jyx_publishing-allowed (fi) =True]", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija.group@korppi.jyu.fi) on 2015-09-02T16:30:58Z\r\nNo. of bitstreams: 2\r\nURN:NBN:fi:jyu-201509022795.pdf: 1334249 bytes, checksum: 5772a25d49f8e5e990ef91258e379eb6 (MD5)\r\nlicense.html: 4815 bytes, checksum: 79565059cef68e3b688e5eb2707594a0 (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2015-09-02T16:30:59Z (GMT). No. of bitstreams: 2\r\nURN:NBN:fi:jyu-201509022795.pdf: 1334249 bytes, checksum: 5772a25d49f8e5e990ef91258e379eb6 (MD5)\r\nlicense.html: 4815 bytes, checksum: 79565059cef68e3b688e5eb2707594a0 (MD5)\r\n Previous issue date: 2015", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (86 sivua)", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "stokastiikka", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Wattsin ja Strogatzin satunnaisverkkomallin klusteroituneisuus", "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-201509022795", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "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": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.date.updated", "value": "2015-09-02T16:30:59Z", "language": "", "element": "date", "qualifier": "updated", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": "fi", "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": null, "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "verkkoteoria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "klusterit", "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.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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