2014美国数学建模大赛论文

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1、TeamControlNumberForofficeuseonlyForofficeuseonlyT1________________31729F1________________T2________________F2________________T3________________F3________________ProblemChosenT4________________F4________________CUsingNetworkstoMeasureInfluenceandImpa

2、ctWiththedevelopmentofscienceandtechnology,therelationshipbetweenthingsbecomemoreandmorecomplex.Howtofindoutthemostinfluentialvertexinthenetworkbecomemoreandmoreimportant.Accordingtothecooperationdatagiveninthetopic,wefilterthe511authorswhodirectlyco

3、operatedwithErdos,andbuildtheconnectionbasedoncooperation.Eventually,wegeta511511relationshipmatrix.Thegraphoftheundirectedco-authornetworkisfiguredbysoftwarePajek.Then,weintroducethek-coreanddegreeindicators,proposetheco-degreeandcollindicatorsande

4、stablishthecomprehensiveevaluationmodel.Wegettheinfluencerankingofco-authorsbycomputingcomprehensiveindex,thetop4areSOSVERATURAN，PACHJANOS，GRAHAMRONALDLEWIS，CHUNGFANRONGKING(GRAHAM).Inthecitationrelationship,weclassifythepaperswhichareretrievedfromwe

5、bofscienceintothreelevelsbasedontheirImpactFactor.Weestablishthecitationnetworkaccordingtothecitingandcitiedrelationship.WeintroducetheSCIindicatorbasedonthePageRankalgorithm,andestablishacomprehensivecentralitymodel.Givingweighttoeachlevel,thencalcu

6、latethesumofweightstogetthecomprehensivecentralityindex(CCI).TheresultsshowthatthemostinfluentialpaperisCollectivedynamicsof`small-world'networks.Onthebasisofthedirectednetworkestablishedabove,weapplythemodelintoChinesedomesticairlinesnetwork.Usingth

7、eairportsofeachroutetocreateadomesticairlinesnetwork(asseenfigure5).Afterhavingrobustnessanalysis,itturnsoutthatonlymostoftraffichubsareinterfered,theairlinenetworkmaygraduallyparalyzed.Tosumup,themodelsweestablishcannotonlybeusedfortheresearchfield,

8、butalsocanbeappliedtootherfieldsinsociety.Ithasgreatpotentialvalueintheguidanceofdeterminationforindividuals,organizationandnations.Team317291ofPage18Content1.Introduction...............................................................................