Social and Economic Networks [Jackson] (2008) .pdf

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1、SocialandEconomicNetworks1MatthewO.JacksonThisDraft:February2008Forthcoming:PrincetonUniversityPressccopyright:MatthewO.JacksonDonotdistribute,post,orreproduceinanywaywithoutexplicitpermissionoftheauthor12ContentsPreface111Introduction171.1WhyModelNetworks?....

2、.......................171.2ASetofExamples:.............................181.2.1FlorentineMarriages........................181.2.2FriendshipsAmongHighSchoolStudents.............211.2.3RandomGraphsandNetworks..................251.2.4TheSymmetricConnectionsModel..

3、..............311.3Exercises...................................352RepresentingandMeasuringNetworks392.1RepresentingNetworks...........................392.1.1NodesandPlayers.........................392.1.2GraphsandNetworks........................402.1.3PathsandC

4、ycles..........................432.1.4DirectedPaths,Walks,andCycles................452.1.5ComponentsandConnectedsubgraphs..............472.1.6Trees,Stars,Circles,andCompleteNetworks..........492.1.7Neighborhood............................502.1.8DegreeandNetwork

5、Density....................512.2SomeSummaryStatisticsandCharacteristicsofNetworks.......522.2.1DegreeDistributions........................522.2.2DiameterandAveragePathLength................542.2.3Cliquishness,Cohesiveness,andClustering............572.2.4Central

6、ity..............................612.3Appendix:SomeBasicGraphTheory...................6934CONTENTS2.3.1Hall’stheoremandBipartiteGraphs...............692.3.2SetCoveringsandIndependentSets................712.3.3Colorings..............................722.3.4Euleri

7、anToursandHamiltonCycles...............742.4Appendix:EigenvectorsandEigenvalues.................772.4.1DiagonalDecompositions......................792.5Exercises...................................803EmpiricalBackgroundonSocialandEconomicNetworks833.1ThePrevalen

8、ceofSocialNetworks....................843.2ObservationsabouttheStructureofNetworks..............853.2.1DiameterandSmallWorlds....................853.2.2Clustering...........