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[book]Social and Ecnomic Networks(Princeton University Press 2010)

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Social and Economic Networks1

Matthew O.Jackson

This Draft:March2008

Forthcoming:Princeton University Press

c copyright:Matthew O.Jackson

Do not distribute,post,or reproduce in any way without explicit permission of the author

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Contents

Preface11

1Introduction17

1.1Why Model Networks? (17)

1.2A Set of Examples: (18)

1.2.1Florentine Marriages (18)

1.2.2Friendships Among High School Students (21)

1.2.3Random Graphs and Networks (24)

1.2.4The Symmetric Connections Model (32)

1.3Exercises (36)

2Representing and Measuring Networks39

2.1Representing Networks (39)

2.1.1Nodes and Players (39)

2.1.2Graphs and Networks (40)

2.1.3Paths and Cycles (43)

2.1.4Directed Paths,Walks,and Cycles (45)

2.1.5Components and Connected subgraphs (47)

2.1.6Trees,Stars,Circles,and Complete Networks (49)

2.1.7Neighborhood (51)

2.1.8Degree and Network Density (52)

2.2Some Summary Statistics and Characteristics of Networks (53)

2.2.1Degree Distributions (53)

2.2.2Diameter and Average Path Length (55)

2.2.3Cliquishness,Cohesiveness,and Clustering (57)

2.2.4Centrality (62)

2.3Appendix:Some Basic Graph Theory (70)

3

2.3.1Hall’s theorem and Bipartite Graphs (70)

2.3.2Set Coverings and Independent Sets (71)

2.3.3Colorings (73)

2.3.4Eulerian Tours and Hamilton Cycles (74)

2.4Appendix:Eigenvectors and Eigenvalues (77)

2.4.1Diagonal Decompositions (79)

2.5Exercises (80)

3Empirical Background on Social and Economic Networks83

3.1The Prevalence of Social Networks (84)

3.2Observations about the Structure of Networks (85)

3.2.1Diameter and Small Worlds (85)

3.2.2Clustering (88)

3.2.3Degree Distributions (90)

3.2.4Correlations and Assortativity (97)

3.2.5Patterns of Clustering (99)

3.2.6Homophily (100)

3.2.7The Strength of Weak Ties (102)

3.2.8Structural Holes (103)

3.2.9Social Capital (104)

3.2.10Di¤usion (104)

4Random Graph-Based Models of Networks109

4.1Static Random-Graph Models of Random Networks (111)

4.1.1Poisson and Related Random Network Models (111)

4.1.2“Small World”Networks (112)

4.1.3Markov Graphs and p networks (115)

4.1.4The Con...guration Model. (117)

4.1.5An Expected Degree Model (122)

4.1.6Some Thoughts about Static Random Network Models (123)

4.2Properties of Random Networks (123)

4.2.1The Distribution of the Degree of a Neighboring Node (124)

4.2.2Thresholds and Phase Transitions (127)

4.2.3Connectedness (133)

4.2.4Giant Components (139)

4.2.5Size of the Giant Component in Poisson Random Networks (139)