9780521387071

Social Network Analysis: Methods and Applications

by
  • ISBN13:

    9780521387071

  • ISBN10:

    0521387078

  • Format: Paperback
  • Copyright: 11/25/1994
  • Publisher: Cambridge University Press

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Summary

Social network analysis is used widely in the social and behavioral sciences, as well as in economics, marketing, and industrial engineering. The social network perspective focuses on relationships among social entities and is an important addition to standard social and behavioral research, which is primarily concerned with attributes of the social units. Social Network Analysis: Methods and Applications reviews and discusses methods for the analysis of social networks with a focus on applications of these methods to many substantive examples. It is a reference book that can be used by those who want a comprehensive review of network methods, or by researchers who have gathered network data and want to find the most appropriate method by which to analyze it. It is also intended for use as a textbook as it is the first book to provide comprehensive coverage of the methodology and applications of the field.

Table of Contents

List of Tables
xxi
List of Illustrations
xxiv
Preface xxix
Part I: Networks, Relations, and Structure 1(66)
Social Network Analysis in the Social and Behavioral Sciences
3(25)
The Social Networks Perspective
4(6)
Historical and Theoretical Foundations
10(7)
Empirical Motivations
11(2)
Theoretical Motivations
13(2)
Mathematical Motivations
15(1)
In Summary
16(1)
Fundamental Concepts in Network Analysis
17(4)
Distinctive Features
21(1)
Organization of the Book and How to Read It
22(5)
Complexity
23(1)
Descriptive and Statistical Methods
23(1)
Theory Driven Methods
24(1)
Chronology
24(1)
Levels of Analysis
25(1)
Chapter Prerequisites
26(1)
Summary
27(1)
Social Network Data
28(39)
Introduction: What Are Network Data?
28(2)
Structural and Composition Variables
29(1)
Modes
29(1)
Affiliation Variables
30(1)
Boundary Specification and Sampling
30(5)
What Is Your Population?
31(2)
Sampling
33(2)
Types of Networks
35(8)
One-Mode Networks
36(3)
Two-Mode Networks
39(2)
Ego-centered and Special Dyadic Networks
41(2)
Network Data, Measurement and Collection
43(16)
Measurement
43(2)
Collection
45(10)
Longitudinal Data Collection
55(1)
Measurement Validity, Reliability, Accuracy, Error
56(3)
Data Sets Found in These Pages
59(8)
Krackhardt's High-tech Managers
60(1)
Padgett's Florentine Families
61(1)
Freeman's EIES Network
62(2)
Countries Trade Data
64(1)
Galaskiewicz's CEOs and Clubs Network
65(1)
Other Data
66(1)
Part II: Mathematical Representations of Social Networks 67(100)
Notation for Social Network Data
69(23)
Graph Theoretic Notation
71(6)
A Single Relation
71(2)
xcirc;Multiple Relations
73(2)
Summary
75(2)
Sociometric Notation
77(7)
Single Relation
79(2)
Multiple Relations
81(2)
Summary
83(1)
◯Algebraic Notation
84(1)
◯Two Sets of Actors
85(4)
&otime;Different Types of Pairs
86(1)
◯Sociometric Notation
87(2)
Putting It All Together
89(3)
Graphs and Matrices
92(75)
Why Graphs?
93(1)
Graphs
94(27)
Subgraphs, Dyads, and Triads
97(3)
Nodal Degree
100(1)
Density of Graphs and Subgraphs
101(2)
Example: Padgett's Florentine Families
103(2)
Walks, Trails, and Paths
105(4)
Connected Graphs and Components
109(1)
Geodesics, Distance, and Diameter
110(2)
Connectivity of Graphs
112(5)
Isomorphic Graphs and Subgraphs
117(2)
◯Special Kinds of Graphs
119(2)
Directed Graphs
121(15)
Subgraphs - Dyads
124(1)
Nodal Indegree and Outdegree
125(4)
Density of a Directed Graph
129(1)
An Example
129(1)
Directed Walks, Paths, Semipaths
129(3)
Reachability and Connectivity in Digraphs
132(2)
Geodesics, Distance and Diameter
134(1)
◯Special Kinds of Directed Graphs
134(2)
Summary
136(1)
Signed Graphs and Signed Directed Graphs
136(4)
Signed Graph
137(1)
Signed Directed Graphs
138(2)
Valued Graphs and Valued Directed Graphs
140(5)
Nodes and Dyads
142(1)
Density in a Valued Graph
143(1)
◯Paths in Valued Graphs
143(2)
Multigraphs
145(1)
&otime;Hypergraphs
146(2)
Relations
148(2)
Definition
148(1)
Properties of Relations
149(1)
Matrices
150(14)
Matrices for Graphs
150(2)
Matrices for Digraphs
152(1)
Matrices for Valued Graphs
153(1)
Matrices for Two-Mode Networks
154(1)
ôMatrices for Hypergraphs
154(1)
Basic Matrix Operations
154(5)
Computing Simple Network Properties
159(5)
Summary
164(1)
Properties
164(1)
Reflexivity
164(1)
Symmetry
165(1)
Transitivity
165(1)
Summary
165(2)
Part III: Structural and Locational Properties 167(178)
Centrality and Prestige
169(51)
Prominence: Centrality and Prestige
172(5)
Actor Centrality
173(1)
Actor Prestige
174(1)
Group Centralization and Group Prestige
175(2)
Nondirectional Relations
177(21)
Degree Centrality
178(5)
Closeness Centrality
183(5)
Betweenness Centrality
188(4)
&otime;Information Centrality
192(6)
Directional Relations
198(17)
Centrality
199(3)
Prestige
202(8)
A Different Example
210(5)
Comparisons and Extensions
215(5)
Structural Balance and Transitivity
220(29)
Structural Balance
222(11)
Signed Nondirectional Relations
223(5)
Signed Directional Relations
228(2)
◯Checking for Balance
230(2)
An Index for Balance
232(1)
Summary
232(1)
Clusterability
233(6)
The Clustering Theorems
235(3)
Summary
238(1)
Generalizations of Clusterability
239(4)
Empirical Evidence
239(1)
◯Ranked Clusterability
240(2)
Summary
242(1)
Transitivity
243(4)
Conclusion
247(2)
Cohesive Subgroups
249(42)
Background
250(3)
Social Group and Subgroup
250(2)
Notation
252(1)
Subgroups Based on Complete Mutuality
253(4)
Definition of a Clique
254(1)
An Example
254(2)
Considerations
256(1)
Reachability and Diameter
257(6)
n-cliques
258(1)
An Example
259(1)
Considerations
260(1)
n-clans and n-clubs
260(2)
Summary
262(1)
Subgroups Based on Nodal Degree
263(4)
k-plexes
265(1)
k-cores
266(1)
Comparing within to Outside Subgroup Ties
267(3)
LS Sets
268(1)
Lambda Sets
269(1)
Measures of Subgroup Cohesion
270(3)
Directional Relations
273(4)
Cliques Based on Reciprocated Ties
273(1)
Connectivity in Directional Relations
274(1)
n-cliques in Directional Relations
275(2)
Valued Relations
277(6)
Cliques, n-cliques, and k-plexes
278(4)
Other Approaches for Valued Relations
282(1)
Interpretation of Cohesive Subgroups
283(1)
Other Approaches
284(6)
Matrix Permutation Approaches
284(3)
Multidimensional Scaling
287(3)
◯Factor Analysis
290(1)
Summary
290(1)
Affiliations and Overlapping Subgroups
291(54)
Affiliation Networks
291(1)
Background
292(6)
Theory
292(2)
Concepts
294(1)
Applications and Rationale
295(3)
Representing Affiliation Networks
298(9)
The Affiliation Network Matrix
298(1)
Bipartite Graph
299(4)
Hypergraph
303(3)
◯Simplices and Simplicial Complexes
306(1)
Summary
306(1)
An example: Galaskiewicz's CEOs and Clubs
307(1)
One-mode Networks
307(5)
Definition
307(2)
Examples
309(3)
Properties of Affiliation Networks
312(14)
Properties of Actors and Events
312(2)
Properties of One-mode Networks
314(8)
Taking Account of Subgroup Size
322(2)
Interpretation
324(2)
&otime;Analysis of Actors and Events
326(16)
&otime;Galois Lattices
326(8)
&otime;Correspondence Analysis
334(8)
Summary
342(3)
Part IV: Roles and Positions 345(158)
Structural Equivalence
347(47)
Background
348(8)
Social Roles and Positions
348(3)
An Overview of Positional and Role Analysis
351(3)
A Brief History
354(2)
Definition of Structural Equivalence
356(5)
Definition
356(1)
An Example
357(2)
Some Issues in Defining Structural Equivalence
359(2)
Positional Analysis
361(5)
Simplification of Multirelational Networks
361(2)
Tasks in a Positional Analysis
363(3)
Measuring Structural Equivalence
366(9)
Euclidean Distance as a Measure of Structural Equivalence
367(1)
Correlation as a Measure of Structural Equivalence
368(2)
Some Considerations in Measuring Structural Equivalence
370(5)
Representation of Network Positions
375(16)
Partitioning Actors
375(10)
Spatial Representations of Actor Equivalences
385(3)
Ties Between and Within Positions
388(3)
Summary
391(3)
Blockmodels
394(31)
Definition
395(2)
Building Blocks
397(11)
Perfect Fit (Fat Fit)
398(1)
Zeroblock (Lean Fit) Criterion
399(1)
Oneblock Criterion
400(1)
α Density Criterion
400(1)
Comparison of Criteria
401(1)
Examples
401(5)
Valued Relations
406(2)
Interpretation
408(15)
Actor Attributes
408(3)
Describing Individual Positions
411(6)
Image Matrices
417(6)
Summary
423(2)
Relational Algebras
425(36)
Background
426(2)
Notation and Algebraic Operations
428(5)
Composition and Compound Relations
429(3)
Properties of Composition and Compound Relations
432(1)
Multiplication Tables for Relations
433(9)
Multiplication Tables and Relational Structures
435(4)
An Example
439(3)
Simplification of Role Tables
442(7)
Simplification by Comparing Images
443(2)
&otime;Homomorphic Reduction
445(4)
&otime;Comparing Role Structures
449(11)
Joint Homomorphic Reduction
451(1)
The Common Structure Semigroup
452(1)
An Example
453(4)
Measuring the Similarity of Role Structures
457(3)
Summary
460(1)
Network Positions and Roles
461(42)
Background
462(6)
Theoretical Definitions of Roles and Positions
462(2)
Levels of Role Analysis in Social Networks
464(2)
Equivalences in Networks
466(2)
Structural Equivalence, Revisited
468(1)
Automorphic and Isomorphic Equivalence
469(4)
Definition
470(1)
Example
471(1)
Measuring Automorphic Equivalence
472(1)
Regular Equivalence
473(10)
Definition of Regular Equivalence
474(1)
Regular Equivalence for Nondirectional Relations
475(1)
Regular Equivalence Blockmodels
476(3)
◯A Measure of Regular Equivalence
479(2)
An Example
481(2)
``Types'' of Ties
483(4)
An Example
485(2)
Local Role Equivalence
487(7)
Measuring Local Role Dissimilarity
488(3)
Examples
491(3)
&otime;Ego Algebras
494(8)
Definition of Ego Algebras
496(1)
Equivalence of Ego Algebras
497(1)
Measuring Ego Algebra Similarity
497(2)
Examples
499(3)
Discussion
502(1)
Part V: Dyadic and Triadic Methods 503(100)
Dyads
505(51)
An Overview
506(2)
An Example and Some Definitions
508(2)
Dyads
510(12)
The Dyad Census
512(1)
The Example and Its Dyad Census
513(1)
An Index for Mutuality
514(4)
&otime;A Second Index for Mutuality
518(2)
◯Subgraph Analysis, in General
520(2)
Simple Distributions
522(6)
The Uniform Distribution - A Review
524(2)
Simple Distributions on Digraphs
526(2)
Statistical Analysis of the Number of Arcs
528(7)
Testing
529(4)
Estimation
533(2)
&otime;Conditional Uniform Distributions
535(4)
Uniform Distribution, Conditional on the Number of Arcs
536(1)
Uniform Distribution, Conditional on the Outdegrees
537(2)
Statistical Analysis of the Number of Mutuals
539(5)
Estimation
540(2)
Testing
542(1)
Examples
543(1)
&otime;Other Conditional Uniform Distributions
544(8)
Uniform Distribution, Conditional on the Indegrees
545(2)
The U\MAN Distribution
547(3)
More Complex Distributions
550(2)
Other Research
552(3)
Conclusion
555(1)
Triads
556(47)
Random Models and Substantive Hypotheses
558(1)
Triads
559(16)
The Triad Census
564(10)
The Example and Its Triad Census
574(1)
Distribution of a Triad Census
575(10)
&otime;Mean and Variance of a k-subgraph Census
576(3)
Mean and Variance of a Triad Census
579(2)
Return to the Example
581(1)
Mean and Variance of Linear Combinations of a Triad Census
582(2)
A Brief Review
584(1)
Testing Structural Hypotheses
585(13)
Configurations
585(5)
From Configurations to Weighting Vectors
590(2)
From Weighting Vectors to Test Statistics
592(3)
An Example
595(1)
Another Example --- Testing for Transitivity
596(2)
Generalizations and Conclusions
598(3)
Summary
601(2)
Part VI: Statistical Dyadic Interaction Models 603(122)
Statistical Analysis of Single Relational Networks
605(70)
Single Directional Relations
607(28)
The Y-array
608(4)
Modeling the Y-array
612(7)
Parameters
619(14)
&otime;Is p1 a Random Directed Graph Distribution?
633(1)
Summary
634(1)
Attribute Variables
635(14)
Introduction
636(1)
The W-array
637(3)
The Basic Model with Attribute Variables
640(6)
Examples: Using Attribute Variables
646(3)
Related Models for Further Aggregated Data
649(7)
Strict Relational Analysis --- The V-array
651(3)
Ordinal Relational Data
654(2)
◯Nondirectional Relations
656(2)
A Model
656(1)
An Example
657(1)
&otime;Recent Generalizations of p1
658(4)
&otime;Single Relations and Two Sets of Actors
662(3)
Introduction
662(1)
The Basic Model
663(1)
Aggregating Dyads for Two-mode Networks
664(1)
Computing for Log-linear Models
665(8)
Computing Packages
666(5)
From Printouts to Parameters
671(2)
Summary
673(2)
Stochastic Blockmodels and Goodness-of-Fit Indices
675(50)
Evaluating Blockmodels
678(14)
Goodness-of-Fit Statistics for Blockmodels
679(9)
Structurally Based Blockmodels and Permutation Tests
688(1)
An Example
689(3)
Stochastic Blockmodels
692(27)
Definition of a Stochastic Blockmodel
694(2)
Definition of Stochastic Equivalence
696(1)
Application to Special Probability Functions
697(6)
Goodness-of-Fit Indices for Stochastic Blockmodels
703(3)
◯Stochastic a posteriori Blockmodels
706(2)
Measures of Stochastic Equivalence
708(1)
Stochastic Blockmodel Representations
709(3)
The Example Continued
712(7)
Summary: Generalizations and Extensions
719(6)
Statistical Analysis of Multiple Relational Networks
719(2)
Statistical Analysis of Longitudinal Relations
721(4)
Part VII: Epilogue 725(10)
Future Directions
727(8)
Statistical Models
727(2)
Generalizing to New Kinds of Data
729(2)
Multiple Relations
730(1)
Dynamic and Longitudinal Network Models
730(1)
Ego-centered Networks
731(1)
Data Collection
731(1)
Sampling
732(1)
General Propositions about Structure
732(1)
Computer Technology
733(1)
Networks and Standard Social and Behavioral Science
733(2)
Appendix A Computer Programs 735(3)
Appendix B Data 738(18)
References 756(46)
Name Index 802(9)
Subject Index 811(8)
List of Notation 819

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