Social Network Analysis: Methods and Applications

by Stanley Wasserman , Katherine Faust

• ISBN13: 9780521387071
• ISBN10: 0521387078
• Format: Paperback
• Copyright: 1994-11-25
• Publisher: Cambridge University Press

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