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Network Analysis
The size and availability of network information has exploded over the
last decade. Social scientists now share the stage of network analysis
with computer scientists, physicists, and statisticians. While a number
of introductions to network analysis are now available, most focus on
theory, methods, or application alone. This book integrates all three.
Network Analysisis an introduction to both the why and how of social
network analysis (SNA). It presents a broad theoretical overview rooted
in social scientiﬁc approaches and guides users in how network analysis
can answer core theoretical questions. It provides a comprehensive
overview of descriptive and analytical approaches, including practical
tutorials in R with sample data sets. Using an integrated approach, this
book aims to quickly bring novice network researchers up to speed
while avoiding common programming and analysis mistakes so that
they might gain insight into the fundamental theories, key concepts, and
methodological application of SNA.
 .is Associate Professor of Sociology at Duke
University, where he is afﬁliated with the Duke Network Analysis
Center. His work focuses on the connections between social structures
and culture, including belief systems, knowledge, meaning-making pro-
cesses, and attitude change. His publications have appeared in the
American Journal of Sociology,American Sociological Review,Social
Forces,Sociological Science, andPoetics.
 .is Senior Policy Analyst in Mental Health and
Addictions at the Nova Scotia Health Authority. He has done meth-
odological work on network sampling and missing data, as well as more
substantive work on network processes, drug use, and health outcomes.
His work has been published in theAmerican Sociological Review,
Sociological Methodology,Social Networks, and other venues.
  is Professor of Sociology at Duke University and
focuses on the network foundations of social cohesion and diffusion,
using network analysis to help understand topics including racial segre-
gation, disease spread, and the development of scientiﬁc disciplines. He
has won the Freeman Award for contributions to network analysis and
a James S. McDonnel Foundation Complexity Scholars award.

 .is Professor of Education and (by courtesy)
Sociology and Organizational Behavior at Stanford University, where
he founded Stanford’s Center for Computational Social Science. His
past work studied social network dynamics of communication, relation-
ships, afﬁliations, and knowledge structures in educational contexts.
His current work integrates social network analysis and natural lan-
guage processing to study the development of scientiﬁc knowledge.

STRUCTURAL ANALYSIS IN THE SOCIAL SCIENCES
Edited by Mark Granovetter
The series Structural Analysis in the Social Sciences presents studies that ana-
lyze social behavior and institutions by reference to relations among such
concrete social entities as persons, organizations, and nations. Relational analy-
sis contrasts on the one hand with reductionist methodological individualism
and on the other with macro-level determinism, whether based on technology,
material conditions, economic conﬂict, adaptive evolution, or functional
imperatives. In this more intellectuallyﬂexible, structural middle ground, ana-
lysts situate actors and their relations in a variety of contexts. Since the series
began in 1987, its authors have variously focused on small groups, history,
culture, politics, kinship, aesthetics, economics, and complex organizations,
creatively theorizing how these shape and in turn are shaped by social relations.
Their style and methods have ranged widely, from intense, long-term ethno-
graphic observation to highly abstract mathematical models. Their disciplinary
afﬁliations have included history, anthropology, sociology, political science,
business, economics, mathematics, and computer science. Some have made
explicit use of social network analysis, including many of the cutting-edge
and standard works of that approach, whereas others have kept formal analysis
in the background and used“networks”as a fruitful orienting metaphor. All
have in common a sophisticated and revealing approach that forcefully illumin-
ates our complex social world.
Recent Books in the Series
Mario L. Small, Brea L. Perry, Bernice A. Pescosolido, and Edward B. Smith,
Personal Networks: Classic Readings and New Directions in Egocentric
Analysis
David Knoke, Mario Diani, and Dimitris Christopolous, and James Holloway,
Multimodal Political Networks
Claire BIdart, Alain Degenne, and Michel Grossetti,Living in Networks: The
Dynamics of Social Relations
William Sims Bainbridge,The Social Structure of Online Communities
Michael Kenney,The Islamic State in Britain: Radicalization and Resilience in
an Activist Network
Wouter De Nooy, Andrej Mrvar, and Vladimir Batagelj,Exploratory Social
Network Analysis with Pajek: Revised and Expanded Edition for Updated
Software

Sean F. Everton,Networks and Religion: Ties that Bind, Loose, Build-up and
Tear Down
Darius Mehri,Iran Auto
Navid Hassanpour,Leading from the Periphery and Network Collective
Action
Cheol-Sung Lee,When Solidarity Works
Benjamin Cornwell,Social Sequence Analysis
Mariela Szwarcberg,Mobilizing Poor Voters
Luke M. Gerdes, ed.,Illuminating Dark Networks
Silvia Domínguez and Betina Hollstein, eds.,Mixed Methods in Studying Social
Networks
Dean Lusher, Johan Koskinen, and Garry Robins, eds.,Exponential Random
Graph Models for Social Networks: Theory, Methods, and Applications
Sean F. Everton,Disrupting Dark Networks
Wouter de Nooy, Andrej Mrvar, and Vladimir Batagelj,Exploratory Social
Network Analysis with Pajek
Noah E. Friedkin and Eugene C. Johnsen,Social Inﬂuence Network Theory
Zeev Maoz,The Networks of Nations: The Evolution and Structure of
International Networks, 1816–2001
Martin Kilduff and David Krackhardt,Interpersonal Networks in
Organizations
Ari Adut,On Scandal: Moral Disturbances in Society, Politics, and Art
Robert C. Feenstra and Gary G. Hamilton,Emergent Economies, Divergent
Paths
Eiko Ikegami,Bonds of Civility: Aesthetic Networks and the Political Origins
of Japanese Culture
Peter Carrington, John Scott, and Stanley Wasserman,Models and Methods in
Social Network Analysis
Patrick Doreian, Vladimir Batagelj, and Anujka Ferligoj,Generalized
Blockmodeling
James Lincoln and Michael Gerlach,Japan’s Network Economy
Robert Franzosi,From Words to Numbers
Sean O’Riain,The Politics of High-Tech Growth
Philippe Bourgois,In Search of Respect: Selling Crack in El Barrio(Second
Edition)
Isabella Alcañiz,Environmental and Nuclear Networks in the Global South

Network Analysis
Integrating Social Network Theory, Method, and
Application with R
CRAIG M. RAWLINGS
Duke University
JEFFREY A. SMITH
Nova Scotia Health Authority
JAMES MOODY
Duke University
DANIEL A. MCFARLAND
Stanford University

Shaftesbury Road, Cambridge CB2 8EA, United Kingdom
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education, learning and research at the highest international levels of excellence.
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Information on this title:www.cambridge.org/9781107037786
DOI:10.1017/9781139794985
© Craig M. Rawlings, Jeffrey A. Smith, James Moody, and Daniel A. McFarland 2023
This publication is in copyright. Subject to statutory exception and to the provisions
of relevant collective licensing agreements, no reproduction of any part may take
place without the written permission of Cambridge University Press & Assessment.
First published 2023
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Library of Congress Cataloging-in-Publication Data
Names: McFarland, Daniel A., 1971- author. | Smith, Jeffrey A., 1983- author.
Title: Network analysis : integrating social network theory, method, and application with R /
Daniel A. McFarland, Stanford University, Jeffrey A. Smith, University of Nebraska, Lincoln,
James Moody, Duke University, North Carolina, Craig M. Rawlings, Duke University, North
Carolina.
Description: 1 Edition. | New York : Cambridge University Press, [2023] | Series: Sass structural
analysis in the social sciences
Identiﬁers: LCCN 2023011794 (print) | LCCN 2023011795 (ebook) | ISBN 9781107037786
(hardback) | ISBN 9781107611900 (paperback) | ISBN 9781139794985 (epub)
Subjects: LCSH: Social sciences–Network analysis. | Social networks–Research–Methodology. |
Application software. | Web applications.
Classiﬁcation: LCC HM741 .M3864 2023 (print) | LCC HM741 (ebook) | DDC 302.3072–dc23/
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Cambridge University Press & Assessment has no responsibility for the persistence
or accuracy of URLs for external or third-party internet websites referred to in this
publication and does not guarantee that any content on such websites is, or will remain,
accurate or appropriate.

Contents
List of Figures page ix
List of Tables xv
Acknowledgments xvii
1 Introduction: Network Analysis Today 1
   
2 What Is Social Structure? 19
3 What Is a Social Network? 45
4 How Are Social Network Data Collected? 67
5 How Are Social Network Data Visualized? 88
   
6 Structuration and Egocentric Networks 117
7 Sociality and Elementary Forms of Structure 143
8 Cohesion and Groups 161
9 Hierarchy and Centrality 190
10 Positions and Roles 216
11 Afﬁliations and Dualities 246
12 Networks and Culture 269
    
13 Models for Networks 301
14 Models for Network Diffusion 340
vii

15 Models for Social Inﬂuence 364
16 Conclusion: Network Analysis Tomorrow 390
References 421
Index 447
viii Contents

Figures
1.1 Types of systems page4
1.2 High school sexual relations network (Bearman, Moody,
& Stovel2004) 10
1.3 Structural forces in international relations 11
2.1 Schematic of rendering reality into knowledge 20
2.2 Networks from slices of interactions using classroom
observation data (Bender-deMoll & McFarland2006) 22
2.3 Schematic of social structure (adapted from Hinde 1976) 25
2.4 Social structure constructed in notes passed between two high
school students (McFarland & Wolff2022) 30
2.5 Hypothetical romantic network 36
2.6 Role structure of a Western family unit 37
2.7 Role structure of the Trobriand Island Kula Ring
exchange network 39
3.1 The Königsberg bridge problem and its graph representation46
3.2 A basic network structure 48
3.3 Four types of networks 52
3.4 Kinship/business relations among Florentine families in
the Renaissance 53
3.5 Southern women and their social event attendance 55
3.6 Example graph and basic network deﬁnitions 57
3.7 Walks of length 3 from Tim 57
4.1 The difference between complete and partial network data 68
4.2 The consequences of missing network data 80
4.3 Simple imputation options for missing network data 82
5.1 Scatterplots of three bivariate distributions shown in
Table 5.1 89
ix

5.2 “Circus Sideshow”by Georges Seurat, with detail 90
5.3 Girls ’cabin signed network from Moreno (1934) 91
5.4
(a–c)
Three visualizations of Zachary’s(1977) karate club data94
5.5 Visualization of a dyadic distance matrix of select US cities96
5.6 Spatial representation of Moreno’s(1934) data 98
5.7 Hospital exchange network using ZIP codes for coordinates99
5.8 Tree diagram 101
5.9 Family tree diagram (Kaplanis et al.2018) 102
5.10 Girls’cabin network as positive, negative, and joint ties,
using positive ties for layout 104
5.11 Using colors and weights to modify the default image for
publication display 106
5.12 Modi ﬁed image of Moreno data 107
5.13 Removing nodes to clarify relations 108
5.14
(a and b)
Suppressing nodes on a large, dense graph clariﬁes relations
between authors and topics in large-scale science network109
5.15 Contour sociogram of natural science disciplines 109
5.16 Contour sociogram of Scholars@Duke data 110
5.17 Alluvialﬂow diagram of small STD simulation data
(Bender-deMoll2016) 112
5.18 Dynamic senate co-voting blocks (Moody & Mucha2013) 112
6.1 Ideal-typical self in Western society 120
6.2
(a and b)
Typiﬁed egocentric networks 128
6.3 A typical Facebook friend network 130
6.4 Racial homophily as a function of high school racial
heterogeneity (Moody2001) 134
6.5 Racial mixing matrix in one high school 135
6.6 The density of an egocentric network 136
6.7 Egocentric networks and structural holes 136
6.8 Redundancy and constraint in an ego’s network structure137
6.9 Five types of brokers (Gould & Fernandez1989) 141
7.1 Three types of dyads in directed networks: mutual,
asymmetric, and null 146
7.2 Example calculation of reciprocity 147
7.3 The four types of triads for undirected networks 149
7.4 The sixteen types of triads for directed networks 150
7.5 Triad census 151
7.6 The bank wiring room friendship network (Roethlisberger,
Dickson, & Wright1947[1939]) 151
7.7 Forty triadic motifs in networks with two types of symmetric
ties (shown in red and blue) 153
7.8 Fritz Heider’s POX System 156
x List of Figures

8.1 Conceptualizing the social cohesiveness of networks 163
8.2 Network density versus connectivity 165
8.3 A simple ridge structure 166
8.4 Connectivity as robustness to node removal 169
8.5 Ideal-typical small-world network structure 171
8.6 Small network with many overlapping cliques 176
8.7 Network with two 3-cores 177
8.8 Comparing four approaches to deriving
cohesive subgroups 181
8.9 Resolution parameter sweep 182
8.10 Connectivity sets forFigure 8.3 185
9.1 The conundrum of network degree centrality 197
9.2 Poisson distribution of centrality in a random network 204
9.3 Degree centrality distribution, 10,000 node network with a
nearly scale-free degree distribution 206
9.4 Varieties of hierarchy 207
9.5 Two macrostructures with no violations of balance rules 209
9.6 Relaxing the A4 balance rule allows for multiple clusters210
9.7
(a and b)
Relaxing the A4 and A3 rules (a) and relaxing the A4, A3,
and A2 rules (b) affords hierarchical macrostructures210
9.8 Idealized image matrices of hierarchical structures depicted
inFigure 9.4 213
10.1 Stereotypical school role relations 219
10.2 Roles derived from compound relations 220
10.3 Structural equivalence in a formal hierarchy 222
10.4 Automorphic equivalence 223
10.5 Regular equivalence 224
10.6 A typical hierarchical structure 225
10.7 Reduced macrostructure of hierarchy inFigure 10.6 227
10.8 Reduced macrostructure of hierarchy inFigure 10.6based
on regular equivalence 227
10.9 Illustrating stacking multiple relations within a family
exchange network 228
10.10 Illustration of the CONCOR algorithm 230
10.11 Illustrating hierarchical cluster analysis 232
10.12 Triad-position census for deriving role equivalence 236
10.13
(a–d)
Role positions in a classroom friendship network 238
10.14 Comparing role structures in two high schools 240
10.15
(a and b)
Generalized blockmodels with four or more positions241
11.1
(a and b)
Two structures of overlapping social circles of
four individuals 247
List of Figures xi

11.2 Two-mode network of faculty and departments via
joint appointments 251
11.3
(a and b)
One-mode projections of southern women’safﬁliations
through events 253
11.4 Academic careers in high school math course–taking
(McFarland 2006) 260
11.5 Correspondence analysis of southern women and
club events 263
11.6
(a and b)
Five organizational forms in a two-dimensional Blau
space, depicted as overlapping niches (a) and a network (b)266
12.1 Journal co-citation network in the social sciences (Moody &
Light2006) 273
12.2
(a and b)
Correspondence analyses of tastes in music and
undergraduate major (1993 GSS) 279
12.3 Three-dimensional factor analysis of music tastes with
undergraduate major centroids 282
12.4 Two-dimensional MDS of music tastes (1993 GSS) 284
12.5
(a–d)
Four correlational classes of music tastes (1993 GSS)288
12.6 Attitude network of music tastes (1993 GSS) 292
12.7 Topic contour plots of core sociology journals, 1990–92 and
2009–11 294
12.8 A prioridecision tree for choosing clustering methods
(Pimentel2014) 296
13.1 QAP on “same race”in one Add Health school 315
13.2 Edgewise expected values from“p1”simple random
graph models 317
13.3 Exemplar data matrix for simple ERGM change statistics 320
13.4 Three latent space models of Sampson’s monastery data 328
13.5 3D plot of Sampson’s monastery data 329
13.6 Role structure mobility matrix 331
13.7 The STERGM framework jointly models tie formation and tie
dissolution (Statnet Development Team; see Morris et al.
2014) 335
14.1 Common SIR model representation 343
14.2 Example of SIR compartmental model dynamics 344
14.3 US COVID-19 infections over time 345
14.4 School 2 from the Add Health network, with edges weighted
by the number of activities students reported doing with
one another 350
14.5 Simulated SIR on network fromFigure 14.4, with constant
transmission probability (0.1), proportional to
edge weights 352
14.6 Temporal constraints on diffusion exposure 354
xii List of Figures

14.7 Varying thresholds for adoption given a single source set
(yellow) 359
14.8 Distribution of the proportion of students joining the movement
by average threshold level–ensemble of 500 random
threshold distributions 360
15.1 Simulated peer inﬂuence on heterodox opinion 368
15.2 The structural alignment of friends and interests 381
16.1 GitHub network 395
16.2
(a and b)
Two details of GitHub network 396
16.3 Follower network of 300,000+ Twitter users 396
16.4 Block-image network for a PROSPER school, with lines
shaded by difference from expected value 399
16.5 Second-order clustering of triadic role positions 400
16.6 Example of a multiplex network as a multilayer network 414
16.7 Idealized adjacency matrices from multilayering of networks
of southern women’s clubs data 415
16.8 Newcomb ’s fraternity data presented as a multilayer
(temporal) network 416
List of Figures xiii

Tables
2.1 Types of causal social-structural questions and social network
research agendas page33
3.1 Adjacency matrix of Florentine family relations 60
3.2 Afﬁliation matrix of southern women data 61
3.3 Edgelist of Florentine family relations 63
3.4 Adjacency list of Florentine family relations 64
4.1 Sample network questionnaire 73
4.2 Comparison of realist and nominalist data collection strategies79
5.1 Three bivariate distributions 89
5.2 Distance matrix ofﬁve US cities 95
6.1 Common ego network measures related to
structuration features 139
7.1 Uncertainty in relating 154
8.1 Odds ratios as a measure of group segregation 174
8.2 Blocking matrix 186
9.1 Typology of centrality scores (Borgatti & Everett2006) 196
9.2 Triadic forms forbidden by one or more balance theory rules211
10.1 Summarized positional relations 219
10.2 Permuted adjacency matrix based on the blockmodel of
hierarchy inFigure 10.6 225
10.3 Image matrix reduction of the blockmodel solution in
Table 10.2 226
12.1 Factor analysis of music tastes (1993 GSS) 282
13.1 Common structural and actor effects included in ERGMs 322
13.2 Statistical models for longitudinal networks 332
13.3 Inventory of p-shifts with examples (Gibson2003) 337
15.1 SAOM of peer inﬂuence on smoking (see Schaefer, Haas, &
Bishop2012) 384
xv

Acknowledgments
This book is the product of an invisible college that spans hundreds of
campuses with thousands of faculty, students, and researchers in academia
and industry. Members belong to disciplines across the social and natural
sciences, engineering, and the humanities. But this college has no lecture halls
or gardens of its own. Some of its members meet regularly at conferences or
online, while many know each other only on paper. And yet, it is a college in the
sense that it exists as a network of scholars who share the same intellectual
goals and jointly add to a shared body of knowledge. We were educated in this
college when it was somewhat smaller and mainly consisted of social scientists.
We offer this book as an attempt to afﬁrm and strengthen some of those social
scientiﬁc roots, and in the hope that doing so will help nourish and integrate the
many branches of this invisible college today.
Our primary thanks go to those who helped to build this college. And to be
clear, there are so many we are certain to have forgotten to cite and thank all
those who deserve it. We stand on the shoulders of generations of scholars who
pioneered network analysis. We have known many of these scholars personally,
and they continue to inspire us. Weﬁrst acknowledge our direct teachers and
formal mentors in network analysis: Peter Bearman, Charles Bidwell, Peter
Blau, Noah Friedkin, Roger Gould, Maureen T. Hallinan, Edward Laumann,
J. Miller McPherson, John Mohr, John Padgett, and Doug White. We also
thank our teachers’teachers: Harrison White, James Coleman, Paul DiMaggio,
Walter Powell, and Scott Boorman. We have learned a great deal through the
informal networks of friendship and advice that are also vital to the integration
of the invisible college, especially the following individuals: jimi adams, Chris
Bail, Ronald Breiger, Ronald Burt, Carter Butts, Karen Cook, Linus Dahlander,
David Diehl, Paul DiMaggio, Jan Fuhse, Amir Goldberg, Sharique Hasan,
Henning Hillman, Lisa A. Keister, John Levi Martin, Paul McLean, Ann
xvii

Mische, Jonathan Morgan, Martina Morris, Andrej Mrvar, Peter J. Mucha,
Paolo Parigi, Sanne Smith, Lynn Smith-Lovin, Steve Vaisey, Alex Volfovsky,
and Stanley Wasserman. We would also never have gotten here without the
students we have taught over the years and the need to try to distill so much of
this knowledge into a course of learning. Special thanks to graduate students
Gabriel Varela, Tom Wolff, and Joe Quinn for sundry reviews of the R labs and
speciﬁc text details. We have each taught elements of this text in our courses
and thank the students who suffered through early and incomplete versions of
this manuscript for their feedback on the text and labs, as it was always
welcome and wonderful. You know who you are, and we thank you for
teaching us how to better teach this material through trial and much error.
Many of the R labs presented in this textbook were built from prior versions
developed at Stanford University by Daniel A. McFarland, Solomon Messing,
Michael Nowak, Sean J. Westwood, and Sanne Smith.Chapter 5’s lab for
NDTV drew on Skye Bender-deMoll’s materials;Chapter 12on LDA/CA came
from Love Börjeson and Daniel A. McFarland;Chapter 13concerning
“ERGM”and“relevant”drew on Carter Butts’materials; andChapter 15on
SIENA/SAOM drew on ICS materials. Finally, a great many resources from the
Duke Network Analysis Center (DNAC) helped us in formulating elements in
many of the labs. For example,Chapter 4on missing data imputation drew on
James Moody and Jeffrey A. Smith’s work in the DNAC, as didChapter 14on
diffusion. We are grateful to these institutions and individuals for sharing code
and helping us formulate applications for each chapter’s theories.
We have been fortunate to beneﬁt from the time and research opportunities
provided by external funding throughout the lifetime of this project. This
includes the Social Networks and Health (SN&H) NICHD Workshop grant
(NICHD, 2 R25 HD079352–06), which supported the development of many of
the pedagogical ideas, and a James S. McDonnell Foundation Complexity
Scholars award to James Moody (220020397). Examples in the text draw on
data collected or analysis completed in whole or in part from numerous funded
projects, including NSF (0624134, 1633036, 1827477, SMA-1829240,
2022435; BCS-2024271-1; SES-2029790), NIH (R01 DA018225–05A1, R01
HD075712–01; R21HD104431), and DARPA (FA8650–18-C-7826).
This manuscript beneﬁted from several individuals who read it in part or
whole. We are extremely grateful to Kevin Lewis for reading the entire manu-
script and providing detailed comments. We cannot overstate how helpful his
insights were in clarifying points large and small. Our deep thanks also go to
Tom Snijders for expert advice and detailed comments onPart IIIof the book.
These insights were invaluable. Others have supported this endeavor in import-
ant ways. We are very grateful for expert editorial assistance provided by Laura
Tesch. We also thank Colin Birkhead for additional editorial help. We are also
grateful to Robin Gauthier and Sela Harcey for their helpful comments and
suggestions on the R tutorials. Craig Rawlings thanks Moira Killoran and
xviii Acknowledgments

Clayton Childress for their expert advice on many occasions. Finally, we thank
Mark Granovetter for believing in this endeavor and supporting it along its
long journey. It was a long, well-traveled road, crowded with assistance, and
that has made all the difference.
The authors would like to dedicate the book to:
CMR: JMR
JAS: GRG & EAAS
JWM: LAK
DAM: SMS
Acknowledgments
xix

1
Introduction
Network Analysis Today
1.1  
Stop. Take a moment to look around. What do you see? No matter where you
are, you are likely perceiving a world consisting ofthings. Maybe you are
reading this book in a coffee shop, and if so, you probably see people, cups,
books, chairs, and so on. You see a world of objects with properties, yourself
included: white cups are on wooden tables, people sitting in chairs are reading
books and talking with one another. At the same time, you are a subject,
responding to this world and actively bringing yourself and these objects into
interrelation. And yet, the world of objects with properties that you are per-
ceiving is but one slice of a complex reality.
What is less obvious and often taken for granted is all therelationshipsthat
come together to make this world of things a sensible, navigable reality. In the
coffee shop you are unlikely to notice the complex patterns of exchanges in
resources that brought the coffee to your table, the hierarchy of relationships
that organizes the work roles in the coffee shop, or the stable pattern of
interactions among customers coming and going that make the coffee shop a
hub in theﬂows in so many people’s everyday lives. You take those exchanges
and relationships for granted; and yet, you are embedded within them. You and
the world of things you perceive are inextricably tied together through these
invisible webs ofﬂows, exchanges, and more or less stable relationships. They
uphold and provide meaning for your subjectively experienced reality.
The natural and social worlds areﬁlled withﬂows, exchanges, and relation-
ships like these. By studying these largely unseen patterns, ornetworks,we
come to understand myriad social phenomena–for example, how persons
assume distinct roles, like barista, and the role relations between employees and
patrons; the ways in which personal relationships form and evolve from that of
employee–patron or coworkers to something more intimate, like friends or
1

romantic partners; and how gossip spreads information across some of these
role relations more than others. Many of our dearest social institutions are
replete with persistent associations, such as peer groups, families, and schools.
Even our casual dinner conversations can be viewed as having recognizable
patterns that we interpret as either a positive bonding moment or an awkward
one. These all entailsocialnetworks–that is,ﬂows, exchanges, and relation-
ships that exist only within human experience and behavior.
But take a moment to consider all the other phenomena that also have relational
properties. Molecules are structures formed by an assortment of atomic bonds.
Brains function through structures of neural connections. Ecosystems entail struc-
tures of food webs where various animals and plants consume one another,
thereby creatingﬂows of carbon and energy. The Internet is organized by links
that connect web pages. Markets move in response to a system of patterned
transactions. Language creates meaning by assembling a complex set of relation-
ships between words, sentences, and grammar. These are also networks.
We cannot understand either the social or wider world without understanding
relationships and the networks they form. These structures deﬁne the environ-
ments in which core scientiﬁc phenomena take place. They are not just back-
ground connections in the understanding of life, but are integral to explaining and
modeling complex phenomena in accurate and meaningful ways. It is hard to
imagine a discussion of brain functioning without references to brain regions and
neural activity linking neurons and those regions. Likewise, it is hard to imagine
studying the social aspects of life without examining actions and relationships that
connect people. In short, the interconnectedness of objects is a fundamental
property of the world, and makes the world possible. Regardless of the social
actors or objects being connected (i.e., networked), the properties and dynamics of
being interconnected are something all phenomena share. And this is what net-
work analysis seeks to understand. Many disciplines andﬁelds concern networks,
and the speciﬁccontentof these disciplines vastly differs, but it is the focus on
structures and the interdependencies to which structures give rise that unites them.
1.2  ?
If we ever get to the point of charting a whole city or a whole nation, we would
have...a picture of a vast solar system of intangible structures, powerfully
inﬂuencing conduct, as gravitation does in space. Such an invisible structure
underlies society and has its inﬂuence in determining the conduct of society as
a whole.
J. L. Moreno,New York Times, April 13,1933
In the most general terms, a structure is an arrangement of related objects that
form apattern. Patterns arise everywhere, but most remain largely unseen,
discernable only at a physical or conceptual distance. This is especially true of
social structures, which are patterns of interactions among people, such as
2 Introduction: Network Analysis Today

those envisioned in the preceding quote by Jacob Moreno, a founder of the
social network approach, or our envisioning of the coffee shop at the beginning
of this chapter. In trying to discern social structures, people are a bit likeﬁsh in
a school: each individual perhaps sees someﬂeeting aspects of structure, but
always from a partial, subjective viewpoint. A more objective structural under-
standing requires the aid of tools that allow us to see beyond our own senses
and cognitive limitations. As network researchers, we are in the business of
devising such tools for understanding the world. Unlikeﬁsh, people have
created schools of thought (forgive the pun) dedicated to the discovery, preser-
vation, and transmission of knowledge and tools for addressing these problems.
The network tradition is one such school of thought. It stands in contrast to
more traditional schools in the social and physical sciences that use tools focusing
on individual objects and their characteristics. Such individual-level approaches
have dominated entire disciplines in the social sciences, such as psychology and
economics. Even in the clearly less individual-centered discipline of sociology, the
primary tool for understanding behavior for decades was the survey. In seeking
generalizability, surveys draw random samples ofindividualsfrom populations,
thereby sacriﬁcing most of the local structures of family, friends, coworkers,
neighborhoods, and communities (McPherson & Smith2019). In random survey
designs, the connections among respondents violate statistical assumptions of
independent observations and must therefore be avoided. An independent,
random sample of persons is easy to collect and analyze, but this practice comes
at a cost: by divorcing the respondents from their social context, the concepts and
tools of traditional survey research treat each person as an isolated entity and
regard their characteristics as having reiﬁed meaning. Such data tend to yield
variable-based explanations for social phenomena in which individual character-
istics, like age and education, are treated as causal factors (Abbott1988).
Network scholars see the interdependencies among actors (i.e., my behavior
is shaped by my relationships with others) not as a complication to avoid but
instead as the subject of inquiry. Within these networks–and by virtue of their
links and position–individual objects derive their meaning. A person is deﬁned
by their unique position and trajectory across networks over time (Mead1934).
By virtue of the network pattern, we also identify larger social constructs, like
groups and roles. A community’s internal process is in great part reﬂected by
the patterns of associations that deﬁne them. In effect, the network of relations
is a dualistic means of discerning what it means to bebothindividuals and
groups, and it regards their deﬁnition in a contextualized, situated light. The
exact objects of interest (e.g., people, animals, or airports) can vary widely
across substantiveﬁelds, as can the relations, or links, that connect them (e.g.,
friendship, kinship, advice,ﬁghting, or grooming). The interconnectedness of
things makes them interdependent and reactive to one another. In short, when
observed over time, objects affecting one another through ties aresystems.
In general, we can think of systems as falling under four main types, with
very different types of objects and links (Figure 1.1).
Introduction: Network Analysis Today 3

(a)
(b)
FIGURE1.1 Types of systems. (a)Mechanical systems(machines): elements and their
interactions are designed, tightly coupled, and restricted to efﬁciently achieve a goal. The
electrical grid is a good example of a mechanical system. (b)Living systems(cells,
bodies, ecosystems): elements are subsystems with a degree of autonomy, with
communication and inﬂuence in multiple directions. These often include interactional
feedback loops and adaptive learning processes. (c)Social systems(groups or larger
collectivities): elements are often persons interrelated in patterns of exchange that reﬂect
group memberships and hierarchies. These systems can vary in their differentiation and
volatility. The Western European kinship system is a good example of a social system
that organizes gender roles, such as being an aunt to a focal individual. (d)Cultural
systems(interrelated meanings): elements are symbols that form semiotic systems
through cognitive and affective connections of similarity and difference. Networks of
semantic relations can be used to depict cultural systems, such as that organizing the
classiﬁcation of animals as mammals.
4 Introduction: Network Analysis Today

Tracing such systems can be conceptually and computationally challenging.
Researchers from an array ofﬁelds have formulated conceptual and analytic
tools to help us see structures and to understand their importance. In fact,
since the 1940s, theﬁeld ofcyberneticshas been an interdisciplinary attempt to
unite the sciences through the study of various systems. As with a variety of
other scientiﬁc endeavors, network analysis seeks to better understand the
underlying reality that our world is structured by overlapping and often
complex systems.
Sister
Ego
Aunt 1
Cousin 1
Cousin 4
Cousin 2 Cousin 3
Uncle 2 Male
Female
Aunt 2
Aunt 3
Mother Father
Uncle 1
Brother
(c)
Mammal Vertebrae
Cat
has
is a
Animal
is a
Fur
has
Whale
is a
Fish
is a
Water
lives in
lives in
(d)
FIGURE1.1 (cont.)
Introduction: Network Analysis Today 5

1.3   
Contributions to the origins of network analysis have come from a variety of
other scientiﬁc domains with diverse analytical and theoretical orientations (see
Freeman2004for a detailed history). Involvedﬁelds included graph theory
(Euler1736), sociology (Davis, Gardner, & Gardner1941; Roethlisberger,
Dickson, & Wright1947[1939]; Simmel1909), education (Almack1922),
anthropology (Barnes1954; Nadel1957), and psychology (Heider1946). In
the early period, most of the effort was placed on developing a set of concepts,
theories of tie formation (e.g., how individuals decide to become friends), and
exploratory research on small groups (N<100). It is in this era that funda-
mental theories and concepts emerged. Many of these early concepts and
theories will be covered in this volume.
From the 1960s to the 1990s, theﬁeld witnessed a wide assortment of
concurrent interdisciplinary work on social networks (Scott2002), mostly in
the disciplines of sociology, anthropology, and social psychology. Much of this
work focused on larger samples of persons and groups (N<2,000), such as
clubs, schools, and organizations. This work used more complex methods to
analyze social systems than previous work. What became known as The Harvard
School is exemplary of this period and centered on the work and ideas of
Harrison White, a scholar with PhDs in physics and sociology. Academics
aligned with this school of thought created mathematical approaches to identify-
ing structurally equivalent persons in graphs (Lorrain & White1971), techniques
for revealing network positions and their interrelations as role structures (White,
Boorman, & Breiger1976), and approaches to the study of afﬁliation networks–
that is, ties that are based on belonging to the same groups or events (Breiger
1974). From this school emerged other scholars who established many of the
core concepts used in network analysis today; examples include Mark
Granovetter’s(1973) notions of weak ties and structural embeddedness (1985),
and Peter Blau’s(1977) notion of structural differentiation. Much of this work
extended the core ideas of the prior generation (e.g., Nadel1957;Simmel1909)
by exploring their mathematical elaboration and operationalization using math-
ematical models and statistical tools. What resulted was a fruitful period in social
network analysis that produced complex descriptive research on groups and their
relations and introduced hypothesis testing.
With the advance of computing and the popularization of the Internet in the
1990s, the size and availability of network information exploded, and scholars
from theﬁelds of engineering and physics entereden masse. Social scientists now
share the stage in the development of network analysis with computer scientists
(e.g., Kleinberg2000; Leskovec, Kleinberg, & Faloutsos2005), physicists
(e.g., Barabási & Frangos2002;Newman2003;Watts&Strogatz1998), and
statisticians (e.g., Handcock2003; Snijders2001). Network analysis now regu-
larly uses information on large, longitudinal graphs representative of entire
populations (N>2,000) and entails information on multiple species and
6 Introduction: Network Analysis Today

phenomena–from humans to dolphins, from neurons to power grids. In
addition, network analyses now examine multiple types of relationships between
entities in the same network–from friendships to marriage, from advice-giving
to chain of command. Network analysis also continues to harness advances in
software, computational power, and analytical methods to encompass even more
expansive networks, such as social media interactions with even millions of
observations, and to look at different ways that people relate through texts,
shared activities or identities, or memberships in groups and organizations.
Network studies are also going deeper into individuals’understandings of rela-
tionships through their perceptions of their own and others’relations. Going
beyond descriptive accounts, today, a variety of structural hypotheses can be
tested, and issues of causation can be explored in the context of networks.
Moreover, decision processes (and algorithmic models thereof ) are becoming
central to our understanding of network formation (Jackson2003,2008). We
further discuss some of these frontiers in our concluding chapter (Chapter 16).
In sum, the history of network analysis has been marked by steady concep-
tual, empirical, and methodological expansion, and by a cross-disciplinary
focus on relational phenomena. However, in spite of the cross-disciplinary
focus, theﬁeld lacks clear integration of the many theories and analytical
methods now available to scholars. Network analysis is a pastiche of methods
that span different software implementations and different disciplinary views,
with no clear unifying perspective. Nearly every textbook on network analysis
has been written forﬁeld-speciﬁc audiences by methodologists or authors using
aﬁeld-speciﬁc set of tools and software packages. Moreover, there is a lack of
awareness acrossﬁelds currently engaging in network research–exempliﬁed in
particular by the tendency of hard scientists to overlook prior work in the social
sciences only to“rediscover”what social scientists learned long ago. Physicists
like Duncan Watts missed Granovetter’s notion of bridges and weak ties in his
concept of small worlds; the concept of Google’s PageRank
TM
rests on the same
metric as Bonacich’s notion of power centrality and the Friedkin–Johnsen
centrality measure (see Friedkin & Johnsen2014); and even high-proﬁle publi-
cations likeScientiﬁc Americanreproduceﬁndings that social scientists identi-
ﬁed decades prior (Paulos2011; cf. Feld1991).
We see the need for a more integrative approach to network analysis. The
potential for less redundant, more fruitful collaborations is possible if researchers
can integrate what increasingly appears to be a transdisciplinary perspective dis-
tinct from other scientiﬁc views. In our view, this integration requires recognition of
network analysis’ssocialscientiﬁc origins in theory and core empirical questions,
and how these remain relevant to present research agendas and methods.
1.4     - 
To clarify our motivations in writing this book, we begin with a clear statement
of how we see the aims of network analysis. In our view, network analysis aims
Introduction: Network Analysis Today 7

to characterize the pattern of transactions and relationships nested in the
natural and social world and to examine both their antecedents and conse-
quences. It entails understanding how associations form larger patterns and
arrangements and how those relationships shift over time. Network analysis is
grounded in systematic and purposeful data collection and analysis strategies,
relies heavily on the use of graphic visualizations, and employs a far-reaching
set of mathematical and computational models. Network analysis also encom-
passes efforts to understand how deeper structural principles shape relation-
ships and how the conﬁgurations of relationships inﬂuence phenomena of
interest, such as actor behaviors and attitudes.
The brief history we have related illustrates several clear divides in the
growth of a transdisciplinary perspective of network analysis. The earliest
period (from the 1930s to the 1950s) was denoted by mostly theoretical and
qualitative research exploring basic concepts and relating them to social theory.
The second period (from the 1960s to the 1980s) saw the emergence of a set of
metrics and methods further elaborating network properties and their vari-
ation. Most recently (since the 1990s), a period of massive increases in scale and
computing power has enabled network comparisons and hypothesis testing
about network formation to a degree not previously possible. Each age has
brought shifts in the type of scholar leading the charge–from theorist, to
exploratory social scientist, to hypothesis-testing physical scientists and engin-
eers–and a disconnect across what was learned in one era after the next.
In this text, we propose to integrate these views and to center the develop-
ment of network concepts and methods around core questions of network
structure and its formation. The key, we believe, is to tightly couple the
methodological treatment with substantive questions that a researcher may
hope to answer empirically. Such an approach is particularly important given
the increasing availability of network data. Social networks and network
thinking are more ubiquitous than ever because of the use of networking
platforms like LinkedIn, Facebook, Instagram, and Twitter. Social networks
are present in the endless number of forums, conversational threads, and
streams of comments found on websites, online courses, and listservs.
Companies, too, are awash with digital records and transactional data repre-
sented in streaming relational databases that they are not sure how to use.
In short, today research is experiencing a new empirical watershed of digit-
ized communications, which has hastened the emergence ofmethodological
transactionalism–that is, the capacity to empirically capture and theoretically
explaininteractions, which are frequently the traces of relations, observed at
various levels from face-to-face encounters to globalﬂows of goods (Kitts &
Quintane2020; McFarland, Diehl, & Rawlings2011). For much of the mid- to
late twentieth century, the individual was a practical, reiﬁed source of infor-
mation collected through surveys. Today, that information comes from digit-
ized social transactions, and the streaming of relational information has made
the individual merely a point buffeted along within rivers of transactional data.
8 Introduction: Network Analysis Today

So what is not to love for a social researcher? The trouble with much of the
contemporary research on networks is that novices learn a single method, acquire a
network data set (e.g., Twitter), and then without reﬂection apply the method to the
data. This approach, like using a hammer so ubiquitously that everything comes to
look like a nail, can often lead to poorly executed or inappropriate analyses given
the data and research questions. Most methods appeal to a particular question or
class of questions and therefore do not apply to every problem. In addition, the
problem that a method was meant to address can often have little relevance to the
focal phenomenon in question. For example, in studying who retweets whom, a
researcher may pick up a few network ideas of social inﬂuence that were based on
how individuals in small groups experience conformity pressures, using these to
“make sense”of thousands of tweets among total strangers for whom the original
network conformity pressures have almost no chance of actually operating. Thus,
there is often a gap between technical capabilities and more conceptual understand-
ings. And many treatments of current methods in network analysis have only
widened this gap by presenting methods with little conceptual context.
In contrast, this volume offers an integrative approach to network analysis
that will be useful forﬁlling the gap between methodological sophistication and
theoretical and empirical purpose. For those scholars lacking technical capabil-
ities, this volume canﬁll the technical gap concerninghowto do structural
analysis while helping to build and develop their theoretical agendas. For those
scholars with more advanced methodological skills, our approach can help to
bring these technical capabilities to bear on the broader theoretical landscape to
elucidatehow,when, andwhythese methods are so vital. We will demonstrate
repeatedly that what students of network analysis often think is a methodo-
logical problemis really a theory problem in disguise.
Our main conviction is thatsocialnetworks are the best possible bases for
illustrating intuitive examples that bring together theory and practice and thus
help integrate the transdisciplinaryﬁeld of network analysis. All researchers,
regardless of their discipline, can relate to the social world–for example,
through the common experiences of attending schools and coming of age in
high school or its equivalent. Most people wanting to learn about networks
share a common set of understandings and experiences rooted in tangible, if not
often surprising, social network phenomena. The same cannot be said of the
many other types of networks–neural networks, gene networks, and so on–
that are the bases for otherﬁelds. These are vitally important areas of research,
but they cannot help unify theﬁeld of network scientists; only social networks
can. Social networks are historically the origins of theﬁeld, and we believe that
social scientists hold a key source of knowledge that can lead theﬁeld forward
into a more fully integrated transdisciplinary future.
1
1
And, as we discuss inChapter 12, sociology in particular holds a unique position as source of
knowledge integration within the social sciences due to its central position and fairly weak
paradigm that allows it to assimilateﬁndings from numerousﬁelds and disciplines.
Introduction: Network Analysis Today 9

1.5  
All networks comprise interdependent parts. But how do we illustrate and
begin to analyze such interdependencies? A simple, yet powerful example of
interdependence is easy toﬁnd in most American high schools and adolescents’
onset to sexual encounters.Figure 1.2shows a network of sexual encounters–
in this case, within a single high school in the Midwestern United States in the
1990s. Each dot is a student, and the connections represent one or more sexual
encounters over the year.
The structure matters. Individuals with the same number of partners vary in
important ways in their position in the larger structure. Some individuals are
indirectly connected to a large portion of the network, vulnerable to a sexually
transmitted disease (STD) spreading through the large branch-like structure
shown at the top of the image. Others are more isolated. Thus, individuals with
the same number of partners (i.e., exhibiting the same behavior) may have very
different risk proﬁles. If the researcher wants to understand how such a struc-
ture comes about (its etiology), how it affords students different opportunities
for sexual partners, and the implications for the transmission of (for example)
STDs, then the overall connectivity of the structure and each individual’s
position within that structure are of vital interest. The structure looks like a
spanning tree because these youths mainly limited themselves to one or two
Male
129
63
2
Female
FIGURE1.2 High school sexual relations network (Bearman, Moody, & Stovel2004)
10 Introduction: Network Analysis Today

romantic partners per year, mostly within the same school context. Some
students more central to the network have greater access to other partners
and are key players in the potential transmission of an STD within the school
sex network. Clearly, taking these individuals and relationships out of context
would lead to the omission of this vital information.
These structural principles can extend to other sorts of actors, such as
countries.Figure 1.3offers an illustration using three countries instead of
people. The main question is whether Country C will attack Country B. From
a network perspective, the answer depends not simply on the characteristics of
Country C (e.g., its gross domestic product [GDP], military history, and party
in power) but also on its relationship with Country A and the relationship
between Country A and Country B. As shown in panel (b), Country C is in fact
embedded in a larger system of relations: Country C is in a coalition with
Country A, which in turn has attacked Country B. This means that Country
C is allied with a country (A) that has gone to war with Country B. This may
force Country C itself into a conﬂict with Country B (as an ally of Country A)
even if B and C have no direct dispute with each other. In short, an enemy of a
Country A
Country C
Country B
Will Country C attack Country B?
That depends on the relationship
between A and C
and A and B.
Attack
Coalition
?
Country A
Country C
Country B
Will Country C attack Country B??
(a)
(b)
FIGURE1.3 Structural forces in international relations
Introduction: Network Analysis Today 11

friend is an enemy. The behavior of Country C would be difﬁcult to explain if
one considers each country in isolation, as in panel (a).
Hopefully, these brief examples and our discussion leading up to them has
convinced you that structure matters and that social networks offer intuitive
ways to begin to think about structures more broadly. But how to actually
begin seeing and analyzing structures is no simple task and requires a set
of tools.
1.6      
How should a researcher go about answering network-based questions? While
there are many options, this book uses the R statistical programming language
and platform to practically walk through the application of network analysis
(R Core Team2020).
2
We believe that R provides the best and most compre-
hensive set of tools, and becoming competent in this programming environment
presents the fewest barriers for those with less coding experience. R is ideal, in
part, because it avoids many of the drawbacks of other options, particularly
those based on drop-down menus (i.e., point-and-click logic). Although these
other packages often have a gently sloped learning curve, they make it difﬁcult
to custom-tailor the analysis to the data and research question under consider-
ation. More importantly, they are not designed for replicability or extensibility.
Accomplishing desired data transformations and routines to replicate analysis
with these other packages often requires hacks involving a complicated give-
and-take between a spreadsheet editor and other graphical user interface tools.
This process is inefﬁcient and error prone, and it can make diagnosing errors
difﬁcult. Moreover, these software packages are mostly stand-alone, closed-
source applications, which means that building in additional functionality and
creating methodological innovations are difﬁcult, if not impossible.
In contrast, R has a vast array of powerful scripting functionality, excep-
tional visualization capabilities, and thousands of libraries to facilitate data
management and statistical analysis. R excels in facilitating the development of
new methods and approaches relative to other programming languages, while
making it easy for an advanced R programmer to write interfaces to high-
performance tools available in compiled languages, such as C and Java. It also
interfaces with other environments (notably, Python), which is convenient for
scientists and engineers who have already invested in those programming
languages. Although no convention is a perfect solution, R has the added
advantage of being shareware, both free to the user and open to improvements
on existing techniques as well as the incorporation of techniques at the cutting
2
For an excellent introduction to exploratory network analysis with the stand-alone program
Pajek, we strongly recommend De Nooy, Mrvar, and Batagelj (2018).
12 Introduction: Network Analysis Today

edge. R also allows access to myriad other statistical methods that many
network researchers will likely want to draw on in their analyses.
Obviously, no single and perfect tool exists for performing network analysis.
The tutorials we offer as accompaniments to the following chapters are meant
to be adaptable to a number of research interests and to set the practical
foundation for the conceptual material we present in respective chapters. We
believe that having a common research tool such as R is also a basis for
integrating theﬁeld as researchers across disciplines and for building a shared
language and repository for generic structural analyses.
1.7     ’ 
This book is the result of a collaboration among four social network scholars
with distinct but overlapping areas of expertise. Rawlings has developed a
number of ways to interrelate social structures with mental structures (e.g.,
attitudes, beliefs, tastes) using social network theories and methods. Smith has
published work on social networks and health, methodological issues in net-
work sampling and missing data, and has extensive experience in developing
network methods in R. Both Moody and McFarland have published extensively
on social networks, with particular strengths in building tools for better under-
standing dynamic social networks. Moody has additional strengths in social
diffusion models and cohesion. McFarland has applied network methods
extensively in educational and organizational settings. Together, the four of
us have more than sixty combined years of experience teaching social network
analysis at the undergraduate and graduate levels. We have sought to distill that
collective experience into this volume.
The book can be many things for many different people. It is primarily
offered as a research tutorial, offering students the opportunity to develop
and answer questions that exemplary social network scholars ask when study-
ing social phenomena. The book’s orientation is to introduce methods of social
network analysis in a theoretically grounded fashion; it does not cover math-
ematical modeling and simulation except when necessary. We hope to take the
reader through every step necessary to answer core questions and to learn how
to evaluate and interpret empirical results. The material can be tailored for
more general or speciﬁc goals. For the network scholar who is already familiar
with network theory and methods but wants to become more proﬁcient at R,
the research tutorials afford an opportunity to moveﬁrmly into this new
programming environment in a way that is more theoretically grounded than
many other texts. Instructors of graduate or undergraduate courses might rely
on the book in its entirety or instead choose portions that are appropriate to
cover conceptual and empirical applications or laboratory work as the
course requires.
Each chapter contains several elements: (1) identify core research questions; (2)
relate the inﬂuential texts and their concerns bearing on these questions;
Introduction: Network Analysis Today
13

(3) postulate an appropriate plan of analysis; (4) choose the appropriate methods
(and compare them); and (5) interpret the results, their quality, and how to present
them asﬁndings. The text offers concrete examples–many from contexts most
readers have experiencedﬁrsthand (e.g., classrooms)–with real data. The tutorials
are available on the web at:https://inarwhal.github.io/NetworkAnalysisR-book/.
We divide the book into three main sections.Part Ifocuses on structural
thinking, introducing the main concepts of network analysis, identifying the
key visual and mathematical abstractions that form its core, and discussing issues
of data collection.Parts IIandIIIcover two, often interrelated, analytic goals of
network analysis. Theﬁrst, presented inPart II, concerns using a number of
exploratorytechniques to see structures at various levels and degrees of abstrac-
tion. In particular, we help the reader develop connectionist and positional
perspectives on network structures.Part IIIconcerns making structural predic-
tions using a variety of more dynamic, longitudinal, andexplanatorymodels.
No textbook can cover every method, and we have made some painful but
necessary omissions. We therefore end each chapter, except for the conclusion,
with a short list of works that will expand on some of the core ideas developed
in the chapter, either by building depth or extending to detailed areas that are
beyond the scope of the chapter itself. The universe of works we could include
is vast, so any such lists are necessarily incomplete and idiosyncratic, but we
hope these serve as useful jumping-off points for readers. In addition, given the
rapid development of theﬁeld, it is likely that new techniques are currently
being developed that could surely join those presented in theﬁnal sections of
Part III. We hope to include such exciting new work in future editions.
  
Overviews and Introductions.The following works are recommended as general intro-
ductory works that cover history, theory, and applications.
Barabási, Albert-László. 2002.Linked: The New Science of Networks, Cambridge MA:
Perseus Press. (Provides an interesting systems-science foil for social science
approaches. Barabasi, Watts, and Newman are keyﬁgures in the late 1990s rise
of“network science”as distinct from social network analysis. See also Watts2003;
Newman2018.)
Butts, Carter T. 2009.“Revisiting the Foundations of Network Analysis.”Science325:
414. (A critical summary of the idea that all connected systems are“a network,”and
highlights the need to tailor approaches to the complexities of empirical settings.)
Easly, David, and Jon Kleinberg. 2010.Networks, Crowds, and Markets: Reasoning
about a Highly Connected World. New York: Cambridge University Press. (An
overview introduction with a focus on network science approaches to economic and
ﬁnancial questions.)
Freeman, Linton C. 2004.The Development of Social Network Analysis: A Study in the
Sociology of Science. Vancouver, British Columbia, Canada: Empirical Press.
14 Introduction: Network Analysis Today

(Provides a rich history of the development of social network analysis as a substan-
tive discipline.)
Jackson, Matthew O. 2008.Social and Economic Networks. Stanford, CA: Stanford
University Press. (Brings economic modeling/theory to networks.)
Kadushin, Charles. 2011.Understanding Social Networks: Theories, Concepts and
Findings. New York: Oxford University Press. (A substantive introduction to
structural theories of social life, with clear applications. The“ten master ideas”
chapter, in particular, provides a succinct summary of why networks are funda-
mental to understanding social processes.)
Light, Ryan, and James Moody. 2020.The Oxford Handbook of Social Networks. New
York: Oxford University Press. (A broad overview covering multiple contemporary
topics byﬁeld experts.)
Lin, Nan. 2002.Social Capital: A Theory of Social Structure and Action. New York:
Cambridge University Press. (Lin’s work illustrates how social connections and
social relations can be a key resource.)
Watts, Duncan J. 2003.Six Degrees: The Science of a Connected Age. New York,
Norton. (A substantive introduction to the network science approach. See also
Barabási2002; Newman2018.)
Wellman, Barry. 1988.“Structural Analysis: From Method and Metaphor to Theory
and Substance.”InSocial Structures: A Network Approach, edited by Barry
Wellman and S. D. Berkowitz. Cambridge: Cambridge University Press. (A nice
introduction to the what and why of networks.)
Key Historical Works.Theﬁeld has evolved over the last 100 years with touchstone
works that are guideposts for much of what drives our contemporary understanding of
network theory. This list is far from complete and chosen mainly to represent the
substantive breadth of foundational approaches rather than completeness.
Baker, Wayne. 1984.“The Social Structure of a National Securities Market.”American
Journal of Sociology89: 775–811. (An exemplar of how structural realities under-
mine pure market assumptions. A classic work linking networks to economic
sociology.)
Coleman, James S. 1961.The Adolescent Society. New York: Free Press. (Demonstrated
that adolescent networks and schools worked as largely self-contained social
systems characterized by social networks. See also Hollingshead1949.)
Davis, James A. 1963.“Structural Balance, Mechanical Solidarity, and Interpersonal
Relations.”American Journal of Sociology68: 444–62. (The set of papers by Davis,
Lienhardt, and Holland translated models for social balance to directed social
relations and set the stage for much of the statistical modeling and network testing
tradition to come. See also Davis1970; Holland & Leinhardt1970.)
1970.“Clustering and Hierarchy in Interpersonal Relations: Testing Two Graph
Theoretical Models on 742 Sociomatrices.”American Sociological Review35:
843–51. (See the note for Davis1963.)
Fischer, Claude. 1982.To Dwell among Friends. Chicago: University of Chicago Press.
(An early application of ego-network analysis providing detailed description of
social embeddedness across the urban–rural continuum.)
Granovetter, Mark S. 1973.“The Strength of Weak Ties.”American Journal of
Sociology78: 1360–80. (Classic paper showing that unique, nonredundant
Introduction: Network Analysis Today 15

information travels through weak ties; in contrast to much prior work that focused
network research only on strong durable ties.)
1974.Getting a Job: A Study of Contacts and Careers. Chicago: University of Chicago
Press. (A deep investigation into how people use their networks to obtain hard-to-
ﬁnd resources; introduced the importance of weak ties in social capital. See also Lee
1969.)
Holland, Paul W., and Samuel Leinhardt. 1970.“A Method for Detecting Structure in
Sociometric Data.”American Journal of Sociology76: 492–513. (See the note for
Davis1963.)
Hollingshead, August. 1949.Elmtown’s Youth: The Impact of Social Classes on
Adolescents. New York: John Wiley. (See the note for Coleman1961.)
Lee, Nancy Howell. 1969.The Search for an Abortionist. Chicago: University of
Chicago Press. (See the note for Granovetter1974.)
Moreno, Jacob L. 1953 [1934].Who Shall Survive? A New Approach to the Problem of
Human Interrelations. New York: Beacon Press. (Arguably the foundation of
sociometric data collection, visualization, and analysis. Moreno was also instru-
mental in foundingSociometry, which published lovely early case studies on organ-
izational, community, and family networks.)
Roethlisberger, Fritz Jules, William John Dickson and Harold A. Wright. 1947 [1939].
Management and the Worker: An Account of a Research Program Conducted by
the Western Electric Company, Hawthorne Works, Chicago. Cambridge, MA:
Harvard University Press. (A classic study of workers engaged in different activities
and their relation to friendship and cliques.)
White, Harrison. 1963.Anatomy of Kinship. Englewood Cliffs, NJ: Prentice Hall. (This
work lays the foundation for using compound social relations as representations of
roles. This forms the roots of all the following work on blockmodeling.)
General Methods Texts
Borgatti, Stephen P., Martin G. Everett, and Jeffrey C. Johnson. 2018.Analyzing Social
Networks. Thousand Oaks, CA: Sage Press. (Clear and concise methods text for
applied network analysis; extended in 2022 in collaboration with Filip Agneessens
to include direct instruction in R.)
Knoke, David, and Song Yang. 2021.Social Network Analysis, 3rd ed. Thousand Oaks,
CA: Sage. (The third edition of Knoke’s text [theﬁrst was in 1982], each with
different collaborators. An excellent quick-start guide to applied network analysis.)
Newman, Mark E. J. 2018.Networks. New York: Oxford University Press. (Core
network science text, particularly good for mathematical details of network distri-
butions. See also Barabási2002; Watts2003.)
Scott, John. 2012.Social Network Analysis, 3rd ed. Thousand Oaks, CA: Sage. (This
has been the quick go-to reference text since itsﬁrst edition in 1991.)
Wasserman, Stanley, and Katherine Faust. 1994.Social Network Analysis. New York:
Cambridge University Press. (The“Big Red Book”that sits on all our shelves;
provides an encyclopedic history of theﬁeld and foundational methods works.
Many of us keep copies in each of our ofﬁces.)
16 Introduction: Network Analysis Today

 
THINKING STRUCTURALLY
Network analysis formalizes the study of relationships, and social network
analysis pertains to relationships among individuals, groups, or other social
entities. While an assortment of social network approaches exists, greater
integration is needed to guide our efforts. In this section, weﬁrst outline our
theoretical integration based on (1) describing social structures and (2) pursu-
ing strategies for better understanding social structures within a causal frame-
work. We then cover in more detail how network analysis formalizes the
conceptualization, data collection, and visualization of relational data.

2
What Is Social Structure?
The primary aim of social network analysis is building and evaluating theories
of social structure–that is, enduring patterns of human interaction and ways of
thinking about and organizing human groups. The sheer complexity of social
structure prevents encapsulation in any single model, and this complexity is
compounded as we incorporate cultural beliefs and social expectations in
addition to interactions. Networks link actors to one another in systems, raising
tricky questions about the locus of control and activity, particularly regarding
the extent to which people are active agents or passive puppets (to put it
bluntly) of social structure. While acknowledging deep and ultimately unsettled
issues in theﬁeld, we provide readers with an overarching though still evolving
theoretical account of social structure that can guide both inductive and
deductive social network research and allow plug-in points for different per-
spectives on agency, culture, and constraint.
2.1 : 
 
Research often begins with imagination. One might have an interesting idea
about how things work in the world that goes beyond current assumptions.
One is sometimes right, but one is often wrong. And realizing when and how
one is right or wrong often requires insights from others working on similar
problems. Research therefore builds on the wisdom and cumulative efforts of
countless individuals because reality is often hidden and far too complex for
any one of us to see on our own. In fact, left to our own mental devices, we are
likely to hold onto bad ideas in the hope that our cherished imagination of
something interesting will eventually prove true. Thus, research can be deﬁned
as thecollectiveprocess of rendering some aspect of reality into data and then
processing those data into useful information (i.e., knowledge).
19

Theory is present at all stages of the research process. When we observe
phenomena, we do so through the lens of established research traditions and
paradigms of thought. These traditions entail their own language and ontology
as well as distinct epistemology or means of sense-making and inference. These
theories act like frameworks of interpretation, leading researchers to observe
certain aspects of a phenomenon over others. Even highly inductive research is
guided by sensitizing concepts (i.e., theoretically informed ideas) that select on
certain social aspects of reality over others. Likewise, theoretical perspectives
guide the choice of certain data collection tools. For example, as we discussed in
theprevious chapter,methodological individualism led researchers to collect
individual-level responses to survey questions and interviews, and these became
state-of-the-art tools for data collection in the 1940s. Social network theory,
however, shifts the focus to relations, and it is aided by a different set of data
collection tools that nudge researchers closer to the reality of the interdependen-
cies among objects. The focus on relationships guides the researcher toﬁnd data
in transactions, afﬁliations, links, and comparisonsacrossobjects. In this way,
theories lead us to discover and collect certain forms of data from social reality.
Data are merely traces and representations of social reality guided by theory.
Transforming these data into useful information is also guided by theory. For
example, in social psychology, transforming self-reported feelings into a meas-
ure of self-esteem presumes a theory of self-esteem and some latent mental
mechanism that enables those sentiments to work together. The same holds for
social network theory. It sensitizes researchersﬁrst to collecting data on the
interrelation of objects and then to identifying processes and patterns in those
relations. These processes and patterns become information that is interrelated
into larger, holistic understandings about social structures. For example, the
social network theory linking social proximity to feelings of intimacy
entails collecting reports on the strength of personal ties and measuring the
social distances between persons, and then ascertaining the incidence of
stronger interpersonal affect with social proximity. As depicted inFigure 2.1,
researchers use theories to identify the observations or data they collect, the
ideational constructs and measures derived from them, and how the
Reality Data
Unstructured
Data
Information
Methods and
Processing
Techniques
Knowledge
Theory and
Understanding
FIGURE2.1 Schematic of rendering reality into knowledge
20 Thinking Structurally

relationships contained in these pieces of information are useful for some
broader understanding.
Some social realities and phenomena are more tractable with certain kinds of
data and seem best suited to particular constructs and measures, which in turn
are best suited to certain methods and theories. Of course, the reverse can be
true: one’s preconceived knowledge and theories determine one’s choice of
methods, which can determine the constructs one builds and in turn shape the
data one collects and the social reality one observes. The point is to not be naïve
about this process of translation but instead to enter it with eyes wide open to
make the most reasonable decisions possible at each juncture. Consider
whether you are biased in perspective and weigh alternative data, measures,
methods, and explanations. Consider the phenomenon and whether you are
representing it fairly or whether your training guides what you see (Hollis
1994).
We argue that a social network approach often renders a more accurate
representation of social reality than other social scientiﬁc approaches because it
recognizes the fundamentally interdependent nature of social life: to be social
means to be connected to others (Blau1977). This is not to say that one method
supplants all; rather, a reﬂexive, smart analyst must step back and ask, What
representation of this reality is most suited? What constructs and alternative
forms are best suited to these data? And what methods and explanations–
again, including alternatives–are most relevant? This approach also highlights
a core distinction between building understanding and mere prediction (see
Turco & Zuckerman2017; Watts2014). Prediction alone is insufﬁcient for
most social science questions; the researcher simultaneously seeks description
and explanation–that is, understanding. Understanding centers on linking
theory, data, and prediction in a way that recognizes their mutual information.
The purpose of this chapter is therefore to begin to orient the reader’s imagin-
ation toward a view of social structure that will help guide these research
efforts.
2.2 :    
Social network scholars seek to identify and understand patterns in relations
between actors. This patterning is calledsocial structurewhen it is stable
enough to be reproduced and recognized via some ostensive label, such as
“friendship,”“marriage,”or“trade.”Social structure is at once a pattern of
interactions in the world and a set of schemas (simpliﬁed mental abstractions)
for recognizing and enacting such interactions.
Imagine someone who has never seen a classroom. How would they make
sense of its complex set of interactions? A bell rings; individuals (generally
younger ones) scurry toward desks oriented in the same direction, and often
choose seats near the same people each time; and at last, a single individual
(generally an older one) enters and moves to the front of the class to speak, as
What Is Social Structure? 21

those who are seated start to settle. As Berger and Luckmann (1966) describe it,
the social construction of reality involves individuals seamlessly engaging in a
process of externalization (relating), objectiﬁcation (naming), and internaliza-
tion (learning) of structures. The social structure of the classroom is therefore
one that exists in schematic form in the minds of the individuals via roles and
relations. But the performance of these roles and relations is contingent on how
individuals coordinate their interactions to more or less successfully cue and
enact those schemas. The result might be a loose performance of roles with
much humor in one class and a strict script with lots of private grumbling in
another. Both settings share a structural semblance of being classrooms in terms
of how people interact, but they vary in the speciﬁc instantiations.
But how can one begin to see and understand such a structure? Learning
how to do social network analysis isﬁrst and foremost about learning to have
theoretically guided hunches and the hunger to solve puzzles about social
structure–that is, an informed social-structural imagination. By the time of
data collection, the researcher has already engaged in some conceptualization
of social structure. Consider the networks inFigure 2.2, all taken from the same
single class in a high school (Bender-deMoll & McFarland2006). Ties depicted
in black are task-related interactions, blue ties are sociable interactions, and red
ones are conﬂictual ones. Circles are girls, and squares are boys. Yellow squares
are male teachers, and the other nodes are students. Notably, the class has two
teachers: one lead teacher and a volunteer.
Structure begins to emerge as interactions aggregate over larger chunks of
time. At one-minute intervals, only sequences of dyads are observed.
FIGURE2.2 Networks from slices of interactions using classroom observation data
(Bender-deMoll & McFarland2006)
22 Thinking Structurally

Aggregating these interactions over a wider time span ofﬁve-minute intervals
reveals patterned relations reﬂective of activity structures and the speaker roles
adopted to accomplish them. For example, on the left side of theﬁgure,
consistent star structures are reﬂective of a teacher repeatedly emitting broad-
casts, small blue dyads reﬂect side socializing, and black dyads reﬂect clariﬁca-
tion efforts. Moving left to right in theﬁgure, some students grow closer to the
teacher. These are instances of recitation in which a teacher uses broadcasts to
demonstrate and explain things but then calls on particular students for
question–answer sequences. Moving further to the right, some students assume
a broadcasting position, reﬂecting their broadcasting information to the class,
such as when they report out or give a speech. And to the far right of theﬁgure
are clustered social and task interactions reﬂective of free time and group work
activities. When interactions are aggregated to ten minutes, one begins to see
general activity structures, not just momentary ones and their instantiation. The
classroom is characterized by a contentious lecture (with a student challenger),
a“group work”instructional format, and then a collaborative group structure.
If one aggregates to a typical class period of thirty-ﬁve minutes, distinct activ-
ities are melded into one graph revealing the daily social structure, as an
abstraction, for a classroom: the teacher is in the center, most students and
another volunteer teacher are clustered around the teacher (some via social and
others via task interactions), and some peers are at the periphery.
Such an aggregated image of a micro-level social structure reﬂects what the
teacher might regard as aninteractome, a term used in biology to refer to the
entire set of molecular interactions in a particular cell. Here, one can think of an
interactome as the manifest social structure and the typical associations among
setting members. Extending this notion further aﬁeld to many classrooms, one
can abstract out social roles and styles, such as central teachers, social and task-
oriented students, and isolates. These schemas can be cued in interaction,
framing expectations, and inﬂuence ensuing social interaction. They can also
fail to come about, reﬂecting the processual and contingent nature of social
structure. None of this structure would be visible from a random survey of
students and teachers.
Still, such snapshots of social structure leave open questions–for example,
what drives this structuring at each level? This question is much more theoretical
than methodological. A variety of factors can establish opportunities and models
for the observed interactions. It may be that persistent interactions follow expect-
ations of preexisting friendships and formal roles (teacher–student), differenti-
ated and developed styles of interaction (e.g.,“nerds”in tasks,“jokers”in social
antics), or the opportunities afforded by proximate seating or shared histories
(other classes and clubs), attributes (boys vs. girls), and attitudes (liking of class).
In prior forms of structuralism, researchers relied on the logic offunctionalismto
explain observed structures–that is, they argued that resultant social structure
served the deeply held social purposes of their members (generally some need for
social stability and group cohesion) and that the structure evolved to fulﬁll these
What Is Social Structure?
23

purposes in presumably optimal ways. Sociology as a discipline and social
network research as a subﬁeld have largely rejected structural-functionalist
explanations as overly speculative and untestable, leaving us to account for
structures in more falsiﬁable ways involving both endogenous and exogenous
forces, which we will cover in detail in this book.
Network analysts are interested in studying theprocess of structuring and
how structural variation arises. But how does one gather and analyze suitable
data on such a complex andﬂuid reality? The answer is aptly illustrated by the
parable of the three blind men and the elephant: while each man feeling a
different part of the elephant believes it to be a different object (the trunk a
snake, the leg a tree, the ear a fan), the men are able to communicate and put
their stories together to form a more developed representation of social reality.
Knowing something about social structure entails thousands of partial truths
discovered by researchers making strategic trade-offs in targeting their efforts.
But, once again, when researchers studying the same reality communicate and
learn from one another, they get closer to a shared, replicable, and sustained
notion of reality.
This book is, in part, an attempt to help consolidate these efforts to better
guide the strategic directions researchers take. Any attempt to draw a picture of
the current understanding of the“elephant”of social structure is bound to be
both complicated and incomplete. Why would one need social network analysis
if social structures were so easily seen? In the following, we provide a heuristic
for seeing social structures and broad research agendas for making structural
predictions. In the remaining chapters ofPart I, we outline the basic tools for
gathering and visualizing relational data. InParts IIandIII, we outline in
greater detail the inductive and predictive methods that are frequently involved
in the rendering of these data into knowledge.
2.3  
The core motivation of social network analysis from its inception was addressing
the question, If one could see social structure, what would it look like? Although
no single image can capture social structure, we revisit a classic attempt by Hinde
(1976), reproduced and adapted inFigure 2.3, which shows several important
aspects of social structure and can help focus future efforts by shaping research
questions and research designs. Hinde was a primate ethologist (Jane Goodall’s
advisor, in fact). As such, he spent a lot of time observing primate interactions
and trying to identify generalizable patterns and potential mechanisms shaping
primate social structures. Theﬁgure is adapted from his effort to encapsulate the
reality of social structure as both interactions among individuals and schemas or
types of relations and mechanisms, which in turn compound into groups com-
prising different types of positions among individuals.
Although Hinde’s model concerned troops of chimpanzees, he was able to
abstract to more generalizable features of social structures. We adapt Hinde’s
24 Thinking Structurally

view to apply to the social structure within a high school classroom rather than
among a troop of apes (although, technically speaking, a classroom is com-
posed of a group of apes). For our purposes, theﬁgure captures two key aspects
of rendering any social structure into knowledge: (1) the conceptual degree of
abstraction and (2) the empirical level of abstraction. Moving from the left to
the right, one engages in a greater amount of conceptual abstraction–that is,
Middle School
Supporting
Friend Role
Socializing
Instructing
Opportunity
Structures
Institution of School
jk Friendship
Relation
ij Student-Teacher
Relation
High School
Classroom
Social Structure
Classroom x’s
Social Structure
Classroom z’s
Social Structure Cultural
Meanings
Teacher-
Student
Role
j supports k
j socializes
with k
i instructs j
i advises j
j supporting k
j socializing with
k
i instructing j
i advising j
Sports Team q’s
Social Structure
i evaluating j
i evaluates j
Evaluating
Advising
Role Frame
Types of Ties
Relational Events
Relational Frame
FIGURE2.3 Schematic of social structure (adapted from Hinde1976)
What Is Social Structure? 25

from concrete instances of individuals interacting in particular ways (relational
events) to abstract schemas of that interaction (types of social ties). Moving
from bottom to top, one compounds abstractions to higher-order levels of
structure–that is, from micro-interactions to role relations to groups to
macro-institutions.
We use Hinde’s image as the basis for depicting the social structure of a high
school. Here, one sees concrete relational events between individuals occurring
in the school as the base unit on the lower-left side of theﬁgure. At the level of
concrete interactions, one sees relational events speciﬁc to moments wherei
advises, instructs, and evaluatesj. These relational events share a semblance
and point to the ways thatiandjrelate with each other–that is, more general
ways thatiadvises, instructs, and evaluatesj. Moving to greater abstraction,
one can see that these relation-speciﬁc instantiations of tie types resemble one
another across pairs of individuals and reﬂect different types of ties (advising,
instructing, and evaluating). Each move to the right entails further generaliza-
tion and abstraction.
Moving upward in theﬁgure, types ofijties can come to reﬂect a generalij
relation–say, how Craig and Jim usually relate to one another. Relation-
speciﬁc types of ties combine in a patterned way to characterize other rela-
tions and their expectations–say, how Jim and Dan usually relate. These
built-up histories for speciﬁc relationships establish relational expectations
orrelational frames. If we consider the similarities across these relationships,
we start to see more general social roles like that of friends or teacher–
student roles. Roles emerge from patterns of consistent social actions origin-
ating from and pointing toward actors (Nadel1957). These patterns of
consistent role relations often stem from following and conforming to insti-
tutionalizedrole frames.
To this point, we have drawn on Hinde’s depiction of the most elemental
unit of relational events and, through recognition of events’shared resem-
blance, identiﬁed types of ties. We have then aggregated these types of ties
across particular pairs of individuals to characterize their particular relation-
ships. And from there, a recognition of shared resemblance across particular
relationships, has emerged general role relations. From here, we can aggregate
again into larger conﬁgurations of social structure, such as the structure of a
particular group or type of group and a society and even a type of society. If we
observe and interrelate the set of relations within a context such as a speciﬁc
classroom (say, classroomxorz), we come to see the social structure of those
social networks. At an even higher level of abstraction–having observed many
different classrooms with varying ages, compositions, seating, and activities–
we may come to see classrooms sharing another family resemblance, mostly
entailing centralized teachers in task types of interactions with students and
students clustering in friendships and social types of interactions with one
another.
26 Thinking Structurally

Moving out of the classroom, but remaining in the same building, one then
observes other individuals: in ofﬁces sorting papers, in kitchens making food, in
sterile rooms taking sick adolescents’temperatures, and so on. Looking outside
the window, perhaps one sees a sports team wearing uniforms that bear the
name on the school building and engaging in activities involving an entirely
separate set of agonistic interactions. All of these could be appended to
Figure 2.3as separate descending branches with their own relational events,
relationships, roles, and role structures, as well as their accompanying schemas
of expectation. Finally, one might thenﬂy across the world, walk into a village
building, and see children and adults arranged and interacting in similar ways
to what one observed in the United States. At the highest level of abstraction,
one may begin to see an institution: the supra-level of organization that reﬂects
the deep cultural structure of school itself.
Rendering knowledge from snapshots of relating requires theory and a
developed understanding of social structuration processes. Social structures
are at once interactional, relational, and institutional requiring researchers to
make choices about when, where, how, and why they gather data and render
reality into knowledge. Otherwise, researchers may observe the same social
reality of a classroom but be attuned to very different processes shaping that
social structure. In what follows, we offer some of the many ways that social
network researchers begin to make sense of social realities and usefully
represent them.
2.3.1 Seeing Structure in Interactions
Once again, in contrast to much of sociology, which draws on reiﬁcations of
social structures in the form of self-reports or records of enduring patterns of
activity, social network analysis has been said to extend from an“anti-categorical
imperative”(Emirbayer & Goodwin1994)–that is, it seeks to move beyond the
use of prescribed categories such as age, party membership, race, class, or gender
as sufﬁcient explanations of what motivates thought and action. Instead, social
network analysis seeks to examine individuals’attitudes, beliefs, and behaviors
through the lens of structures of interactions and relations (of which the afore-
mentioned categories are simpliﬁed proxies or relational schemas). Beginning at
the most fundamental level of individuals interacting and relating with one
another, some scholars are interested in how face-to-face and moment-by-
moment data can reveal structure, as well as how actors are motivated in some
way to use that structure as a resource for pursuing various interests. Micro-
sociology and scholars studying talk-in-interaction have repeatedly shown how
social reality is an ongoing accomplishment in the form and content of interaction
(e.g., Schegloff2007). Thus, some network researchers train their eye on the
lower-left quadrant of Hinde’s image, rendering networks through actual
moments of talk and interaction.
What Is Social Structure? 27

At the level of ongoing activity, social structure can be driven byinteraction
moves–that is, how individuals refer to themselves and others, as well as to the
roles and rules within institutions. Interactions both form and reveal relation-
ships: piggybacking statements and reciprocal turns may form friendships,
changing topics and usurping turns may generate animosity, and commencing
sequences may generate status (Gibson2012; Heritage & Raymond2005;
McFarland, Jurafsky, & Rawlings2013). For other researchers, preexisting
relationships guide interactions. A classroom, for example, is composed of
particular friendships, proximate seating, and speciﬁc activity structures that
bring persons into relation–all of which motivate certain forms of interaction
(e.g., reciprocation) and establish social expectations. These relational arrange-
ments can give a class its particular style and ethos. For yet other scholars,
institutionalized roles and norms deﬁne expectations, determining what rela-
tions and activities are salient, which in turn deﬁnes what types of interactions
individuals are likely to employ in a given setting. Of course, these levels of
concern and reference need not align in reality: individuals may adopt inter-
action moves that run counter to relations and institutional roles, such as when
observing classroom resistance. And such mismatches of preexisting norms and
ongoing behaviors can lead to gradual and long-term changes in social struc-
tures (McFarland2001).
2.3.2 Seeing Structure in Relationships
Much of social network analysis is concerned with enduring relations rather
than surface-level moments, although (as we will discuss in several places
in this book) the techniques and approaches are amenable to modeling real-
time interaction data (Moody, McFarland, & Bender-deMoll2005). The
interpolation fromﬂuid to structural, however, is no small task. One knows
a relationship when one sees it, but how the researcher operationalizes a
relationship is already full of consequence. One generally has to infer a
relationship from interactions, but how much of an actor’s mental model of
what is going on in a given interaction is needed? What types of indicators
best capture the existence of a tie? A reﬂection on what relationships are and
what it means to relate (in common-sense terms) quickly reveals relationships
to be perceived, enacted, emotionally experienced, and socially conﬁrmed;
relationships havecognitive,behavioral, affective,andinterpersonalaspects
(see Bandelj2012;Fuhse2015).
ﬁThecognitiveaspect of a relationship is the relationalframeworkthat
one perceives the relationship to be in or wants to form. For example,
many relationships are perceived to befriendships, acquaintanceships,
or dating relations, and each entails different social expectations and
obligations.
28 Thinking Structurally

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"Up! men of Beilstein!" he roared. "Your master is murdered.
Surround his assassin and take him, dead or alive, to the castle.
Beilstein! Beilstein!"
"I ask your protection, gentlemen," appealed Rodolph, turning to the
remaining officers. "I claim adherence to the rule of the combat. I
fought reluctantly, and only by compulsion. I demand the right to go
without further opposition."
"Beilstein! Beilstein! Beilstein!" The cry reechoed through the town
and soldiers came running from all quarters with weapons drawn.
"He speaks truth," said the Elector's man. "He has won his liberty,
and may go for all I care."
"Not so," cried Winneburg. "It was no fair contest, but devil's
swordsplay. To the castle with him and his brood."
The angry soldiery now pressed round Rodolph, but took good care
to keep out of the reach of his flashing weapon.
"Get a pike," said one; "that will outreach him."
"Pikes, lances, pikes!" ran from mouth to mouth. Rodolph saw he
must speedily be overpowered, and a scream from the affrighted
women in the hands of the soldiery decided him to try a desperate
remedy for a desperate case.
He sprang upon the prostrate body of his foe, and towering over the
heads of the clamouring throng, raised his sword aloft and shouted,
"The Archbishop! The lady is the Countess Tekla, ward of Arnold von
Isenburg, insulted by these Moselle ruffians, while you cravens stand
by and see it done. Officer, you have already nearly compassed your
own damnation. Redeem yourself by instantly falling to the rescue.
Treves! Treves! Is there an Archbishop's man within hearing? Treves!
Treves! Treves!"
The Archbishop's officer at once gave the word, and his men,
beating down opposition, formed around Rodolph and the Countess.

Winneburg stood undecided, and before he made up his mind, the
fight was over, the Beilstein men being demoralised for lack of a
leader.
"You have entangled us in this affair," said the officer to Rodolph,
"and if you have cried the Archbishop's name unwarranted, your
head is likely to roll off in consequence. I have seen the Countess
Tekla. Will she, therefore unveil so that I may be sure I have not
been deluded, or do you prefer to wait until I hear from his
Lordship?"
Before Rodolph could reply, the Countess threw back her veil.
"I am indeed, as you see, the Countess Tekla, ward of the
Archbishop," she said.
"A fine watch you keep on the Moselle," cried Rodolph, with
simulated indignation, "when the Countess Tekla cannot journey to
her guardian's Castle of Cochem without having his Lordship insulted
in her person by unmannerly marauders at Bruttig, where he
supposes he holds through you, control and safe-conduct for all
properly authenticated travellers!"
The officer bowed low to the Countess and to Rodolph.
"I crave your Lordship's indulgence and forgiveness. Had you but
given me the slightest hint of this I would have protected you."
"I gave you all the hint I could, but you paid little heed to it."
"I am deeply to blame, and I implore your intercession with my Lord
the Archbishop. I will myself, with a troop of horse, instantly escort
you to Cochem and see you safely bestowed there."
"All I ask of you is to secure our boat and let us depart as we came."
"Alas! the boat is gone, and is now most likely half-way to Cochem.
Shall I order you accommodation here until you can communicate
with the Archbishop?"

"No, we will at once to Cochem. Have you horses for the Countess
and myself and for our servants?"
"Yes, my Lord."
"Then we will set out on our journey as soon as they are ready."
The officer saluted, and departed to give his orders.
"What shall we do? oh, what shall we do?" asked the Countess,
wringing her hands.
"Do not be afraid," said Rodolph, with a confidence he did not
himself feel. "We will be so much the further from Treves and so
much the nearer to Thuron. We will ride side by side to Cochem, and
then consult on what is best to be done when we get there.
Meanwhile, keep a firm command of your agitation, and do not show
fear. The officer has no suspicion, and will do whatever I ask of him.
They, perhaps, do not know yet of your flight at Treves, and even if
they did they cannot get here much before this time to-morrow, and
not then unless they come by boat. Have no fear; I will, as I
promised, see you safe in Thuron gate."
The Countess impulsively held out her hand, and gave a warm
pressure to the one extended to her.
"Forgive me," she whispered, "for my distrust of you last night. You
are a brave and true soldier."

CHAPTER IX.
A PALATIAL PRISON.
The Captain presently appeared with a dozen mounted men at his
back, and four led horses.
"I hold it well," he said to Rodolph, "to get as speedily away from
Bruttig as may be. The lieutenant of Count Beilstein has gone in
haste to the castle to tell his Highness what has happened, and it
was not within my right to detain him. The Count will be beside
himself with rage at the loss of his Captain, so it is safer that you
lodge within Castle Cochem as soon as possible. He will think twice
before he attacks the Archbishop's stronghold. Is it your will that I
send a messenger to Treves to acquaint his Lordship with the
welfare of his ward?"
"That is not necessary," replied Rodolph. "The Archbishop will
doubtless prefer to hear of our safe arrival at Cochem, and a
messenger can be sent from there. Is there a chance that we may
be intercepted by the forces of Count Beilstein?"
"No interception is possible. His men here are without a leader, and
will attempt nothing, even if they were able to accomplish anything.
The Count himself will likely come in haste to Bruttig, but by that
time we shall be in Cochem, I hope and although the road by the
river is none of the best, it is as bad for him as for us."
"Let us get on, then," said Rodolph. He assisted the Countess to
mount, sprang into his own saddle, and felt that exhilaration which
comes to a horseman when he finds a spirited steed under him.
Four of the cavalry headed the procession, with eight to bring up the
rear, the Countess and her attendants riding between. Rodolph rode
by the side of the Countess, with Conrad and Hilda out of earshot

behind them, the Captain leading the four horsemen in front. Their
rough way led along the right bank of the river.
"Nothing has been heard from the Archbishop, I trust," said the
Countess.
"There is little to fear from him until late to-morrow, and not even
then unless your escape was discovered early to-day—a most
unlikely event."
"But might not the pursuers ride all night?"
"A difficult and hazardous task they would set themselves in passing
through the forest in the dark, and slow work even if successfully
accomplished."
"Then we need have no apprehension if we can get clear of Cochem
before the pursuers from Treves arrive at Bruttig?"
"Once quit of Cochem, pursuit will be futile. My plan is to keep a
sharp look-out for the drifting boat. Conrad will secure it if possible,
and we will get away from Cochem to-night, if we can leave the
castle; but I know nothing of its conformation, nor of how it is
guarded."
The Countess shook her head. "I am afraid it will be difficult to leave
Cochem at night," she said. "The castle is always well and strictly
guarded, and occupies an almost inaccessible position on the top of
a hill."
"There is nothing for it then but to go with this escort to Cochem,
and trust to Providence and our own ingenuity thereafter. I may
have something to suggest when I have seen the place."
The increasing roughness of the road made conversation more and
more difficult. An hour's riding and a turn in the river brought them
in sight of the grand castle of Cochem, its numerous pinnacles
glittering in the last rays of the setting sun. It was another hour
before the cavalcade arrived opposite the place. A trumpeter of the

troop blew a bugle blast that was echoed back from the rock-ribbed
conical hill on which the castle stood. The signal was answered by
another from the ramparts of the fortification itself, and presently a
boat put out from the foot of the rock. In this boat the Countess and
her attendant were placed, while those on horseback set their steeds
to the swift current and landed some distance below, at the lower
end of the little village that clustered from the foot of the hill,
extending down the valley. The Countess mounted her dripping
horse, and the troop rode slowly up a winding path that partly
encircled the vine-clad hill, and at last arrived at the northern gate,
which was the chief entrance to the castle. Here, after a brief parley,
the portcullis was raised and the party admitted to a large courtyard
that hung high above the Moselle, overlooking a long stretch of the
river as it flowed toward the Rhine.
The custodian of the castle received his distinguished guest with that
humble deference which befitted her lofty station, assisting her to
dismount and evidently entertaining not the remotest suspicion that
the visit was unauthorised. The Countess enacted her part well.
"I commend to your care," she said, imperiously, "my Lord Rodolph,
who has conducted me from Treves. Until the Archbishop himself
arrives you are to hold yourself entirely at his orders."
The custodian bowed low, first to the Countess and then to Rodolph.
"How soon may we look for his Highness the Archbishop?" he asked.
"You will most likely hear from him to-morrow. Is my suite of
apartments ready?"
"They are now being prepared as speedily as possible; but as no
messenger brought us word of your coming, I hope your Ladyship
will pardon the delay," answered the custodian, with some
trepidation.
The Countess made no reply, but with her whip beckoned Rodolph
to her side.

"Do the troopers remain in the castle, or return to Bruttig to-night?"
"I have told their officer to keep them here until morning. If a
messenger from the Archbishop arrives at Bruttig sooner than we
look for, he will likely remain there until this officer returns. The
Archbishop would count on the Captain being at his post, and it is
not likely that the messenger's instructions would run further than
Bruttig, which will give us further time."
"Will you then give your commands to the custodian regarding the
disposal of the men? I think he will obey you; but it is well to
discover this by bestowing orders first that are unimportant, before
we put our power to a supreme test."
Rodolph gave directions, which, to his relief, were instantly obeyed.
The custodian escorted Countess Tekla into the castle, while Rodolph
walked round the courtyard to get some idea of the lay of the land
and the construction of the fortifications. The view down the river
was magnificent, as also was the outlook up the Endertsbach valley,
with the huge round tower of Count Winneburg's castle standing out
against the evening sky, built on a hill nearly equal in height to the
one crowned by Schloss Cochem.
Rodolph's short examination of the castle's position speedily showed
him that it was a place difficult to get into or escape from. To steal
away at night was hardly practicable, unless one had a ladder of
ropes, while to escape by day was equally hopeless, as a fugitive
could be seen for miles in any direction until he was lost in the
forest.
As the Emperor stood at the corner of the elevated terrace, gazing
down the river, he became aware of some one's approach, and a
moment later the deferential voice of the aged custodian broke the
silence.
"A goodly sight, my Lord," he said, "and although I have looked at it
for many a year, it never becomes less lovely to my eyes. It is rarely

the same, varying with every change in the atmosphere, but always
beautiful."
"It is indeed a marvelous view, and not to be the less enjoyed
because your position up here is well nigh impregnable," answered
Rodolph.
"Altogether so, I think," replied the custodian, with the pride of an
old retainer in his castle and a belief in its unassailableness, the
result of many futile assaults he had seen. "Before Cochem falls the
souls of hundreds of its assailants will seek a final abiding place, in
bliss or other where, as God wills."
"Does the road we came by from Bruttig, follow the river further
down?"
"No, my Lord, it ends opposite the castle. On this side, however,
there is a path that follows the river from village to village, but how
far it goes, I do not know, for I never explored it to the end."
"Are there many castles between here and the Rhine?"
"Only three or four, some standing back from the river in the valleys
that run into the Moselle. The chief castle is that of the Black Count,
robber and marauder that he is, and it is called Thuron. Were it less
strong, I think the good Archbishop would have smoked him out
long ere this. Count Heinrich has a chain across the river, stopping
all honest traffic until tribute is paid, and if there is any cavilling
about it, he takes the whole cargo and casts the merchant into a
dungeon to teach him respect for the nobility, as he says. But some
day there will be a reckoning, for Black Heinrich, while compelling
due respect to be paid by all inferiors, is himself most disdainful to
those above him."
"Flouts he the Emperor, then?"
"Oh, the Emperor!" said the custodian, with a shrug of his shoulders,
that might have been held contemptuous, "the Emperor is but a
name, and commands scant respect along the Moselle. He is some

young man recently elected, who loves better the dallying of his
Court than the risking of good stout blows in the field. They tell me
he comes from a noble family in Switzerland, and is not of Germany
at all, and I warrant the Archbishop does not wait to ask his leave if
he wishes to pull down a castle about the ears of a truculent Baron."
"Then it seems to me our friend, the Archbishop, may be accused of
the same want of respect for higher authority that you lay at the
door of Count Heinrich the Black."
"The worthy Archbishop, God bless him, recognises no over-lord but
the Pope himself and I have sometimes doubted whether Arnold von
Isenberg paid very much attention even to his Holiness; but then I
am letting my tongue run away with me, and am talking of what
concerns me not."
"It will do you no harm as long as I am the sole listener. Does Castle
Thuron stand on this side of the river or on the other?"
"On the other. It crowns a hill somewhat similar to this and as high,
but it is as unlike Cochem as one castle can be unlike another, for
this is part palace and part fortress, while Thuron is a fortress pure
and simple, and a strong one at that. A stout wall has been built
from the castle down to the river, and it is said that there is a
passage within, where ten men can walk abreast, although that I
doubt. There is certainly a passage by which food or water can be
taken up to the castle, while the carriers pass unscathed, protected
by strong stone walls."
"It seems, then, that the first duty of besiegers would be to break
that wall, and thus cut communication between the castle and the
river."
"That is easy to suggest, but there would be difficulty in the doing.
The walls are stout and will stand some battering; then the two
great round towers of the castle are armed with catapults which,
they say, will fling round stones even across the river itself. Besides
this, there are engines along the wall for a similar purpose. The

attacking party would have to remove solid cemented stone, while
the defenders would merely have to sweep down along the hillside
unprotected men who had little to cling to. I think it is no secret that
the Archbishop had Thuron examined by spies with a view to its
capture, but they strongly advised him to leave it alone; safe
counsel, which his Lordship followed."
"When the assault takes place I hope we shall be there to see."
"Ah," said the ancient keeper, with a sigh of regret, "I fear I shall
have no such pleasure, for I grow old and Arnold grows cautious. My
only hope comes from Heinrich himself, for he is like enough to hurl
some insult at the Archbishop that cannot well result in anything but
the uprising of pikes; indeed, he once threatened to attack Cochem
itself, and for a day or two we had merry preparation, but he
thought better of it, and no more came of the threat, much to my
regret, for I should have liked to see Heinrich crack his crown
against Cochem. And now, my Lord, if you will come within, you will
find a meal prepared, for which I doubt not you have sufficient
appetite."
The young man and the old entered the castle together.

CHAPTER X.
THE INTERCEPTED FUGITIVES.
In spite of his anxiety, Rodolph slept that night with a soundness
that carried him, unconscious, further into the morning than he had
intended when he lay down. It had been his purpose to rise early,
and perfect some scheme for quitting the castle without arousing the
suspicions of its inmates. The getting off, he knew, must be
accomplished that day, and as soon as possible in the day, for
undoubtedly the pursuers of the Countess must now be well down
the river.
The Emperor, on breakfasting, learned that the Countess had been
up long before, and was at that moment praying in the chapel. The
Captain and the escort had left for Bruttig, and when Rodolph went
out upon the terrace he saw the band far below, climbing up the
opposite bank on dripping horses, rising from the clear waters like
spirits of the river, into the thin transparent mist that floated over
the stream. The morning sun was gently gathering up the airy, white
coverlet of the Moselle, promising a clear and brilliant day. The troop
below, seen dimly through the intervening haze, had formed in
regular order, two and two, the Captain at their head, with the
Archbishop's pennant flying above them, and were now trotting
slowly up the river road.
"Always beautiful, and never the same, changing with every hour of
the day. In a short time the slight fog will have lifted, and the
heightening sun will reveal the full glory of the view."
Rodolph turned quickly and saw standing at his elbow the old
custodian of the place, as he had stood on the same spot the
evening before.

The young man wondered if any suspicion of the real state of the
case had entered the custodian's mind; whether his cat-like steps
and unexpected appearances, his haunting of his guest, did not
betoken some distrust that all was not as it should be. The custodian
had likely learned from the Captain that the Countess came from
Treves to Bruttig in a small boat, practically without escort, and that
there was trouble before the identity of the party had been
disclosed. On the other hand the custodian must know that the
Archbishop often adopted a course of action, the object of which
was known to none but himself, and his Lordship had small patience
with any underling who exhibited inconvenient curiosity regarding
the intentions of those above him. Rodolph resolved to set his
doubts at rest by a practical test.
"The day," he said, "indeed promises to be fine. To a man of action,
however, the precincts of the castle are somewhat circumscribed,
and the marvellous view makes him more and more conscious of the
limited extent of this most charming terrace. Has the Archbishop
some good horses in his stables, or does he keep them all at
Treves?"
"His Lordship has a rare fondness for a choice bit of horse-flesh, and
there is here an ample variety. Does your Lordship wish to ride this
morning?"
"Is the country round about safe? I have no desire to be captured
and thus put the Archbishop to the trouble of knocking down some
castle in effecting my rescue."
"The district is reasonably safe. Perhaps it may be well not to
venture into the territory of the Count of Winneburg, up the valley of
Endertsbach yonder, but down the river there is little chance of
molestation; still, I can provide you with an escort that will most
likely leave you free from attack wherever you go."
"No," said Rodolph, with unconcern. "It is not worth while to turn
out a guard, besides the Archbishop himself may be here at any

moment and I think he would like to find the whole garrison ready to
receive him, although he said nothing to me about it."
"Yes, Arnold von Isenberg does not overlook scant ceremony when
he takes himself abroad. Would you care to see the horses, my
Lord?"
Rodolph thanked his host for the invitation, and together they went
to the stables, where he selected four horses, and directed that they
should be accoutred for riding, two for women and two for men.
"The Countess," he said, to the custodian, "has been accustomed to
out-door recreation, and is an excellent horsewoman. I am sure she
will desire to take advantage of this exhilarating morning, but I shall
now wait upon her and learn her wishes."
To the Emperor's relief, the custodian remained behind to see that
the orders were promptly carried out, while Rodolph went back to
the castle. He sought the chapel, which was reached by passing
through the castle and crossing another courtyard looking toward
the west. The chapel at the south-west angle of the castle seemed
to hang over the river, standing as it did on a projecting rock, whose
straight sides formed a perpendicular cliff, rising like a castle wall
from the deep slope of the hill. The chapel was a small but very
perfect bit of ecclesiastical architecture, recently built by Arnold von
Isenberg himself. As Rodolph entered the vestibule he was met by
the Countess hurrying out.
"Oh, my Lord, my Lord," she cried, with agitation in her voice, "the
troops of the Archbishop are now coming down the river. I have
seen them from the window within." Rodolph closed the door of the
chapel so that they might not be overheard.
"I think," he said, "that the men you saw are those who left us this
morning. They are the troops of the Archbishop indeed, but they are
going toward Bruttig."

"No, no. Hilda has been watching them for a long time, while I
prayed before the altar. Just now she told me she saw a troop
meeting those who escorted us hither. Come and see."
The interior of the chapel was in dim-coloured obscurity, all the
windows being of glass, sombrely stained. The lower part of one
window looking to the south-west opened on hinges, and there Hilda
stood gazing up the river. For a long distance the Moselle ran
straight toward them, apparently broadening as it approached. Far
away Rodolph saw the two troops meet, but the distance was too
great for him to distinguish whose flag flew over the further party.
"It may be that they are retainers of Count Beilstein," said the
Emperor. "If it should so chance, there is like to be a hostile
meeting. If they belong to the Archbishop, there will be a short
conference, then all will probably return to Cochem."
As he spoke the approaching troops came together and it was soon
evident that they had no hostile intentions towards each other. A cry
from the Countess called his attention to the fact that one horseman
was hurrying alone toward Bruttig, and that all the rest were riding
at increased speed for Cochem.
"There are four horses now ready in the courtyard. Countess, I beg
of you to appear calm and to show no haste in getting away. We will
ride slowly to the river and then into the forest: after that we will
make what speed we may to Thuron, and I much doubt if those who
follow will have sight of us before we reach the castle."
The Countess and Hilda went to their apartments to prepare for the
journey, while Rodolph sought Conrad, and told him briefly that he
was to make ready for travel.
The four horses with their attendants stood in the courtyard, and
presently the Countess appeared coming leisurely down the steps,
followed by Hilda. The ancient custodian busied himself in seeing
that everything was to the liking of his guests. The gates were
thrown open, and the portcullis gradually raised with much creaking

of rusty chain. The small cavalcade rode slowly forth, down the
winding way, while the old guardian of the castle stood watching
them as they descended.
No word was spoken until they had rounded the hill and once more
caught a glimpse of the river. The shoulder of the promontory on the
opposite side cut off their view of the Bruttig road, and there was, as
yet, no sign of the oncoming troop.
"Even if there was only the river between us," said Rodolph
reassuringly, "we should win the race for their horses are tired, and
ours are fresh and of the best. We can surely ride as fast as they
along a road that is not well adapted for speed; the good custodian
told me it is but a path, and he seemed uncertain how far even that
extended. Everything is in our favour, and so far as I can learn,
nothing but a few leagues of forest and the waters of this river are
between us and Thuron gate."
"Is the castle, then, on the other side?" asked the Countess.
"Yes, but the path, such as it is, is on this, and I have no doubt our
horses, accustomed to the river, will make little of swimming across,
when we catch a glimpse of the two round towers of Thuron."
"I can scarcely believe that we have come so easily forth from yon
stronghold, for last night my heart sank within me as I heard the
clang of the portcullis descending, and it seemed to me that we
were trapped beyond hope of rescue."
"You showed little fear, Countess, if, indeed, you felt any, which from
your words and manner at the time, I am inclined to doubt."
The Countess shook her head. "I quaked with fear, nevertheless,"
she said, simply, glancing sideways at him.
Reaching the foot of the hill they made their way, still without haste,
along the front of the village, which straggled for some hundreds of
yards facing the river. A short distance below Cochem the cliffs
projected to the Moselle, and the path struggled up the hill in zig-

zag fashion, finally forming a narrow cornice road running parallel
with the stream, but high above it, and when at last it descended to
a lower level Cochem Castle was finally shut from their view as they
looked backward. Rodolph, who was leading, now put spurs to his
horse, and the rest of the company came trotting behind as best
they could, Conrad bringing up the rear. The path kept mostly along
the margin of the stream, frequently diverging into the forest, and
then always mounting upwards, to pass some obstacle where the
banks were steep and the waters of the Moselle lapped the face of
the rocks. On every height Rodolph paused till the others came up
with him, and looked anxiously back where the trees permitted a
retrospect, but no sign of pursuit was ever visible. Thuron Castle
stood but five leagues from Cochem, and between the two places
the river ran nearly in a direct line, forgetting the crooked
eccentricities that had marked its progress further up. The
roughness of the path and its numerous divergencies from the level
made it difficult for the riders to accomplish more than a league an
hour. They had been four hours on the journey when Rodolph called
Conrad to his side, and said to him:
"Have you any knowledge of the distance still between us and
Thuron?"
"No, my Lord. I have no acquaintance with the river below Cochem."
"The sun is at least two hours past meridian, and we must have
food. Ride on to yonder village and see if they will prepare
something for us."
"My Lord, knowing how badly travellers fare who depend on chance
foraging down this valley, I brought with me from Cochem a skin of
wine and food enough for half a dozen. We might rest on the hill top
after passing through the village and there eat."
"Your foresight was wise in one way and dangerous in another.
Asking for food and wine might have aroused suspicion in the castle,
although apparently it has not done so."

"I took none into my confidence, my Lord. The buttery is well
provided, and they keep not such strict watch on it as they do at the
outer gate. I was bidden go there and refresh myself; which I did,
and then took with me what was most portable, palatable and
sustaining."
"In that case you are to be commended as a more thoughtful
campaigner than myself, but, in truth, I was so anxious to get out of
the castle I thought little of bringing anything else with me than
those in my charge."
Passing through the village, which they learned was called Hattonis
Porta, from the hill that overshadowed it to the east, they began the
ascent that was to bring them to their resting-place. The top of the
hill commanded the valley up the Moselle for a distance of two or
three leagues, and they would thus have ample notice of pursuit,
and might therefore lunch in peace. Furthermore, when Rodolph
reached the top, he was delighted to see but a short distance further
on, and across the river which, rounding the promontory, turned
toward the north, the two grey towers of a strong castle, which from
the description he had received of it, he instantly knew to be
Thuron; thus their journey's end was in plain sight. The empty road
far up the river gave him assurance that, should the enemy appear
in view, there was ample time for them to cross the river and reach
the castle before they were even caught sight of by their pursuers.
Rodolph slipped from his horse and stood there awaiting the arrival
of the Countess, whose tired steed was coming slowly up the hill.
Before he assisted her to dismount he pointed out the castle.
"There, my Lady," he said, "is the residence of the Count, your
uncle, and the end of your toilsome march."
"Now may the saints be thanked for their protection," cried the
wearied girl. "How I have prayed this some time past for a sight of
those towers!"

She slipped from her horse into his arms, and he held her perhaps a
moment longer than was necessary to set her safely on the turf. If
the lady resented this, she at least made no complaint about it, but
the colour came swiftly to her fair face, and she sighed, probably
because the haven was so near.
Conrad and Hilda now came up, and assisted each other in setting
forth the meal that the former had brought from Cochem. Then the
horses cropped the grass near by, securely tethered, as Tekla and
Rodolph took their repast together, while Hilda and Conrad did
likewise at a little distance.
"What do you propose to do when we reach Thuron?" asked the
Countess.
"I shall first offer some good advice to the Count Heinrich, if he will
listen to me."
"What advice?"
"To provision his castle instantly for the coming siege."
"The coming siege? I do not understand you. The country is at
peace."
"True, but the peace will be speedily broken. The Archbishop will
invest Thuron Castle as soon as he can collect his forces."
The Countess looked at him for some moments with dilated eyes, in
which apprehension grew more and more pronounced.
"Do you mean that there will be war because—because of me?"
"Most certainly. Did you not know that?"
The girl arose and regarded him with ever-increasing dismay.
"I shall return instantly to Cochem," she said, at last. "I will give
myself up to the Archbishop. There shall not be bloodshed on my
account, no matter what happens to me."

The Emperor smiled at her agitation, and her innocence at not in the
least appreciating the inevitable consequence of her revolt.
"You will do nothing so foolish," he said. "Besides, you are under my
command until I deliver you safely to your uncle, and I assure you I
permit no rebellion in my camp. Even if you returned to the
Archbishop you would merely consign yourself to a prison, and
would not prevent a conflict. I understand that your uncle has on
more than one occasion demanded the custody of your person, and
the crafty Archbishop would never believe that he had no hand in
your flight. His Lordship has for some time been meditating an
attack on Thuron, and I learned at Cochem that the devout Arnold
recently sent spies to discover how best the castle might be taken;
so it is more than likely you are doing your uncle the greatest service
in giving him warning of a struggle which is hardly preventable, and
which might, at any moment, have taken him unaware."
"A siege!" said the Countess, clasping her hands before her,
speaking more to herself than to her listener and gazing across the
blue river at the two grim grey towers on the hill top. "A siege of
Castle Thuron?" Then turning suddenly on Rodolph and flashing
upon him a swift bewildering glance of her splendid eyes, speaking
rapidly, she asked:
"Will you be in the castle during the conflict?"
"I most sincerely hope and trust I shall," cried the young man,
fervently. The girl drew a deep breath that was almost a sigh, but
said nothing. Rodolph stretched forth his hand to her and she put
her hand in his, looking frankly into his honest face. No speech but
that of their eyes passed between them. But there ran rapidly
through her mind the thought that had the Archbishop endeavoured
to force her to marry a man like Lord Rodolph, she might never have
sought escape from Treves.
Conrad at this point interrupted them.

"My Lord," he said, "there is one coming up the hill, who looks like
the archer."
The Emperor rose, and accompanied Conrad to the brow of the
descent, with some anxiety, fearing that the newcomer might prove
to be one of the pursuers who had somehow escaped his vigilance.
There was, however, no cause for alarm; a moment's glance showed
that it was indeed the archer, who being stout and cumbered by
pike, cloak, and various belongings, with longbow slung over his
shoulder, toiled somewhat slowly up the steep ascent, pausing now
and then to mop his brow and gaze around him, a habit of caution
learned during the years of campaigning. On catching sight of the
two men standing above him he stopped, took the bow from his
shoulder, strung it, gazing up at them for a moment, then mounted
leisurely as before, ready for any greeting he might receive.
When within earshot he again stood still, and accosting the two,
said:
"Good day to your honours, who seem to be men of peace and but
scantily armed, the which makes it most unlikely that you can be of
that service to me which doubtless your good nature would give you
pleasure in rendering. I am, as you may have noticed, a man
accustomed to the wars, and now on the outlook for some noble
who has quarrels on hand and the will to pay for a skilful archer
who, I may say in all modesty, seeing there is none to testify on my
behalf, never misses a mark he aims at, providing the object be but
a fair and reasonable distance away. I am desirous of taking upon
me the quarrel of any such noble, all the better pleased if the
quarrel be just, but not looking too closely into the merits of the
dispute, as experience has shown me that few controversies exist, in
which there is not something to be said for both sides; the only
conditions I would be inclined to impose being that pay should be
reasonably sure, and that the provender, such as a man may require
to keep him in health, be ample, for a taut string is of little use
unless there be good muscle behind it."

"Well and truly spoken, Sir Archer," cried Rodolph, "and inaccurate
only in one detail, which is that there stands a man before you who
can testify most enthusiastically regarding your skill with the bow.
Then you have not yet won your way to the Rhine?"
"Ah, my Lord, is it indeed you? I thought there was something
familiar in your appearance; but I saw you before for a short time
only, and that at night. Although I spoke just now of taking service
with any noble who might be in need of a man-at-arms, still I hold
myself in some measure as being under your orders, for I accepted
from you three months' pay, and while it is true that I have had to
provide food at my own expense and lodging where night overtook
me, still neither the quality nor cost of either has been such as to
invalidate our bargain, should you care to hold me to it. Of the food
along the Moselle I can truly and of experience say it is most vile
and swinish, always excepting the supper and breakfast provided me
by the good fellow who stands at your side, and who is, if I mistake
not, the same whom your comrade, having small knowledge of the
dignity of archery, the which is only what might have been expected
of him, being an untaught German, desired me to execute by driving
a good shaft through him at three yards or so distance."
"You have fallen among friends," said the Emperor, "and although I
fear, that, if your fasting has been involuntary, you can claim little
credit from it for the benefit of your soul, yet we are happily in a
position to give you one good meal, which will banish the
remembrance of hunger and at least afford temporary benefit to
your body."
"I am loath to say that I give little thought to my soul," replied the
archer, promptly advancing when he became aware that there was
sustenance on the top of the hill, "and I minister unto it perhaps as
much as any man now under arms in Germany, which is not high
recommendation; still the body has a practice of pressing its claims
upon a man's mind in a way that will not be denied, and therefore I
accept with most hearty gratitude any victual that your Lordship may
have at your disposal, and I trust that in the provisioning of your

expedition such an important item as that of drink has not been
forgotten."
"Your faith in the thoughtfulness of our caterer is far from being
misplaced. I can guarantee you wine as good as the Archbishop
himself keeps in his cellars."
The archer drew the back of his hand across his waiting lips, and
smacked them in anticipation of the unexpected good fortune that
had befallen him. Rodolph asked Conrad to provide as well for their
visitor as the remnants of the feast would allow, and the archer,
wasting no time in further conversation, fell to, and left nothing for a
later guest, should such an one arrive.
While the archer heroically made up for lost time, Conrad brought
round the horses, and Rodolph assisted the Countess to mount.
Hilda and Conrad were also ready for the short journey that lay
before them, but the Emperor stood with bridle rein over his arm,
and waited the finishing of the feast, desiring to give the archer hint
that there was probably action ahead at Thuron Castle.
"You have met with little encouragement, then, on your march down
the river," said the Emperor, as the bowman, with a deep sigh,
ceased operations.
"No encouragement at all, your Lordship. Never in all my travelling,
either in Germany or elsewhere, have I passed through a country so
depressingly peaceful, which weighs heavily on one's spirits: indeed
it is enough to make a man turn monk, and forsake the bow-string
for a string of beads. What better evidence could there be of the
sluggish nature of this district than the fact that there is at this
moment approaching us, doubtless from yonder castle, three
mounted and armed men, who in some sort appear to be trying to
come upon us unmarked, yet here we are, a tranquil group, paying
scant attention to their adjacency."
As the archer, who was gazing toward Thuron Castle, spoke thus in a
tone of complacent dejection, Rodolph, who had been scanning the

district to the west, turned suddenly round, and to his amazement
beheld three men on horseback, who had evidently worked their
way unseen up the opposite side of the hill from which the Emperor
and his party had ascended, and who now stood some distance off,
regarding the startled quartette and their calm guest; the bowman
not having the remotest idea what the sudden appearance of those
to whom he had thus casually called attention meant to his hosts.
To Rodolph they were merely three armed men, but the keener
eyesight of the Countess brought swift knowledge to her, and caused
a quick pallor to overspread her face.
"The Count Bertrich!" she cried.
The Emperor clenched his fist and drew a deep breath, as the
thought of all his useless scouring of the western horizon surged
over him.
"Intercepted!" he muttered to himself, with a half-smothered oath.

CHAPTER XI.
IN QUEST OF A WIFE WITH A TROOP OF
HORSE.
When Count Bertrich flung himself from his horse in front of the
Archbishop's summer palace at Zurlauben, and strode hastily up the
steps that led to the entrance, he passed through the crowded hall,
looking neither to the right nor the left until he reached the ante-
chamber that communicated with the large room in which the
Elector transacted his business. The waiting and excited throng in
the hall made way for him, as the great war-lord and acknowledged
favourite of the powerful Archbishop went clanking through among
them clad in full armour, paying not the slightest heed to their
salutations.
The Count found the secretary ready to conduct him instantly into
the presence of the Archbishop, and together, in silence, they
entered the lofty apartment that was part chapel and part throne-
room.
At the further end of the noble presence-chamber Arnold von
Isenberg paced back and forward across the polished floor, his
hands clasped behind him, a dark frown on his downward bent
brow. He was clad in the long silken robes of his priestly office, and
their folds hissed behind him like a following litter of serpents as he
walked. He paused in his promenade when the Count and the monk
entered, and, straightening his tall form, stood regarding them in
silence, until the secretary slipped noiselessly from the room and left
the summoned and summoner alone together.
"You are here at last," began the Archbishop, coldly. "It is full time
you arrived. Your bride has fled."

"Fled? The Countess Tekla?"
"You have no other, I trust," continued the Prince of the Church, in
even, unimpassioned tones. "My first thought on learning she was
missing made me apprehensive that the girl had anticipated the
marriage ceremony by flying to your notoriously open arms, and I
expected to be asked to bless a bridal somewhat hastily
encompassed; but I assume from your evident surprise that she has
been given the strength to resist temptation which takes the form of
your mature and manly virtues."
The sword cut across Count Bertrich's face reddened angrily as he
listened to the sneering, contemptuous words of the Archbishop, but
he kept his hot temper well in hand and said nothing. The manner of
his over-lord changed, and he spoke sharply and decisively, as one
whose commands admit neither question nor discussion.
"Last night the Countess Tekla took it upon herself to disappear. The
guards say she passed them going outward about ten o'clock, and
no one saw her return. This leads me to suspect that, with childish
craftiness, the passing of the guards was merely a ruse on her part,
intended to mislead, and so although I pay little attention to such a
transparent wile, I have taken all precautions and have already acted
on the clue thus placed in my hands, for there is every chance that
the girl is indeed a fool; we usually err in ascribing too much wisdom
to our fellow creatures. Regarding the proposed marriage, which,
strange and unaccountable as it may appear to me, and must
appear to you, the Countess seemed to view with little favour, she
threatened to appeal to the Emperor and also to his Holiness the
Pope." On mentioning the name of the latter, the Archbishop slightly
inclined his head. "I take small account of the Emperor, but have
nevertheless sent a body of fleet troopers along the Frankfort road
in case she meant what she said, which I suppose may sometimes
happen with a woman. They know not whom they seek, but have
orders to arrest and bring back every woman they find, therefore we
are like to have shortly in Treves a screaming bevy of females,
enough to set any city mad. I have thrown out a drag-net, and we

shall have some queer fish when it is pulled in. But to you and to
you alone, Count Bertrich, do I reveal my mind; see therefore that
you make no mistake. The fool has taken to the water and is now
committed to the sinuous Moselle.
"She said nothing in her protests about her uncle of Thuron, and
unless I am grievously misled, the crooked talons of the black
vulture are in this business. He has doubtless provided boat and
crew, and they are making their way down the river in the night,
concealing themselves during the day. They will avoid Bruttig and
Cochem. Make you therefore for Bruttig with what speed you may,
sparing neither horse nor man; yourself I know you will not spare. If
nothing has been heard of them there, order a chain across the river
that will stop all traffic and set a night guard upon it; then press on
to Thuron across the country by the most direct line you can follow,
coming back up the river to intercept them, for their outlook will be
entirely directed toward what is following them. If, in spite of all our
precautions, the girl reaches Thuron, seek instant entrance to the
castle and audience with the Black Count. Demand in my name,
immediate custody of the body of Countess Tekla; if this is refused,
declare castle and lands forfeit and Heinrich outlaw. Retire at once to
Cochem, where I shall join you with my army. And now to horse and
away. Success here depends largely on speed."
Count Bertrich made no reply but sank on one knee, rose quickly
and left the room. The expression on his face as he passed through
the multitude in the great hall was not such as to invite inquiry, and
no one accosted him.
"There is war in that red scar of Bertrich's," said an officer to
another.
Outside the Count flung himself on his horse, gave a brief word of
command to his waiting troop, and galloped away at the head of his
men.

He made no attempt to pursue the extremely crooked course of the
upper river, but, knowing the country well, he left the Moselle some
distance below Treves, and, taking a rude thoroughfare that was
more path than road, followed it up hill and down dale through the
forest. He was determined to reach Bruttig that night, hoping to
finish the journey by moonlight, taking advantage of the long
summer day and riding as hard as horseflesh could endure. When
the day wore on to evening Bertrich saw that he had set to himself
no easy task, for in the now pathless forest, speedy progress
became more and more difficult, and when the moon rose, the
density of the growth overhead allowed her light to be of little avail.
Several times a halt was sounded and the bugle called the troop
together, for now all attempt at regularity of march had been
abandoned, but on each occasion the numbers thus gathered were
fewer than when the former rally was held. In spite of his temporary
loss of men, Bertrich, with stubborn persistence, determined to push
on, even if he reached Bruttig alone. For an hour they pressed
northward to find the river which they now needed as a guide,
knowing they would come upon it at Bruttig or at least some short
distance above or below it, but before the Moselle was reached they
suddenly met an unexpected check. The outposts of an unseen band
commanded them to stop and give account of themselves.
"Who dares to bar the way of the Archbishop's troops?" demanded
Count Bertrich.
"It is the Archbishop's troops that we are here to stop. Will you fight
or halt?" was the answer.
Bertrich, with his exhausted men and jaded horses, was in no
condition to fight, yet was he most anxious to pursue his way, and
get some information of his whereabouts, so he spoke with less
imperiousness than his impulse at first prompted.
"I am Count Bertrich, commanding a division of his Lordship's army.
I am on a peaceful mission, and, when I left his Lordship this
morning, he had no quarrel with any. There has been some

misunderstanding, and I should be loath to add to it by drawing
sword unless I am attacked."
"You shall not be molested if you stay where you are. If, however,
you attempt to advance, our orders are to fall upon you," said a
voice from the darkness.
Noticing that the voice which now spoke was not the one that had
first challenged, Count Bertrich said,
"Are you in command, or am I speaking to a sentinel?"
"I am in command."
"Then who are you and whom do you serve?"
"Doubtless you are well aware whom I serve?"
"I know no more than the Archbishop himself."
"That I can well believe, and still would not hold you ignorant."
"We are talking at cross purposes, fellow. There must be, as I have
said, some mistake, for the domains of the Archbishop are in a state
of peace. There is no secret about my destination as there is none
about the name which I have rendered to you. I am bound for
Bruttig and hope to reach there before day dawns."
"My master knew of your destination and that is why I am here to
prevent you reaching it."
"What you allege is impossible. None knew of my destination save
the Archbishop and myself, and I have ridden from Treves with such
use of spur that news of my coming could not have forestalled me.
Again I ask you whom you serve."
"That you doubtless guess, for you know whom you are sent
against, and why you ride to Bruttig."
"You speak in riddles; what have you to fear from plain answers?"

"I fear nothing. My duty is not to answer questions but to arrest
your progress toward Bruttig. If you have questions to ask, ask them
of Count Beilstein."
"Oh ho! Then it is to Count Beilstein I owe this midnight discourtesy.
I thank you for that much information, which is to me entirely
unexpected. Where is the Count?"
"He is at Bruttig."
"How far is that from where we stand?"
"Something more than a league."
"I cannot comprehend why Count Beilstein should endeavour to
prevent my reaching Bruttig, nor how he can be aware of an
expedition of which neither the Archbishop nor myself knew aught
this morning. In addition to this, Bruttig is under the joint jurisdiction
of my master and yours and the Count of Winneburg, therefore the
retainers of each over-lord have free entrance to the place."
"Such was indeed the case until the Archbishop broke the truce.
Now Beilstein and Winneburg have combined, overthrown the
Archbishop's jurisdiction, and they hold Bruttig together, with the
men of the Elector prisoners."
"In the Fiend's name when did this take place? We knew nothing of
it at Treves. How broke the Archbishop the truce?"
"It was broken by an emissary of his, who by magic sword-play slew
my master's Captain, leaving in his neck a hole no bigger than a
pin's point, yet enough to let out the life of my fellow soldier. Then
when there was outcry at this foul play, the fellow, being sore
pressed, cries 'Treves, Treves,' claiming that the wench with him was
no other than the ward of the Archbishop——"
"Ha! Say you so? And what then?"

"Thereupon the Archbishop's Captain bugles up the men of Treves,
rallies round the emissary of his crafty Lordship, and makes rescue,
escorting him later, wench and all, to his Lordship's stronghold of
Cochem, where doubtless they think themselves safe. But Beilstein,
issuing from his castle, went forthwith to Bruttig, joined with
Winneburg, made prisoners of the men of Treves, and sent me here
in force to intercept any whom they expected the Archbishop would
shortly send, as indeed he seems to have done under your
distinguished leadership."
"You fill me with amazement. There is, as I surmised, a
misunderstanding, and one of no small moment, which we must
make it our business to set right. It is therefore most important that
I should have speech with your master and that speedily. I pray you
instantly to escort me with your men to Bruttig."
"That may I not do, my Lord. My orders are strict and Count
Beilstein is not the man to overlook divergence from them."
"Then come with me yourself; I shall go as your prisoner or in any
guise you please, so that no time be lost. My men will camp here for
the night."
"I cannot part company from my orders, which are to stop you or to
fight with you if you refuse to stand."
"But the man you call emissary of the Archbishop, who killed your
comrade, is the one I travel in hot haste to arrest. Him the
Archbishop will gladly yield to your master for fitting punishment,
but while we babble here, time flies and he with it."
"It will take more than the bare word of any follower of Treves to
make my master believe that the murderer, who went jauntily with
escort of the Archbishop's men to the Archbishop's castle in Cochem,
is one whom the Archbishop is desirous of handing over to my Lord
for punishment, still this much I may do. I will send at once a fleet
messenger to my Lord at Bruttig, acquainting him with your

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Network Analysis Integrating Social Network Theory Method And Application With R Craig M Rawlings

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