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Analyzing Social Networks 2

Analyzing Social Networks Stephen P Borgatti Martin G Everett Jeffrey C Johnson 3

SAGE Publications Ltd 1 Oliver’s Yard 55 City Road London EC1Y 1SP SAGE Publications Inc. 2455 Teller Road Thousand Oaks, California 91320 SAGE Publications India Pvt Ltd B 1/I 1 Mohan Cooperative Industrial Area Mathura Road New Delhi 110 044 SAGE Publications Asia-Pacific Pte Ltd 3 Church Street #10-04 Samsung Hub Singapore 049483 Editor: Jai Seaman Assistant editor: Anna Horvai Production editor: Ian Antcliff Copyeditor: Richard Leigh Proofreader: Sharika Sharma Indexer: Silvia Benvenuto Marketing manager: Ben Griffin-Sherwood Cover design: Lisa Harper Typeset by: C&M Digitals (P) Ltd, Chennai, India Printed in Great Britain by MPG Printgroup, UK © Stephen P Borgatti, Martin G Everett and Jeffrey C Johnson 2013 4

First published 2013 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted in any form, or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction, in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. Library of Congress Control Number: 2012950169 British Library Cataloguing in Publication data A catalogue record for this book is available from the British Library ISBN 978-1-4462-4740-2 ISBN 978-1-4462-4741-9 (pbk) 5

Contents Preface 1 Introduction 2 Mathematical Foundations 3 Research Design 4 Data Collection 5 Data Management 6 Multivariate Techniques Used in Network Analysis 7 Visualization 8 Testing Hypotheses 9 Characterizing Whole Networks 10 Centrality 11 Subgroups 12 Equivalence 13 Analyzing Two-Mode Data 14 Large Networks 15 Ego Networks References Index 6

Preface Welcome to the world of social network analysis. This book is intended as a general introduction to doing network research. The focus is on methodology, from research design and data collection to data analysis. Of course, since methodology and theory are deeply intertwined, this book is also about network theory. What it is not is a survey of empirical research on social networks. the book’s The book is also not meant to be overly technical. We try not to simplify to the point of misleading, but, when forced to make a choice, we have opted for intelligibility and transmitting the spirit of an idea. In each case, however, we provide pointers to the appropriate technical literature so that the reader can get a fuller picture if desired. Doing network analysis implies using network analysis software. A number of packages exist, including UCINET (Borgatti, Everett and Freeman, 2002) and Pajek (Batagelj and Mrvar, 1998). As two of the authors of UCINET are authors of this book, we use UCINET for most of our examples. However, we do not intend this book to be a tutorial on UCINET. This means we focus on generic data analysis issues and do not give detailed UCINET-specific instructions. For those interested, however, website (https://sites.google.com/site/analyzingsocialnetworks/) gives detailed information on how all of the UCINET examples are done. The one exception to all of this is Chapter 5, which is much more UCINET-focused than the rest of the book. One of the issues we faced in writing this book was how to keep it down to a reasonable size and maintain an understandable flow. We wanted to write a guide rather than an encyclopedia. As a result, we had to leave some things out. In general, our approach to this was to include only methods and concepts that are in demand and tend to be useful in a variety of settings. For example, although the k- plex (Seidman and Foster, 1978) is one of our favorite network concepts, we left it out of the chapter on subgroups because, in general, other approaches tend to be more practical. Similarly, in the chapter on centrality, we successfully resisted the temptation to present even a small fraction of all the measures that are available in the literature. Throughout the book, we use empirical examples to illustrate the material. Because social networks are studied in a variety of traditional academic disciplines, we draw our examples from a wide variety of fields, including anthropology, sociology, management, and health care. The book consists of 15 chapters that, in our minds at least, are logically grouped into four sections. The first section consists of an introduction (Chapter 1) and some mathematical foundations (Chapter 2). Chapter 1 lays out our perspective on the network research enterprise as a whole. It discusses the kinds of things we try 7

to explain, along with the main approaches to explaining them. Chapter 2 reviews – in very simple terms – some of the basic concepts in graph theory and matrix algebra. A reader familiar with network analysis could skip these two chapters, but we think it advisable to familiarize yourself with our notation and terminology. The next section has six chapters which are all about research methods. Chapter 3, on research design, is about the choices we make in setting up a study to investigate a given research question. Some of it applies to social science research in general, but much of it presents issues that are specific to social network analysis, such as the special challenges to respondent privacy. A key concept introduced here is the distinction between whole-network research designs and personal-network research designs. Chapter 4 discusses different options for the collection of network data, focusing specifically on survey methods for full network designs. Chapter 5 is about the data manipulations we often do to prepare network data for different analyses. Because it also discusses the importing and exporting of data, this chapter is more closely tied to UCINET than any other chapter. Chapter 6 is about fundamental exploratory multivariate techniques that are not specifically designed for social network analysis but are often used as part of the analysis process. Chapter 7 is about ways of visualizing network data in order to reveal patterns. Finally, Chapter 8 is about statistical techniques for testing hypotheses with network data. These are techniques specifically tailored for the special challenges of network data, such as non-independence of observations. The first part of the chapter is about using permutation-based versions of standard techniques such as correlation and regression. The second part is about exponential random graph and SIENA models. These techniques are not available in UCINET, and the statistical underpinnings of the models are far outside the scope of this book. However, we have included a brief introduction so that the reader is at least familiar in the broadest terms with these options and can then decide whether to explore them further. The third section of the book is about the core concepts and measures of network analysis. Chapter 9 discusses measures at the whole-network level of analysis, such as the density of ties and the degree of clustering. Chapter 10 is about measures of node centrality, which can be seen as characterizing each node’s position in a network. Chapter 11 is about definitions and methods of detecting groups (sometimes called ‘clusters’ or ‘communities’) within a network. Chapter 12 discusses ways of conceptualizing and measuring structural similarities in how nodes are connected in the network. The final section of the book consists of three cross-cutting chapters organized around different kinds of data. Chapter 13 is about methods of analyzing affiliation- type data, as when we have persons’ memberships in groups. Chapter 14 provides a set of heuristics useful in processing large networks, such as ways of breaking down the problem into a series of smaller ones, or changing the problem to analyze ties among clusters of nodes. Finally, Chapter 15 is concerned with designing, collecting and analyzing ego network data. We note that there is no chapter devoted 8

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